cracking the sat premium edition with 7 practice tests, 2018
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ISBN 9780451487605EbookISBN 9780451487612
SATisaregisteredtrademarkoftheCollegeBoard,whichisnotaffiliatedwithThePrincetonReview.
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“TheWindshield-PittingMysteryof1954.”©2015NationalPublicRadio,Inc.Excerptsfromnewsreporttitled“TheWindshield-PittingMysteryOf1954”byLintonWeekswasoriginallypublishedonNPR.orgonMay28,2015,andisusedwiththepermissionofNPR.Anyunauthorizedduplicationisstrictlyprohibited.PriitVesilindwithJamesandMaureenTusty,TheSingingRevolution.©2008bySkyFilmsIncorporated.www.singingrevolution.com.“ContinentalDriftandPlateTectonics”fromGrolier’sNewBookofPopularScience.Allrightsreserved.ReprintedbypermissionofScholasticLibraryPublishing,Inc.Gardner’sArtThroughtheAgesbyHorstDeLaCroix,RichardG.Tansey,DianeKirkpatrick.9thedition,1991.Copyright©1991byHarcourtBraceJovanovich,Inc.RepublishedwithpermissionofCengageLearningSO.PermissionconveyedthroughCopyrightClearanceCenter,Inc.
“TheParthenonFrieze—AnotherView.”©1977byJohnBoardman.“ScientistsDiscoverChildren’sCellsLivinginMother’sBrains,”byRobertMartone.OriginallypublishedDecember4,2014inScientificAmerican.Copyright©2012ScientificAmerican,adivisionofNatureAmerica,Inc.Allrightsreserved.TheCreators:AHistoryofHeroesoftheImaginationbyDanielJ.Boorstin,copyright©1992byDanielJ.Boorstin.UsedbypermissionofRandomHouse,animprintanddivisionofPenguinRandomHouseLLC.Allrightsreserved.Anythirdpartyuseofthismaterial,outsideofthispublication,isprohibited.InterestedpartiesmustapplydirectlytoPenguinRandomHouseLLCforpermission.AlsousedbypermissionofTheOrionPublishingGroup,London.“RobertRedford:ProtectOurWildHorses”byRobertRedfordinUSAToday,November3,2014.ReprintedbypermissionofReturntoFreedomWildHorseConservation.“AStrangeTaleofaNewSpeciesofLizard”byCarlZimmerintheNewYorkTimes,December18,2014.©2014byTheNewYorkTimes.Allrightsreserved.UsedbypermissionandprotectedbytheCopyrightLawsoftheUnitedStates.Theprinting,copying,redistribution,orretransmissionofthisContentwithoutexpresswrittenpermissionisprohibited.“MakingaBrainMapThatWeCanUse”byAlvaNoë.Originallypublishedin13.7CosmosandCulture,NPR.“Asteroidmayhavekilleddinosaursmorequicklythanscientiststhought”byIreneKlotz.Fromreuters.com,February8,2013©2013reuters.com.Allrightsreserved.UsedbypermissionandprotectedbytheCopyrightLawsoftheUnitedStates.Theprinting,copying,redistribution,orretransmissionofthisContentwithoutexpresswrittenpermissionisprohibited.“Asteroidkilledoffthedinosaurs,saysinternationalscientificpanel,”fromScienceDaily.Copyright©2010ImperialCollegeLondon.Reprintedwithpermission.“Tinybrains,butsharedsmarts,”fromtheNationalScienceFoundation,June17,2015.Reprintedwithpermission.“Iwrotemyownspeechonce.Itdidn’tsoundlikemeatall!”ReprintedbypermissionofCartoonStock.com.“Telehealthexpansionneedspayment,coveragepolicyadvances,”byDr.NabilElSanadi.Reprintedwithpermission,ModernHealthcareSeptember12,2015.©CrainCommunications,Inc.HowToFlyAHorse:TheSecretHistoryofCreation,Invention,andDiscovery.©2015byKevinAshton.TheMatterMyth:DramaticDiscoveriesthatChallengeourUnderstandingofPhysicalReality,byPaulDaviesandJohnGribbin.Copyright©1991byOrionProductionsandJohnGribbin.ReprintedwiththepermissionofSimon&Schuster,Inc.andDavidHighamAssociates,Ltd.Allrightsreserved.“BirthofaNewNation.”ReprintedbyarrangementwithTheHeirstotheEstateofMartinLutherKingJr.,c/oWritersHouseasagentfortheproprietorNewYork,NY.Copyright©1957Dr.MartinLutherKing,Jr.©Renewed1985LorettaScottKing.LicensedintheU.S.andworld:“Jubilee,”fromNightattheFiestas:StoriesbyKirstinValdezQuade.Copyright©2015byKirstinValdezQuade.UsedbypermissionofW.W.Norton&Company,Inc.LicensedintheUK:FromNightattheFiestas:StoriesbyKirstinValdezQuade.PublishedbyW.W.Norton&Company,Inc.Copyright©2013,2015byKirstinValdezQuade.FirstappearedinGuernica.“FreeUpgrades,Unfortunately”byElsaYoungsteadt.Copyright©2006byAmericanScientist.ReprintedwithpermissionofAmericanScientist.“Fillupyourgastankwithbamboo?”byJoeTurner,Science,February2,2015.ReprintedwithpermissionofAAAS.
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v4.1a
AcknowledgmentsAnSATcourseismuchmorethanclevertechniquesandpowerfulcomputerscorereports.Thereasonourresultsaregreat is thatour teacherscaresomuchabout theirstudents.Manyteachershavegoneoutoftheirway to improve thecourse,oftengoingsofaras towrite theirownmaterials, someofwhichwehaveincorporatedintoourcoursemanualsaswellasintothisbook.Thelistoftheseteacherscouldfillthispage.
Special thanks to JonathanChiuandall thosewhocontributed to thisyear’s edition:CatHealey,AmyMinster,andElizabethOwens.
ThankstoSaraSoriano,BrianBecker,JoelleCotham,JuliaAyles,LoriDesRochers,BobbyHood,AaronLindh, Garrison Pierzynski, Nicole-Henriette Pirnie, Ed Carroll, Pete Stajk, David Stoll, and CurtisRetherfordfortheirworkonpreviousiterationsofthistitle.
Special thanks to Adam Robinson, who conceived of and perfected the Joe Bloggs approach tostandardizedtestsandmanyoftheothersuccessfultechniquesusedbyThePrincetonReview.
Finally,wewouldliketothankthepeoplewhotrulyhavetaughtuseverythingweknowabouttheSAT:ourstudents.
ContentsCoverTitlePageCopyrightAcknowledgmentsForewordRegisterYourBookOnline!
PartI:Orientation1TheSAT,ThePrincetonReview,andYou2CrackingtheSAT:BasicPrinciples
PartII:HowtoCracktheReadingTest3TheReadingTest:BasicApproach4MoreQuestionTypes5ReadingDrills
PartIII:HowtoCracktheWritingandLanguageTest6IntroductiontoWritingandLanguageStrategy7Punctuation8Words9Questions
PartIV:HowtoCracktheMathTest10SATMath:TheBigPicture11FunwithFundamentals12Algebra:CrackingtheSystem13OtherAlgebraStrategies14AdvancedArithmetic15FunctionsandGraphs16Geometry17Grid-Ins
PartV:HowtoCracktheEssay18ReadingandAnalyzingtheEssayPassage19WritingtheEssay
PartVI:TakingtheSAT
PartVII:PracticeTests20PracticeTest121PracticeTest1:AnswersandExplanations22PracticeTest223PracticeTest2:AnswersandExplanations24PracticeTest325PracticeTest3:AnswersandExplanations26PracticeTest427PracticeTest4:AnswersandExplanations
ForewordWelcometoCrackingtheSAT!TheSATisnotatestofaptitude,howgoodofapersonyouare,orhowsuccessfulyouwillbeinlife.TheSATsimplytestshowwellyoutaketheSAT.AndperformingwellontheSATisaskill,onethatcanbelearnedlikeanyother.ThePrincetonReviewwasfoundedmorethan30yearsagoonthisverysimpleidea,and—asourstudents’testscoresshow—ourapproachistheonethatworks.
Sure,youwanttodowellontheSAT,butyoudon’tneedtoletthetestintimidateyou.Asyouprepare,remembertwoimportantthingsabouttheSAT:
• Itdoesn’tmeasurethestuff thatmatters. Itmeasuresneither intelligencenor thedepthandbreadthofwhatyou’relearninginhighschool.Itdoesn’tpredictcollegegradesaswellasyourhighschoolgradesdo.Collegesknowthereismoretoyouasastudent—andasaperson—thanwhatyoudoinasingle3-hourtestadministeredonarandomSaturdaymorning.
• Itunderpredictsthecollegeperformanceofwomen,minorities,anddisadvantagedstudents.Historically,womenhavedonebetterthanmenincollegebutworseontheSAT.Foratestthatisusedtohelppredictperformanceincollege,that’saprettypoorrecord.
Yourpreparationfor theSATstartshere.WeatThePrincetonReviewspendmillionsofdollarseveryyear improvingourmethodsandmaterialssothatstudentsarealwaysreadyfor theSAT,andwe’llgetyoureadytoo.
However, there isnomagicpill: Justbuying thisbook isn’tgoing to improveyourscores.Solidscoreimprovementtakescommitmentandeffortfromyou.Ifyoureadthisbookcarefullyandworkthroughtheproblemsandpractice tests includedin thebook,notonlywillyoubewell-versedin theformatof theSATandtheconceptsittests,youwillalsohaveasoundoverallstrategyandapowerfularsenaloftest-takingstrategiesthatyoucanapplytowhateveryouencounterontestday.
InadditiontothecomprehensivereviewinCrackingtheSAT,we’veincludedadditionalpracticeonline,accessiblethroughourwebsite—PrincetonReview.com—tomakeitevenmoreefficientathelpingyoutoimproveyourscores.Beforedoinganythingelse,besuretoregisteryourbookatPrincetonReview.com/cracking.Whenyoudo,you’llgainaccesstothemostup-to-dateinformationontheSAT,aswellasmoreSATandcollegeadmissionsresources.
Themoreyoutakeadvantageoftheresourceswe’veincludedinthisbookandtheonlinestudenttoolsthatgowithit,thebetteryou’lldoonthetest.Readthebookcarefullyandlearnourstrategies.Takethefull-length practice tests under actual timed conditions. Analyze your performance and focus your effortswhereyouneedimprovement.Perhapsevenstudywithafriendtostaymotivated.AttendafreeeventatThePrincetonReviewtolearnmoreabouttheSATandhowitisusedinthecollegeadmissionsprocess.Searchourwebsiteforaneventthatwilltakeplacenearyou!
Thistestischallenging,butyou’reontherighttrack.We’llbewithyoualltheway.
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RegisterYourBookOnline!
GotoPrincetonReview.com/cracking
You’llseeawelcomepagewhereyoucanregisteryourbookusingthefollowingISBN:9780451487612
Afterplacingthisfreeorder,you’lleitherbeaskedtologinortoanswerafewsimplequestionsinordertosetupanewPrincetonReviewaccount.
Finally,clickonthe“StudentTools”tablocatedatthetopofthescreen.Itmaytakeanhourortwoforyourregistrationtogothrough,butafterthat,you’regoodtogo.
Ifyouhavenoticedpotentialcontenterrors,pleaseemailEditorialSupport@review.comwiththefulltitleofthebook,itsISBNnumber(locatedabove),andthepagenumberoftheerror.
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Onceyou’veregistered,youcan…
• Accessandprintoutthreemorefull-lengthpracticetestsaswellasthecorrespondinganswersandexplanations
• Findanylate-breakinginformationreleasedabouttheSAT
• Readourspecial“SATInsider”andgetvaluableadviceaboutthecollegeapplicationprocess,includingtipsforwritingagreatessayandwheretoapplyforfinancialaid
• Sortcollegesbywhateveryou’relookingfor(suchasBestTheaterorDorm),learnmoreaboutyourtopchoices,andseehowtheyallrankaccordingtoTheBest381Colleges
• CheckoutbonusfeaturesinyourPremiumPortal,includingcomprehensivestudyguidesandshortvideostohelpenhanceyourtestprep
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• Checktoseeiftherehavebeenanycorrectionsorupdatestothisedition
LookForTheseIconsThroughoutTheBook
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LET’SGETTHISPARTYSTARTED!Youareabouttounlockavastrepertoireofpowerfulstrategiesthathaveoneandonlyonepurpose:tohelp you get a better score on the SAT. This book contains the collected wisdom of The PrincetonReview,whichhasspentmorethan35yearshelpingstudentsachievehigherscoresonstandardizedtests.We’vedevotedmillionsofdollarsandyearsofourlivestocrackingtheSAT.It’swhatwedo(twistedasitmaybe),andwewantyoutobenefitfromourexpertise.
Welcome!WelcometothePremium
EditionofCrackingtheSAT.Thiseditioncomeschockfull
ofawesomeonlineresources,includingthreemorefull-lengthpracticetests,aswellasvideos,
studyguides,collegeadmissionsarticles,and
more.See“RegisterYourBookOnline!”forstep-by-stepinstructions
foraccessingyourPremiumcontent.Happy
testprepping!
WHATISTHEPRINCETONREVIEW?ThePrincetonReviewistheleaderintestprep.OurgoalistohelpstudentseverywherecracktheSATandabunchofotherstandardizedtests,includingthePSATandACTaswellasgraduate-levelexamsliketheGREandGMAT.Startingfromhumblebeginningsin1981,ThePrincetonReviewisnowthenation’slargestSATpreparationcompany.Weoffercoursesinmorethan500locationsin20differentcountries,aswellasonline;wealsopublishbest-sellingbooks,liketheoneyou’reholding,andonlineresourcestogetstudentsreadyforthistest.
Ourtechniqueswork.WedevelopedthemafterspendingcountlesshoursscrutinizingrealSATs,analyzingthemwithcomputers,andprovingourtheoriesintheclassroom.
ThePrincetonReviewWayThisbookwillshowyouhowtocracktheSATbyteachingyouto:
• extractimportantinformationfromtrickytestquestions• takefulladvantageofthelimitedtimeallowed• systematicallyanswerquestions—evenifyoudon’tfullyunderstandthem
• avoidthetrapsthattheSAThaslaidforyou(andusethosetrapstoyouradvantage)
ThetestiswrittenbyEducationalTestingService(ETS)andadministeredbytheCollegeBoard,andtheyknowthatourtechniqueswork.Foryears,thetestwritersclaimedthattheSATcouldn’tbecoached.Butwe’veproventhatviewwrong,andtheyinturnhavestruggledtofindwaysofchangingtheSATsothatThePrincetonReviewwon’tbeabletocrackit—ineffect,acknowledgingwhatourstudentshaveknownall along: thatour techniques reallydowork. (In fact,ETShas recentlyadmitted that studentscanandshouldpreparefortheSAT.Sothere!)TheSAThasremainedhighlyvulnerabletoourtechniques.AndthecurrentversionoftheSATisevenmoresusceptibletoourmethods.Readthisbook,workthroughthedrills,takethepracticetests,andyou’llseewhatwemean.
Study!Ifyouweregettingready
totakeabiologytest,you’dstudybiology.If
youwerepreparingforabasketballgame,you’d
practicebasketball.So,ifyou’repreparingfortheSAT,youneedtostudy
andpracticefortheSAT.Theexamcan’ttesteverything
youlearninschool(infact,ittestsverylittle),soconcentrateonlearning
whatitdoestest.
Chapter1TheSAT,ThePrincetonReview,andYouWelcome!OurjobistohelpyougetthebestpossiblescoreontheSAT.ThischaptertellsyouwhattoexpectfromtheSATaswellassomespecificsaboutthetest.ItwillalsoexplainhowtomakethemostofallyourPrincetonReviewmaterials.
GENERALINFORMATIONABOUTTHESATYoumayhavebought thisbookbecauseyouknownothingabout theSAT,orperhapsyou took the testonceandwanttoraiseyourscore.Eitherway,it’simportanttoknowaboutthetestandthepeoplewhowriteit.Let’stakeasecondtodiscusssomeSATfacts:Someofthemmaysurpriseyou.
WhatDoestheSATTest?JustbecausetheSATfeaturesmath,reading,andwritingquestionsdoesn’tmeanthatitreflectswhatyoulearnedinschool.YoucanacecalculusorwritelikeFaulknerandstillstrugglewiththeSAT.Thetestwritersclaimthatthetestpredictshowwellyouwilldoincollegebymeasuring“reasoningability,”butalltheSATreallymeasuresishowwellyoutaketheSAT.Itdoesnotrevealhowsmart—orhowgoodof—apersonyouare.
WhoWritestheSAT?EventhoughcollegesanduniversitiesmakewideuseoftheSAT,they’renottheoneswhowritethetest.That’sthejobofEducationalTestingService(ETS),anonprofitcompanythatwritestestsforcollegeandgraduateschooladmissionsonbehalfof theCollegeBoard, theorganization thatdecideshowthe testswillbeadministeredandused.ETSalsowritestestsforgroupsasdiverseasbutchersandprofessionalgolfers(whoknew?).
ETSandtheCollegeBoardareoftencriticizedfortheSAT.Manyeducatorshavearguedthatthetestdoesnotmeasuretheskillsyoureallyneedforcollege.Thisledthemin2005tooverhaultheentiretest,onlytorevise italloveragain inearly2016.Theimportant takeawayhere is that thepeoplewhowrite theSATareprofessionaltestwriters,and,withsomepractice,it’spossibletobeatthemattheirowngame.
Wait,WhoWritesThisTest?
YoumaybesurprisedtolearnthatthepeoplewhowriteSATtestquestionsareNOT
necessarilyteachersorcollegeprofessors.The
peoplewhowritetheSATareprofessionaltestwriters,notsuperhuman
geniuses,soyoucanbeatthemattheirowngame.
What’sontheSAT?TheSAT is3hours long,or3hoursand50minutes long ifyouchoose to take theoptional50-minuteessay.Note thatwhile the essay is optional for somecolleges,many schoolsdo require it.Be sure toresearch thecollegesyou’re interested in to findout if they require theessay.TheSATconsistsof thefollowing:
• 1multiple-choiceReadingTest(52questions,65minutes)
• 1multiple-choiceWritingandLanguageTest(44questions,35minutes)• 1MathTest,consistingofaNoCalculatorsection(20questions,25minutes)andaCalculator
section(38questions,55minutes)• theoptionalessay(50minutes)
KeyTakeawayWhatreallymattersto
youasatesttakerishowthetestisdividedupandwhatYOUneedtoknow
tocrackit!
BothsectionsoftheMathTestcontainsomestudent-produced-responsequestionscalledGrid-Ins,butallother questions on the exam are multiple choice. All multiple-choice sections on the SAT have fourpossibleanswerchoices.
Eachpartofthisbookcoversthesetestsindetail,buthere’sabriefrundownofwhatyoucanexpect.
ReadingTestYourscoresontheReadingTestandtheWritingandLanguageTest(seebelow)togethercompriseyourEvidence-BasedReadingandWritingscoreontheSAT.TheReadingTestis65minuteslongandconsistsof 52 questions, all of which are passage-based and multiple choice. Passages may be paired withinformationalgraphics,suchaschartsorgraphs,andtherewillbeaseriesofquestionsbasedonapairofpassages.Theselectedpassageswillbefrompreviouslypublishedworksintheareasofworldliterature,history/socialstudies,andscience.Questionsbasedonsciencepassagesmayaskyoutoanalyzedataorhypotheses,whilequestionsonliteraturepassageswillfocusmoreonliteraryconceptsliketheme,mood,andcharacterization.ThemaingoaloftheReadingTestistomeasureyourabilitytounderstandwordsincontextaswellasfindandanalyzeevidence.
WantMore?Forevenmorepractice,
checkout9PracticeTestsfortheSAT.
WritingandLanguageTestTheWritingandLanguageTestis35minuteslongandconsistsof44questions,whicharealsomultiplechoice and based on passages. However, instead of asking you to analyze a passage, questions willrequireyou toproofreadandedit thepassage.Thismeansyouwillhave tocorrectgrammarandwordchoice,aswellasmakelargerchangestotheorganizationorcontentofthepassage.
MathTest
Youwillhavea totalof80minutes tocomplete theMathTest,which,asmentionedearlier, isdividedinto two sections:NoCalculator (Section 3; 25minutes, 20 questions) andCalculator (Section 4; 55minutes, 38 questions). Most questions are multiple choice, but there are also a handful of student-produced response questions, which are also known as Grid-Ins. For Grid-In questions, instead ofchoosingfromfouranswerchoices,you’llhavetoworkthroughaproblemandthenenteryouransweronyouranswersheetbybubblingintheappropriatenumbers.We’lldiscussthisinmoredetail inChapter17.Exactly13ofthe58mathquestionswillbeGrid-Ins.
The Math Test covers four main content areas, which ETS and the College Board have named thefollowing:(1)HeartofAlgebra,(2)ProblemSolvingandDataAnalysis,(3)PassporttoAdvancedMath,and(4)AdditionalTopicsinMath.Thislastsectionincludestopicsingeometryandtrigonometry.PartIVofthisbookcoverseachofthesecontentareasindepth.
OptionalEssayWhiletheessayistechnicallyoptional,manycollegesrequireyoutakeitbeforeyouapplyforadmission.It’simportantthatyouresearcheachoftheschoolsyou’reapplyingtoanddeterminewhethertheessayisanadmissions requirement.Theessay requiresyou to readashortpassageandexplainhowtheauthorbuildshisorherargument.Thetestwriterswanttoseehowyoucomprehendatextanddemonstratethatunderstandinginwriting,usingevidencefromthepassage.
ExpandYourKnowledge
LearnmoreabouttheSATbyloggingintoyourPremiumPortal,whichisfilledwithgreatstufflikeaslewofvideotutorialsandthe“SATInsider”to
helpyounavigatecollegeadmissions,
applications,andtestprep.
ScoringontheSATTheSATisscoredonascaleof400–1600,whichisacombinationofyourscoresforEvidence-BasedReadingandWriting(acombinationofyourReadingandWritingandLanguagescores;scoredfrom200to 800) andMath (also scored from 200 to 800). The exam also has a detailed scoring system thatincludescross-testscoresandsubscoresbasedonyourperformanceoneachofthethreetests.YourscorereportfortheSATwillfeaturescoresforeachofthefollowing:
• TotalScore(1):Thesumofthetwosectionscores(Evidence-BasedReadingandWritingandMath),rangingfrom400to1600
• SectionScores(2):Evidence-BasedReadingandWriting,rangingfrom200–800;Math,also
rangingfrom200to800• TestScores(3):ReadingTest,WritingandLanguageTest,MathTest,eachofwhichisscored
onascalefrom10to40• Cross-TestScores(2):Eachisscoredonascalefrom10to40andbasedonselectedquestions
fromthethreetests(Reading,WritingandLanguage,Math):1. AnalysisinHistory/SocialStudies2. AnalysisinScience
• Subscores(7):Eachofthefollowingreceivesascorefrom1to15:1. CommandofEvidence(Reading;WritingandLanguage)2. WordsinContext(Reading;WritingandLanguage)3. ExpressionofIdeas(WritingandLanguage)4. StandardEnglishConventions(WritingandLanguage)5. HeartofAlgebra(Math)6. ProblemSolvingandDataAnalysis(Math)7. PassporttoAdvancedMath(Math)
This scoring structure was designed to help provide a more holistic profile of students’ skills andknowledge,aswellasreadinessforcollege.
ANoteonEssayScoring
Ifyouchoosetowritetheessay,youwillbegradedbytworeadersinthree
areas:Reading,Writing,andAnalysis.Yourtotal
essayscorewillbeona2-to8-pointscaleforeachofthethreeareas.SeePartVformoreontheessayand
howitisscored.
WhenIstheSATGiven?TheSATschedulefortheschoolyearispostedontheCollegeBoardwebsiteatwww.collegeboard.org.There are two ways to sign up for the test. You can either sign up online by going towww.collegeboard.org and clicking on the SAT hyperlink, or sign up through the mail with an SATregistrationbooklet,whichmaybeavailableatyourschoolguidancecounselor’soffice.
TrytosignupfortheSATassoonasyouknowwhenyou’llbetakingthetest.Ifyouwaituntilthelastminutetosignup,theremaynotbeanyopenspotsinthetestingcenters.
Ifyourequireanyspecialaccommodationswhiletakingthetest(including,butnotlimitedto,extratimeorassistance),www.collegeboard.orghas informationaboutapplyingfor thoseaccommodations.Makesuretoapplyearly;werecommendapplyingsixmonthsbeforeyouplantotakethetest.
StayonScheduleAlthoughyoumaytake
theSATanytimestartingfreshmanyear,most
studentstakeitforthefirsttimeinthespringoftheirjunioryearandmayretakeitinthefalloftheirsenioryear.Inaddition,youmayneedtotake
SATSubjectTests(manycompetitivecolleges
requirethem),sodon’tleaveeverythinguntil
thelastminute.Youcan’ttakeSATandSATSubjectTestsonthesameday.Sitdownandplanaschedule.
HOWTOUSETHISBOOKThis book is organized to provide as much—or as little—support as you need, so you can use it inwhateverwaywillbehelpfultoimprovingyourscoreontheSAT.Butbeforeyoucandecidehowtousethisbook,youshouldtakeapracticetesttodetermineyourstrengthsandweaknessesandfigureouthowtomakeaneffectivestudyplan.Ifyou’refeelingtest-phobic,remindyourselfthatapracticetestisatoolfordiagnosingyourself—it’snothowwellyoudothatmatters,buthowyouusetheinformationgleanedfromyourperformancetoguideyourpreparation.
So,beforeyoureadanyfurther,takePracticeTest1thatstartsonthispageofPartVII.Besuretotakeitinonesittingsoastomimictherealtest-takingexperience,andremembertofollowtheinstructionsthatappearatthebeginningofeachsectionoftheexam.
Afteryoutakethetest,checkyouranswersagainsttheAnswersandExplanationsthatstartonthispage,reflectonyourperformance,anddeterminetheareas inwhichyouneedto improve.Whichsectionsortypesofquestionspresentedthemostdifficultytoyou?Whichsectionsortypesofquestionsdidyoufeelmostconfidentabout?Basedonyourperformanceoneachof thesections,shouldyoufocusyourstudymoreonmath,reading,orwriting?
Howyouanswer thosequestionswillaffecthowyouengagewithPartII (How toCrack theReadingTest),PartIII (HowtoCracktheWritingandLanguageTest),PartIV (HowtoCrack theMathTest),and Part V (How to Crack the Essay) of this book. Each of these parts is designed to give acomprehensivereviewofthecontenttestedontheSAT,includingthelevelofdetailyouneedtoknowandhowthecontentistested.Attheendofeachofthesechapters,you’llhavetheopportunitytoassessyourmastery of the content covered through targeted drills that reflect the types of questions and level ofdifficultyyou’llseeontheactualexam.
ScoringYourPracticeTests
AttheendofeachAnswersandExplanations
chapter,we’veprovided
atableandstep-by-stepequationtohelpyouscore
yourpracticetestanddeterminehowyourperformancewould
translatetotheactualSAT.Youcanalsogeneratea
detailedonlinescorereportinyourStudent
Tools.FollowthestepsontheRegisterYourBookOnline!pagetoaccessthisawesomefeature.
Inadditiontocontentreview,thisbookprovidesessentialtest-takingstrategiesthatwillhelpyouavoidtrapsandmanageyour time inorder tomaximize thenumberofpointsavailable toyou.Strategiesarediscussedineverycontentchapter,butyoucanalsofindahelpfuloverviewinChapter2oftheonesthatcomeupfrequentlythroughoutthebook.Chapter2willhelpyouthinkaboutyourapproachtothevariousquestiontypesontheexam.
You’llhavethechancetoapplythesestrategiesinPartVII,whichcontainstheremainingpracticetests.If youneedadditionalpractice, youcandownload threemorepractice testsonlineby registeringyourbookonourwebsiteandfollowingthestepstoaccessyouronlineresources.(See“RegisterYourBookOnline!”.)Youdonothave to takeeverypractice testavailable toyou,butdoingsowillallowyou tocontinuallygaugeyourperformance,addressyourdeficiencies,andimprove.
Andremember,yourprepshouldnotendwiththisbook.Thereareahostofresourcesavailabletoyouonline,includingtheonlinetoolsaccompanyingthisbook(see“RegisterYourBookOnline!”)aswellastheCollegeBoardwebsite,www.collegeboard.org.
GetMoreOnlineWantevenmorepractice?
BesuretoregisteryourbooktogainaccesstoourPremiumPortal,whichisfilledwithatonofgreatcontenttohelpboost
yourtestprep,includingthreeadditionalfull-lengthpracticetests,alongwith
answersandexplanations.
Chapter2CrackingtheSAT:BasicPrinciplesThefirststeptocrackingtheSATisknowinghowbesttoapproachthetest.TheSATisnotlikethetestsyou’vetakeninschool,soyouneedto learnto lookat it inadifferentway.Thischapterprovidesandexplainstest-takingstrategiesthatwillimmediatelyimproveyourscore.MakesureyoufullyunderstandtheseconceptsbeforemovingontoPartII.Goodluck!
BASICPRINCIPLESOFCRACKINGTHETEST
WhatETSDoesWellThefolksatETShavebeenwritingstandardizedtestsformorethan80years,andtheywritetestsforallsortsofprograms.TheyhaveadministeredtheSATsomanytimesthattheyknowexactlyhowyouwillapproachit.Theyknowhowyou’llattackcertainquestions,whatsortofmistakesyou’llprobablymake,andevenwhatansweryou’llbemostlikelytopick.Freaky,isn’tit?
However,ETS’sstrengthisalsoaweakness.Becausethetestisstandardized,theSATasksthesametypeofquestionsoverandoveragain.Sure,thenumbersorthewordsmightchange,butthebasicsdon’t.Withenoughpractice,youcanlearntothinklikethetestwriters.Buttrytouseyourpowersforgood,okay?
TheSATIsn’tSchoolOurjobisn’ttoteachyoumathorEnglish—leavethattoyoursupersmartschoolteachers.Instead,we’regoing to teachyouwhat theSAT isandhow tocrack it.You’ll soonsee that theSAT involvesaverydifferentskillset.
Bewarnedthatsomeoftheapproacheswe’regoingtoshowyoumayseemcounterintuitiveorunnatural.Someofthesestrategiesmaybeverydifferentfromthewayyoulearnedtoapproachsimilarquestionsinschool,buttrustus!Trytacklingtheproblemsusingourtechniques,andkeeppracticinguntiltheybecomeeasier.You’llseearealimprovementinyourscore.
Let’stakealookatthequestions.
NoMoreWrong-AnswerPenalty!YouwillNOT be penalized on the SAT for anywrong answers. Thismeans you should alwaysguess,evenifthismeanschoosinganansweratrandom.
CrackingMultiple-ChoiceQuestionsWhat’sthecapitalofAzerbaijan?
Giveup?
Unless you spend your spare time studying an atlas, youmay not even know thatAzerbaijan is a realcountry,muchlesswhatitscapitalis.Ifthisquestioncameuponatest,you’dhavetoskipit,wouldn’tyou?Well,maybenot.Let’sturnthisquestionintoamultiple-choicequestion—justlikeallthequestionsontheSATReadingTestandWritingandLanguageTest,andthemajorityofquestionsyou’llfindontheSATMathTest—tofindoutifyoucanfigureouttheansweranyway.
1. ThecapitalofAzerbaijanis
A) Washington,D.C.B) Paris.C) London.D) Baku.
Thequestiondoesn’tseemthathardanymore,doesit?Ofcourse,wemadeourexampleextremelyeasy.(Bytheway,therewon’tactuallybeanyquestionsaboutgeographyontheSAT.)Butyou’dbesurprisedbyhowmanypeoplegiveuponSATquestionsthataren’tmuchmoredifficultthanthisonejustbecausetheydon’tknowthecorrectanswerrightoffthetopoftheirheads.“CapitalofAzerbaijan?Oh,no!I’veneverheardofAzerbaijan!”
Thesestudentsdon’tstoptothinkthattheymightbeabletofindthecorrectanswersimplybyeliminatingalloftheanswerchoicestheyknowarewrong.
YouAlreadyKnowAlmostAlloftheAnswersAllbutahandfulof thequestionson theSATaremultiple-choicequestions,andeverymultiple-choicequestionhasfouranswerchoices.Oneofthosechoices,andonlyone,willbethecorrectanswertothequestion.Youdon’thavetocomeupwiththeanswerfromscratch.Youjusthavetoidentifyit.
Howwillyoudothat?
LookfortheWrongAnswersInsteadoftheRightOnesWhy?Becausewronganswersareusuallyeasiertofindthantherightones.Afterall,therearemoreofthem!RememberthequestionaboutAzerbaijan?Eventhoughyoudidn’tknowtheansweroffthetopofyourhead,youeasilyfigureditoutbyeliminatingthethreeobviouslyincorrectchoices.Youlookedforwronganswersfirst.
Inotherwords,youusedtheProcessofElimination,whichwe’llcallPOEforshort.Thisisanextremelyimportantconcept,onewe’llcomebacktoagainandagain.It’soneofthekeystoimprovingyourSATscore.Whenyoufinishreadingthisbook,youwillbeabletousePOEtoanswermanyquestionsthatyoumaynotunderstand.
It’sNotAboutCirclingtheRightAnswerPhysicallymarkinginyourtestbookletwhatyouthinkofcertainanswerscanhelpyounarrowdownchoices,takethebestpossibleguess,andsavetime!Tryusingthefollowingnotations:
Putacheckmarknexttoanansweryoulike.~ Putasquigglenexttoanansweryoukindoflike.? Putaquestionmarknexttoanansweryoudon’tunderstand.A CrossouttheletterofanyanswerchoiceyouKNOWiswrong.
Youcanalwayscomeupwithyourownsystem.Justmakesureyouareconsistent.
ThegreatartistMichelangelooncesaidthatwhenhelookedatablockofmarble,hecouldseeastatueinside.Allhehadtodotomakeasculpturewastochipawayeverythingthatwasn’tpartofit.YoushouldapproachdifficultSATmultiple-choicequestionsinthesameway,by“chippingaway”theanswersthatarenotcorrect.Byfirsteliminatingthemostobviouslyincorrectchoicesondifficultquestions,youwillbeabletofocusyourattentiononthefewchoicesthatremain.
PROCESSOFELIMINATION(POE)Therewon’tbemanyquestionsontheSATinwhichincorrectchoiceswillbeaseasytoeliminateastheywereontheAzerbaijanquestion.Butifyoureadthisbookcarefully,you’lllearnhowtoeliminateatleastonechoiceonalmostanySATmultiple-choicequestion,ifnottwooreventhreechoices.
Formoretest-takinginformationandstrategies,includingPOE,checkouttheonlinevideosavailableinyourPremiumPortal!
Whatgoodisittoeliminatejustoneortwochoicesonafour-choiceSATquestion?
Plenty.Infact,formoststudents,it’sanimportantkeytoearninghigherscores.Here’sanotherexample:
2. ThecapitalofQatarisA) Paris.B) Dukhan.C) Tokyo.D) Doha.
Onthisquestionyou’llalmostcertainlybeabletoeliminatetwoofthefourchoicesbyusingPOE.Thatmeansyou’re stillnot sureof theanswer.Youknow that thecapitalofQatarhas tobeeitherDohaorDukhan,butyoudon’tknowwhich.
Shouldyouskipthequestionandgoon?Orshouldyouguess?
CloseYourEyesandPointThereisnoguessingpenaltyontheSAT,soyoushouldbubblesomethingforeveryquestion.Ifyougetdowntotwoanswers,justpickoneofthem.There’snoharmindoingso.
You’regoingtohearalotofmixedopinionsaboutwhatyoushouldbubbleorwhetheryoushouldbubbleatall.Let’sclearupafewmisconceptionsaboutguessing.
FALSE:Don’tansweraquestionunlessyou’reabsolutelysureoftheanswer.
Youwillalmostcertainlyhaveteachersandguidancecounselorswhotellyouthis.Don’tlistento them! The SAT does not penalize you forwrong answers. Put something down for everyquestion:Youmightgetafreebie.
FALSE:Ifyouhavetoguess,guess(C).
Thisisaweirdmisconception,andobviouslyit’snottrue.Asageneralrule,ifsomeonesayssomethingreallyweird-soundingabouttheSAT,it’susuallysafestnottobelievethatperson.
FALSE:Alwayspickthe[fillintheblank].
Becarefulwithdirectivesthattellyouthatthisorthatanswerortypeofanswerisalwaysright.It’smuchsafertolearntherulesandtohaveasolidguessingstrategyinplace.
Asfarasguessingisconcerned,wedohaveasmallpieceofadvice.Firstandforemost,makesureofonething:
AnswereveryquestionontheSAT.There’snopenalty.
LETTEROFTHEDAY(LOTD)Sometimesyouwon’tbeabletoeliminateanyanswers,andsometimestherewillbequestionsthatyouwon’thave time to lookat.For those,wehavea simplesolution.Picka“letterof theday,”orLOTD(fromAtoD),andchoosethatanswerchoiceforquestionsforwhichyoucan’teliminateanyanswersordonothavetimetodo.
Thisisaquickandeasywaytomakesurethatyou’veansweredeveryquestion.(Remember,youarenotpenalizedforwronganswers!)Italsohassomepotentialstatisticaladvantages.Ifalltheanswersshowupaboutone-fourthofthetimeandyouguessthesameanswereverytimeyouhavetoguess,you’relikelytogetacoupleoffreebies.
LOTDshouldabsolutelybeanafterthought;it’sfarmoreimportantandhelpfultoyourscoretoeliminateanswer choices. But for those questions you don’t know at all, LOTD is better than full-on randomguessingornostrategyatall.
AreYouReady?CheckoutAreYouReadyfortheSATandACT?to
brushuponessentialskillsfortheseexamsand
beyond.
PACEYOURSELFLOTD should remind us about something very important: There’s a very good chance that you won’tanswereveryquestiononthetest.
Think about it this way. There are 5 passages and 52 questions on the Reading Test. You’ve got 65minutes to complete those questions. Now, everyone knows that the Reading Test is super long andboring,and52questionsin65minutesprobablysoundslikeaton.Thegreatnewsisthatyoudon’thavetoworkall52ofthesequestions.Afterall,doyouthinkyoureadmosteffectivelywhenyou’reinahugerush?YoumightdobetterifyouworkedonlyfourofthepassagesandLOTD’dtherest.There’snothinginthetestbookletthatsaysthatyoucan’tworkatyourownpace.
Pace,Don’tRaceFormoreaboutpacingontheSAT,watchouronline
videosinthePremiumPortal.
Let’ssayyoudoall52Readingquestionsandgethalfofthemright.Whatrawscoredoyougetfromthat?That’sright:26.
Now, let’s say you do only three of the 10-question Reading passages and get all of them right. It’sconceivablethatyoucouldbecauseyou’venowgotallthisextratime.Whatkindofscorewouldyougetfromthismethod?Youbet:30—andmaybeevena littlehigherbecauseyou’llgeta fewfreebies fromyourLetteroftheDay.
Inthiscase,andontheSATasawhole,slowingdowncangetyoumorepoints.Unlessyou’recurrentlyscoringinthe650+rangeonthetwosections,youshouldn’tbeworkingallthequestions.We’llgointothisinmoredetailinthelaterchapters,butfornowrememberthis:
Slowdown,scoremore.You’renotscoredonhowmanyquestionsyoudo.You’rescoredonhow
many questions you answer correctly. Doing fewer questions can mean more correct answersoverall!
EMBRACEYOURPOODEmbraceyourwhatnow?POOD!Itstandsfor“PersonalOrderofDifficulty.”OneofthethingsthatSAThasdispensedwithaltogetherisastrictOrderofDifficulty—inotherwords,anarrangementofproblemsthat places easy questions earlier in the test than hard ones. In the absence of thisOrder ofDifficulty(OOD),youneedtobeparticularlyvigilantaboutapplyingyourPersonalOrderofDifficulty(POOD).
Think about it this way. There’s someone writing the words that you’re reading right now. So whathappens if you are asked,Who is the author of Cracking the SAT?Do you know the answer to thatquestion?Maybenot.Doweknowtheanswertothatquestion?Absolutely.
Soyoucan’texactlysaythatthatquestionis“difficult,”butyoucansaythatcertainpeoplewouldhaveaneasiertimeansweringit.
As we’ve begun to suggest with our Pacing, POE, and Letter of the Day strategies, The PrincetonReview’sstrategiesareallaboutmakingthetestyourown,towhateverextentthatispossible.Wecallthis ideaPOODbecausewebelieve it isessential thatyou identify thequestions thatyou findeasyorhardandthatyouworkthetestinawaymostsuitabletoyourgoalsandstrengths.
Asyoufamiliarizeyourselfwiththerestofourstrategies,keepallofthisinmind.Youmaybesurprisedtofindouthowyouperformonparticularquestiontypesandsections.TheSATmaybestandardized,butthe biggest improvements are usually reserved for thosewho can treat the test in a personalized, non-standardizedway.
Summary◦ When you don’t know the right answer to a multiple-choice question, look for wrong answers
instead.They’reusuallyeasiertofind.
◦ Whenyoufindawronganswer,eliminateit.Inotherwords,usePOE,theProcessofElimination.
◦ There’snomoreguessingpenaltyontheSAT,sothere’snoreasonNOTtoguess.
◦ There’s bound to be at least a few questions you simply don’t get to orwhere you’re finding itdifficulttoeliminateevenoneanswerchoice.Whenthishappens,usetheLOTD(LetteroftheDay)strategy.
◦ Paceyourself.Remember,you’renotscoredonhowmanyquestionsyouanswer,butonhowmanyquestionsyouanswercorrectly.Takeitslowandsteady.
◦ Makethetestyourown.Whenyoucanworkthetesttosuityourstrengths(anduseourstrategiestoovercomeanyweaknesses),you’llbeonyourwaytoahigherscore.
Chapter3TheReadingTest:BasicApproachHalfofyourEvidence-BasedReadingandWritingscorecomesfromtheReadingTest,a65-minutetestthatrequiresyoutoanswer52questionsspreadoutoverfivepassages.Thequestionswillaskyoutodoeverythingfromdeterminingthemeaningofwordsincontexttodecidinganauthor’spurposeforadetailtofindingthemainideaofawholepassagetopinpointinginformationonagraph.Eachpassagerangesfrom500to750wordsandhas10or11questions.Timewillbetightonthis test.Thepurposeof thischapteristointroduceyoutoabasicapproachthatwillstreamlinehowyoutakethetestandallowyoutofocusononlywhatyouneedtogetyourpoints.
SATREADING:CRACKINGTHEPASSAGESYoureadeveryday.Fromstreetsignstonovelstothebackofthecerealbox,youspendagoodpartofyourdayrecognizingwrittenwords.Sothistestshouldbeprettyeasy,right?
Unfortunately,readingontheSATisdifferentfromreadinginreallife.Inreallife,youreadpassively.Youreyesgooverthewords,thewordsgointoyourbrain,andsomestickandsomedon’t.OntheSAT,youhavetoreadactively,whichmeanstryingtofindspecificinformationtoanswerspecificquestions.Onceyou’vefoundtheinformationyouneed,youhavetounderstandwhatit’sactuallysaying.
Readingon theSATisalsoverydifferent fromthe readingyoudo inschool. InEnglishclass,youareoftenaskedtogiveyourownopinionandsupportitwithevidencefromatext.YoumighthavetoexplainhowScoutFinchandBooRadleyinToKillaMockingbirdare,metaphoricallyspeaking,mockingbirds.OryoumightbeaskedtoexplainwhoisactuallyresponsibleforthetragediesinRomeoandJuliet.OntheSAT,however,thereisnoopinion.Youdon’thavetheopportunitytojustifywhyyouransweristherightone.Thatmeansthereisonlyonerightanswer,andyourjobistofindit.It’stheweirdestscavengerhuntever.
Wantmorestrategytips?We’vegotyoucovered.Checkout
ouronlinevideosformoreinformationonstrategies
tohelpyouoneverysectionoftheSAT.
YourMission:
Readfivepassagesandanswer10or11questions foreachpassage (or setofpassages).Getasmanypointsasyoucan.
Okay,sohowdoyougetthosepoints?Let’sstartwiththeinstructionsfortheReadingTest.
DIRECTIONS
Eachpassageorpairofpassagesbelowisfollowedbyanumberofquestions.Afterreadingeachpassageorpair,choosethebestanswertoeachquestionbasedonwhatisstatedorimpliedinthepassageorpassagesandinanyaccompanyinggraphics(suchasatableorgraph).
Greatnews!Thisisanopen-booktest.Noticethedirectionssaybasedonwhatisstatedorimpliedinthepassage.ThismeansthatyouareNOTbeingtestedonwhetheryouhaveread,studied,andbecomeanexpertontheConstitution,TheGreatGatsby,oryourbiologytextbook.Allthetestwriterscareaboutis
whether or not you can read a text and understand itwell enough to correctly answer some questionsaboutit.UnliketheMathandWritingandLanguageTests,therearenoformulastomemorizeorcommarulestolearnfortheReadingTest.Youjustneedtoknowhowtoapproachthepassages,questions,andanswer choices in a way that maximizes your accuracy and efficiency. It’s all about the text! (Nothinking!)
Anotherawesomethingaboutanopen-booktestisthatyoudon’thavetowastetimereadingeverysinglewordofthepassageandtryingtobecomeanexpertonwhateverthetopicis.Youhavethepassagerightthere infrontofyou.So,movebackandforthbetween thepassageand thequestions, focusingonlyonwhatyouneedtoknowinsteadofgettingmireddowninallthelittledetails.
POODandtheReadingTestYouwillgetallfiveofthereadingpassagesatthesametime,sousethattoyouradvantage.Takeaquicklookthroughthewholesectionandfigureoutthebestorderinwhichtodothepassages.Dependingonyour target score,youmaybe able to skip anentirepassageor two, so figureoutwhichpassages arelikelytogetyouthemostpointsanddothosefirst.
Considerthefollowing:
• Typeofpassage:Therewillbe1literaturepassage,2sciencepassages,and2history/socialstudiespassages.Ifyouliketoreadnovelsandshortstories,theliteraturepassagemaybeagoodplacetostart.Ifyouprefernonfiction,youmightconsidertacklingthescienceandhistory/socialstudiespassagesfirst.
• Topicofpassage:Theblurbprecedingthepassagewillgiveyousomebasicinformationaboutthepassage,whichmayhelpyoudecidewhethertodothepassageorskipit.
• Typesofquestions:Dothequestionshaveagoodnumberoflinereferencesandleadwords?Willyoubeabletofindwhatyou’relookingforrelativelyquickly,orwillyouhavetospendmoretimewadingthroughthepassagetofindtheinformationyouneed?
Don’tforget:Onanyquestionsorpassagesthatyouskip,alwaysfillinyourLOTD!
BasicApproachfortheReadingTestFollowthesestepsforeveryReadingpassage.We’llgoovertheseingreaterdetailinthenextfewpages.
1. ReadtheBlurb.Theshortparagraphatthebeginningofeachpassagemaynotcontainalotofinformation,butitcanbehelpfulforidentifyingthetypeofpassage,aswellasthesource.
2. SelectandUnderstandaQuestion.Forthemostpart,dothequestionsinorder,savingthegeneralquestionsforlastandusingyourLOTDonanyquestionsorpassagesyouwanttoskip.
3. ReadWhatYouNeed.Don’treadthewholepassage!Uselinereferencesandleadwordstofindthereferenceforthequestion,andthencarefullyreadawindowofabout10–12lines(usuallyabout5or6linesaboveandbelowthelinereference/leadword)tofindtheanswertothequestion.
4. PredicttheCorrectAnswer.Yourpredictionshouldcomestraightfromthetext.Don’tanalyzeorparaphrase.Often,you’llbeabletofindasentenceorphraseinthetextthatyoucanactuallyunderlinetopredicttheanswer.
5. UsePOE.Eliminateanythingthatisn’tconsistentwithyourprediction.Don’tnecessarilytrytofindtherightanswerimmediately,becausethereisagoodchanceyouwon’tseeananswerchoicethatyoulike.Ifyoucaneliminatechoicesthatyouknowarewrong,though,you’llbeclosertotherightanswer.Ifyoucan’teliminatethreeanswerswithyourprediction,usethePOEcriteria(whichwe’lltalkaboutlateron).
“WheretheMoneyIs”A reporter once asked notorious thiefWillie Suttonwhy he robbed banks.Legend has it that hisanswerwas,“Becausethat’swherethemoneyis.”Whilereadingcomprehensionismuchsaferandmoreproductivethanlarceny,thesameprincipleapplies:Concentrateonthequestionsandanswerchoicesbecausethat’swherethepointsare.Thepassageisjustaplaceforthetestwriterstostashfactsanddetails.You’llfindthemwhenyouneedto.What’sthepointofmemorizingall67peskydetailsaboutplanktonifyou’reaskedaboutonly12?
Let’sseethesestepsinaction!
What follows is a sample reading passage followed by a series of questions.Don’t startworking thepassagerightaway.Infact,youcan’t,becausewe’veremovedtheanswerchoices.Justturntothispage,wherewewillbegingoingthrougheachstepoftheReadingBasicApproach,usingthesamplepassageandquestions.
SAMPLEPASSAGEANDQUESTIONSHereisanexampleofanSATReadingpassageandquestions.WewillusethispassagetoillustratetheReadingBasicApproachthroughoutthischapter.
Questions11–21arebasedonthefollowingpassage.
ThispassageisadaptedfromLintonWeeks’s“TheWindshield-PittingMysteryof1954.”©2015byNPRHistoryDepartment.
Theseare thequestions for thepassage.We’ve removed theanswerchoicesbecause, fornow,we justwantyoutoseethedifferentquestiontypestheSATwillask.Don’tworryaboutansweringthesehere;we’llwalkyouthroughsomeofthemintherestofthischapter.
11. Thecentralclaimofthepassageisthat
12. TheauthormostlikelymentionstheCanadianscientist(line22)andtheUtahresident(line26)inorderto
13. Theauthor’sstatementthatthe“countrymovedontobuildingbackyardfalloutshelters”(lines31–32)impliesthatAmericans
14. Asusedinline41,“common”mostnearlymeans
15. Thepassageindicatesthataneffectofaggregatingeventsis
16. Accordingtothepassage,whatpercentofcarsinWashingtonsuffereddamage?
17. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?
18. TheauthormostlikelymentionsWaroftheWorldsinline73inorderto
19. Thequotationmarksaroundtheword“hysteria”inline94mostlikelyindicate
20. Basedonthepassage,theauthormostlikelyagreesthat“pitting”is
21. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?
Step1:ReadtheBlurbYou should always begin by reading the blurb (the introductorymaterial preceding the passage). Theblurbgivesyouthetitleofthepiece,aswellastheauthorandthepublicationdate.Typically,theblurbwon’thavemuchmoreinformationthanthat,butit’llbeenoughforyoutoidentifywhetherthepassageisliterature, history/social studies, or science. Itwill also giveyou a sense ofwhat the passagewill beabout and can help youmake a POOD (Personal Order of Difficulty) decision about when to do thepassage.
TheStrategy1.ReadtheBlurb
Read the blurb at the beginning of the passage on this page. Based on the blurb, is this a literature,history/socialstudies,orsciencepassage?Whatwillthepassagebeabout?
Step2:SelectandUnderstandaQuestion
Select…Notice that the stepsof theBasicApproachhaveyou jumping straight from theblurb to thequestions.Thereisno“ReadthePassage”step.Yougetpointsforansweringquestions,notforreadingthepassage,sogostraighttothequestions.
TheStrategy1.ReadtheBlurb
2.SelectandUnderstandaQuestion
Ona school test, youprobably answer thequestions inorder.That seems logical and straightforward.However, doing the questions in order on aReading passage can set you up for a serious time issue.AccordingtoETSandtheCollegeBoard,theorderofthequestions“isalsoasnaturalaspossible,withgeneralquestionsaboutcentral ideas, themes,pointofview,overall textstructure,and the likecomingearly in thesequence, followedbymore localizedquestionsaboutdetails,words incontext,evidence,andthelike.”Sotosumitup:Thegeneralquestionscomefirst,followedbythespecificquestions.
ThatquestionstructureworksgreatinanEnglishclass,whenyouhaveplentyoftimetoreadanddigestthetextonyourown.Butwhenyou’retryingtogetthroughfivepassagesinjustoveranhour,youdon’thave time for that. So, instead of starting with the general questions and then answering the specificquestions,we’regoingtoflipthatanddothespecificquestionsfirst.
Lookbackatthequestionsonthispage.
Whatdoesthefirstquestionaskyouabout?
Inordertoanswerthatquestion,you’dhavetoreadwhatpartofthepassage?
Whatyoudonotwanttodoisreadthewholepassage!Soskipthatfirstquestion.You’llcomebacktoit,
but not until you’ve done the specific questions.Once you go through and answer all (ormost) of thespecificquestions,you’llhaveareallygoodideawhatthetestwritersthinkisimportant.You’llalsohavereadmostofthepassage,soansweringthegeneralquestionswillbeeasy.
Rememberwementionedearlierthatthequestionsareinchronologicalorder?Lookatthelinereferencesinthespecificquestions.Whatdoyounoticeaboutthem?
Yep! They’re in order through the passage! So work through them as they’re given, and you’ll workthroughthepassagefrombeginningtoend.Donotgetstuckonahardquestion,though.Ifyoufindyourselfstumped,useyourLOTDandmoveontothenextquestion.Youcanalwayscomebackifyouhavetime.
Basedonthatlogic,let’sskipthefirstquestionandmoveontothesecondquestion.
…andUnderstandOnce you’ve selected a question, you need to make sure you understand what it’s asking. Readingquestions are often not in question format. Instead, they will make statements such as, “The author’sprimaryreasonformentioningthegadflyisto,”andthentheanswerchoiceswillfollow.Makesurethatyouunderstand thequestionby turning it intoaquestion—that is,back intoasentence thatendswithaquestionmarkandbeginswithWho/What/Why.
12. TheauthormostlikelymentionstheCanadianscientist(line22)andtheUtahresident(line26)inorderto
Whatisthisquestionasking?
RephrasetheQuestion……sothatitasks:
Who?What?Why?
Noticethephrase inordertoat theendof thequestion.Thatphrase letsyouknowthequestioncanberephrased as a “why” question. So for this particular question, youwant to figure out “Why does theauthormentiontheCanadianscientistandtheUtahresident?”
Step3:ReadWhatYouNeed
LineReferenceandLeadWordsManyquestionswillreferyoutoaspecificsetoflinesortoaparticularparagraph,soyouwon’tneedtoread theentirepassage toanswer thosequestions.Thoseare linereferences.Otherquestionsmaynotgiveyoualinereference,butmayaskaboutspecificnames,quotes,orphrasesthatareeasytospotinthetext.We’llcallthoseleadwords.It’simportanttorememberthatthelinereferenceorleadwordshowsyouwherethequestionisinthepassage,butyou’llhavetoreadmorethanthatsinglelineinordertofindtheanswerinthepassage.
TheStrategy1.ReadtheBlurb
2.SelectandUnderstandaQuestion
3.ReadWhatYouNeed
Ifyoureadawindowofaboutfivelinesaboveandfivelinesbeloweachlinereferenceorleadword,youshouldfindtheinformationyouneed.It’simportanttonotethatwhileyoudonotneedtoreadmorethanthese10–12linesoftext,youusuallycannotgetawaywithreadingless.Ifyoureadonlythelinesfrom the line reference, youwill very likelynot find the informationyouneed to answer thequestion.Readcarefully!Youshouldbeabletoputyourfingerontheparticularphrase,sentence,orsetof linesthatanswersyourquestion.Ifyousavethegeneralquestionsthatrelatetothepassageasawholeforlast,thenbythetimeyoubeginthosequestions,you’llhaveagreaterunderstandingofthepassageevenifyouhaven’treaditfrombeginningtoend.
Readawindowofabout5linesaboveand5linesbelowthelinereferencetogetthecontextforthequestion.
5Above,5Below5isthemagicnumberwhenitcomestoline
referencequestions.Read5linesabovetheline
referenceandthen5linesbelowittogetalloftheinformationyouneedin
ordertoanswerthequestioncorrectly.
12. TheauthormostlikelymentionstheCanadianscientist(line22)andtheUtahresident(line26)inorderto
Whatarethelinereferencesinthisquestion?
Whatlineswillyouneedtoreadtofindtheanswer?
Onceyouunderlinethelinereferencesandfindyourwindow,drawabracketarounditsoyoucanfinditeasily.Themoreyoucangetoutofyourbrainandontothepage,thebetteroffyou’llbe.Becausethelinereferencesareline22andline26,you’llwanttoreadlines17–31.Inthiscase,thatparagraphwouldbeagoodwindow.
Nowit’stimetoread.Eventhoughyou’reonlyreadingasmallchunkofthetext,makesureyoureaditcarefully.
Step4:PredictYourAnswerThe test writers do their best to distract you by creating tempting but nevertheless wrong answers.However, if you knowwhat you’re looking for in advance, you will be less likely to fall for a trapanswer.Beforeyouevenglanceattheanswerchoices,takethetimetothinkaboutwhatspecific,statedinformationinyourwindowsuppliestheanswertothequestion.Becarefulnottoparaphrasetoofarfromthetextortrytoanalyzewhatyou’rereading.Remember,whatmightbeagood“Englishclass”answermayleadyouinthewrongdirectionontheSAT!Stickwiththetext.
TheStrategy1.ReadtheBlurb
2.SelectandUnderstandaQuestion
3.ReadWhatYouNeed4.PredictYourAnswer
Asyoureadthewindow,lookforspecificlinesorphrasesthatanswerthequestion.Oftenwhatyou’relookingforwillbeinasentencebeforeorafterthelinereferenceorleadword,soit’scrucialthatyoureadthefullwindow.
Onceyou’vefoundtexttoanswerthequestion,underlineitifyoucan!Otherwise,jotdownapredictionfortheanswer,stickingasclosetothetextaspossible.
Let’stakealookatquestion12again,thistimewiththewindow.
12. TheauthormostlikelymentionstheCanadianscientist(line22)andtheUtahresident(line26)inorderto
Here’s your window from the passage. See if you can read it and find something that answers thequestion.Underlineyourpredictionifyoucan.
InCanton,Ohio,some1,000residentsnotifiedpolicethattheirwindshieldshadbeen“blemishedinamysteriousmanner,”theDailyMailofHagerstown,MD,reportedonApril17.AndUnitedPressinNewYorknotedonApril20that“newreportsofmysteriouswindshieldpittingscameintodayalmostasfastastheoriesaboutwhatcausesthem.”ACanadianscientistpositedthatthemarksweremadebytheskeletonsofminutemarinecreaturesthathadbeenpropelledintotheairbyhydrogenbombtestinginthePacificOcean.InUtah,someonesuggestedthatacidfromflyingbugsmightbethesourceofthewindshield-denting,butaBrighamYoungUniversitybiologistdisprovedthetheory,theProvoDailyHeraldreportedonJune27.
Didyouunderlinethephrasenewreportsofmysteriouswindshieldpittingscameintodayalmostasfastas theoriesaboutwhatcauses them?Thepassageprovidesclear evidence that theCanadian scientistandUtah residentarementioned inorder togiveexamplesof someof the theoriesabout thecausesofpittingthatwerezippingin.
Step5:UseProcessofEliminationAmultiple-choicetestisacoolthingbecausetherightanswerwillalwaysbeonthepageinfrontofyou.All you have to do is eliminate the answer choices that are incorrect. Sometimes, especially on theReadingTest,it’seasiertofindwronganswersthataren’tsupportedbythepassageratherthantryingtofindtherightanswerthatmightnotlookthewayyouthinkitshould.
ProcessofElimination,orPOE,involvestwosteps.Thefirststepinvolvesaskingyourselfthequestion,“WhatcanIeliminatethatdoesn’tmatch—orisinconsistentwith—myprediction?”Formanyofthemorestraightforwardquestions,thisstepwillbeenoughtogetdowntotherightanswer.
TheStrategy1.ReadtheBlurb
2.SelectandUnderstandaQuestion
3.ReadWhatYouNeed4.PredictYourAnswer
5.UseProcessofElimination
12. TheauthormostlikelymentionstheCanadianscientist(line22)andtheUtahresident(line26)inorderto
Remember,onthepreviouspage,youusedthetexttopredictthattheCanadianscientistandUtahresidentarementioned in order to give examples of some of the theories about the causes of pitting thatwerezippingin.Eliminateanychoicethathasnothingtodowiththatprediction.
Didyoueliminateallanswerchoicesexcept(A)?Noneoftheotherchoiceshaveanythingtodowithyourprediction.Additionally,onceyou’redowntoananswerchoicethatseemstosupportyourprediction,usethetexttomakesureyoucanproveit.What’sthepreviousstatement?Theoriescominginquickly.What’sthesupport?ExamplesfromCanadaandUtah.
POECriteriaOnmanyquestionsyou’llbeabletoeliminatethreeofthefouranswerssimplybyusingyourprediction.Onmoredifficultquestions,however,yourpredictionwillhelpyougetridofoneortwoanswerchoices,andthenyou’llneedtoconsidertheremaininganswersalittlemorecarefully.Ifyou’venarroweditdowntotwoanswerchoicesandtheybothseemtomakesense,you’reprobablydowntotherightanswerand
the trap answer. Luckily, we know some common traps that the test writers use, and they include thefollowing:
• MostlyRight/SlightlyWrong:Theseanswerslookjustaboutperfectexceptforawordortwothatdonotmatchwhat’sinthetext.
• CouldBeTrue:Theseanswersmightinitiallylookgoodbecausetheymakesenseorseemlogical.YoumightbeabletosupporttheseanswersinanEnglishclass,buttheylacktheconcretesupportfromthetexttomakethemcorrectSATanswers.
• DeceptiveLanguage:You’llbegivenanswerchoiceswithwordsthatlookexactlylikewhatyousawinthepassage,butthewordsareputtogetherinsuchawaythattheydon’tactuallysaywhatyouneedthemtosay.Makesureyou’rereadingcarefullyandnotjustmatchingwords.
PredictionsandPOEUsethesecriteriaafteryouhaveeliminatedany
answerchoicethatdoesn’tmatchyourprediction.
BeingawareofthesetrapswillhelpyouspotthemontheSATandthereforeavoidthem.
USINGTHEBASICAPPROACHNowthatyouknowthestepsoftheBasicApproach,let’spracticethemonsomedifferentquestiontypes.
Infer/Imply/SuggestWhenyouseeaquestion thatcontains theword infer, imply,orsuggest, be extra careful. In real life,thosewordsoftensignifyaquestionaskingyouropinion.Youmaythinkthatthetestwriterswantyoutodo someEnglish-class-level reading between the lines. In actuality, though, they don’t. It’s still just areadingcomprehensionquestion.Youmayhavetodosomereadingbetweenthelines,astheanswerwillnot be directly stated in the text as it usually iswith detail questions; but therewill still be plenty ofevidenceinthetexttosupportthecorrectanswer.
13. Theauthor’sstatementthatthe“countrymovedontobuildingbackyardfalloutshelters”(lines31–32)impliesthatAmericansA) wereawarethatthethreatfrombombswasmoreimminentthanthatfromwindshield
pitting.B) hadlostinterestinthewindshieldpittingphenomenon.C) neededaplacetobeprotectedfromnuclearfallout.D) didnotyethavefalloutsheltersintheirbackyards.
LineReferenceQuestions
Onanylinereferencequestion,youneedtogobacktothepassageandfindthelinereference,markit,andthenread
yourwindow.
Here’sHowtoCrackItFirst,youneedtogobacktothetextandfindthelinereference.Underlineit.Thenmarkandreadyourwindow.Makesureyouknowwhatthequestionisasking.Inthiscase,youwanttofigureoutwhatthelinereferencetellsyouaboutAmericans.Whenyoucarefullyreadyourwindowyouseethatassummerrolled on, reports of pitting decreased everywhere and the country moved on. They are leaving themysteryofpittingbehind.Onceyouhaveyourprediction,usePOEtoworkthroughyouranswers.Choice(A)doesn’tmatch the ideaofAmericansmovingon, soeliminate it.Choice (B) looksprettygood, sohangonto it.Choice(C)might lookgoodinitiallybecausewedidseesomethingearlieraboutnuclearfallout, but it has nothing to dowithmoving on from the pitting phenomenon, so you can eliminate it.Choice(D)mightmakesense—iftheyarebuildingtheshelters,theyprobablydon’thavethemalready—butithasnothingtodowithourprediction.Thatleaves(B),whichanswersthequestionandmatchesthepredictionfromthetext!
Vocabulary-in-ContextAnother way that your reading comprehension will be tested is with vocabulary-in-context (VIC)questions.ThemostimportantthingtorememberisthattheseareINCONTEXT!Gonearethedaysof“SAT vocabulary” when you had to memorize lists of obscure words like impecunious andperspicacious.Nowthefocusisonwhetheryoucanunderstandwhatawordmeansbasedonthecontextof the passage. You’ll see words that look familiar, but are often used in ways that are a little lessfamiliar.Donottrytoanswerthesequestionssimplybydefiningthewordinyourheadandlookingforthatdefinition.Youhavetogobacktothetextandlookatthecontextfortheword.
14. Asusedinline41,“common”mostnearlymeansA) tasteless.B) popular.
C) frequent.D) inferior.
Here’sHowtoCrackItWithVICquestions,youdon’tneedtoreadafull10–12linewindow.Typically,afewlinesbeforeandafewlinesafterwillgiveyouwhatyouneed.Gotoline41andfindthewordcommon.Underlineit.Whenyou read before and after the word, the text talks about a numbers game andmore people. The nextsentence says that something infrequentmay start toappear tobea trend.Use those context clues topredictsomethingthatreferstonumbersgame,morepeople,andsomethingthatwouldbetheoppositeofinfrequent.Putinsomethinglike“often”andthenusePOEtoeliminate(A),(B),and(D).
BecarefulwithVICquestions.Aswiththeotherquestions,youhavetorelyheavilyonthetext,notyourownopinions.Youmight be able to rather convincingly talkyourself into the idea that if something iscommon,it’spopular,becauseifit’scommon,it’severywhere,andifit’severywhere,thatmustmeanalotofpeoplelikeit.Itcanbeeasytotalkyourselfintoatangleifyouuseyourbrain.Trytoavoidthatandinstead focus onwhat the text actually says. In this case, you only have evidence for common havingsomethingtodowithnumbersandfrequency,nothowthegeneralpublicfeelsaboutsomething.
Tryanotherquestion:
15. ThepassageindicatesthataneffectofaggregatingeventsisA) patternsseemtoemergemorefrequently.B) thetruthaboutaconspiracyiseasiertofind.C) atinypercentoftheeventsaresimilar.D) connectionsbetweenunrelatedeventscanbereported.
Here’sHowtoCrackItThisquestiondoesn’thavea line reference,butnotice thatboth thequestionbefore itand thequestionafteritdo.Sincequestion14referencesline41,andquestion18referencesline73,question17shouldfallsomewherebetweenthoselines.Lookthroughthoselinesfortheleadwordsaggregatingeventsandusethatphrasetofindyourwindow.Carefullyreadthewindow,lookingfortheanswertothequestion,“Whatisaneffectofaggregatingevents?”Withinthewindow,youfindsomethingthatisveryinfrequentmaystarttoappeartobeatrendand[i]feveryoneislookingforandreportingit,itwouldappeartobeaconspiracyofsomesort.Gothroughtheanswerchoicesandeliminatethosethathavenothingtodowithappearingtobeatrendorconspiracy.
Choice(A)definitelyseemstomatchanappearingtrend,sohangontoit.
Choice(B)mentionsfindingaconspiracy,whichmightseemtomatch.
Choice(C)doesn’tmatchatall,soeliminateit.
Choice(D)mightbetrue,butdoesn’tmatchtheprediction,soeliminateit.
Basedonour firstpass through theanswerchoices,youarenowdown to (A)and (B).Remember thePOEcriteria?Takeacloserlookatthesetwoanswerchoices.
Choice(A):patternsseemtoemergemorefrequentlyisalmostanexactparaphraseofsomething…maystarttoappeartobeatrend,sothisonestilllooksprettygood.
Choice(B):Althoughthewordconspiracyappears inboththetextandtheanswerchoice,don’tforgetthatyouneed to readcarefully.The text says that itwouldappear tobeaconspiracy,which ismuchdifferent from finding the truth about a conspiracy.Don’t be deceived by deceptive language!Matchcontent,notjustwords.Choice(B)isout,leaving(A)asthecorrectanswer.
Let’stryonemore.
18. TheauthormostlikelymentionsWaroftheWorldsinline73inordertoA) arguesomecasesofmasshysteriaarelegitimate.B) provethemediawasresponsibleforpeople’sreactions.C) pointoutthatmostpeoplewerenotupsetbythebroadcast.D) criticizethemediaforfailingtorecognizetheprogramwasfictional.
Here’sHowtoCrackItFindyourwindowandcarefully read it, looking for the answer to thequestion, “Whydoes the authormentionWar of theWorlds?”When you read your window, you find that the author saysWar of theWorldsisawonderfulexampleofhowthemediaemphasizesthefew‘realcases’ofhysteriawithoutrecognizing that the vast majority of people knew that the radio program was fictional and didnothing.Youarelookingforananswerchoicethathassomethingtodowiththemediaoverplayingthehysteriaandnotacknowledgingthemajorityofpeoplewhodidnothing.
Choice(A):Thisdoesn’tmatchourprediction.Also,don’tbedeceivedbydeceptive language!Noticethat,inthetext,“realcases”isinquotationmarks.Thisindicatestheauthordoesn’tagreewiththephrase,soit’stheoppositeofwhatyou’relookingfor.
Choice(B):Doesn’tmatchtheprediction.
Choice(C):Thatalmostexactlymatchesthesecondpartoftheprediction,sohangontoit.
Choice(D):Doesn’tmatchtheprediction.Itwaspeoplewhodidn’tknowtheprogramwasfictional,notthemedia.
Thatleaves(C)asthecorrectanswer!
So,youcanseethatbyfollowingtheBasicApproach,you’llbeingoodshapetoansweramajorityoftheReadingquestions!You’lluseyourtimemoreefficiently,focusingonthepiecesofthetestthatwillgetyoupoints,andyouraccuracywillbemuchhigher.Thereareafewotherquestiontypeswhichwe’lllookatinthenextchapter.
Summary◦ TheReadingTestontheSATmakesup50percentofyourscoreontheEvidence-BasedReading
andWritingsection.
◦ Readingquestionsarenotpresentedinorderofdifficulty.Don’tbeafraidtoskipahardquestion,anddon’tworryifyoucan’tanswereveryquestion.
◦ UseyourPOODtopickupthepointsyoucanget,anddon’tforgetLOTDontherest!
◦ Readingisanopen-booktest!Usethattoyouradvantagebyfocusingonlyonthetextthatiskeytoansweringthequestions.
◦ Translate each question back into awho, what, orwhy question before you start reading yourwindow.
◦ Uselinereferences,leadwords,andchronologytohelpyoufindtheanswerinthepassage.Alwaysstart reading a few lines above the line referenceor the leadwords and readuntil youhave theanswer.
◦ Usethetexttopredictyouranswertothequestionbeforeyoulookattheanswerchoices.
◦ UsePOEtoeliminateanswersthatdon’tmatchyourprediction.
◦ Ifyouhavemorethanoneanswerleftafteryoueliminatetheonesthatdonotmatchyourprediction,comparetheremaininganswerchoicesanddecideifanyofthem
• aremostlyright/slightlywrong• couldbetrue• containdeceptivelanguage
Chapter4MoreQuestionTypesIn this chapter we’ll take a look at some other types of questions you will see on the Reading Test,including general questions, paired questions, and quantitative questions. For the most part, thesequestionswill follow theBasicApproach, but the general paired questions and quantitative questionswilllookalittledifferent.
MOREQUESTIONTYPESONTHEREADINGTESTInthischapter,we’ll lookatotherquestiontypesyou’llseeontheSATReadingTest, includingpairedquestions,main idea questions, general questions, questions featuring charts and graphs, and questionsbasedondualpassagesets.
Remember the“Windshield-PittingMystery”passagefromthelastchapter?We’llcontinuetouse it forthequestionsinthischaptertoo.
Questions11–21arebasedonthefollowingpassage.
ThispassageisadaptedfromLintonWeeks’s“TheWindshield-PittingMysteryof1954.”©2015byNPRHistoryDepartment.
PairedQuestionsYouwillnoticethatoneverypassagethereisatleastonesetofquestionsthatarepairedtogether.Thefirst question looks and sounds just like a regular question. It may ask about a detail, it may be aninferencequestion,oritmaybeamainideaquestion.Thesecondquestioninthepairwillalwaysask,“Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?”Therearetwotypesofpairedquestions:specificandgeneral.
SpecificPairedQuestionsThe specific pairedquestions are a fabulous two-for-onedeal. If you’re following all the steps of theBasicApproach,you’llfindwhenyougettothe“bestevidence”questionofaspecificpairedset,you’vealreadyansweredit.Thisisbecauseyou’vealreadyfoundthebestevidencewhenyoucarefullyreadyourwindowandunderlinedyourprediction.Let’stakealookataset.
16. Accordingtothepassage,whatpercentofcarsinWashingtonsuffereddamage?A) About20%B) Approximately10%C) Between5%and6%D) Lessthan1%
17. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines6–11(“Theepidemic’s…March”)B) Lines15–18(“InCanton…April17”)C) Lines44–48(“Thereare…cars”)D) Lines55–57(“Thecause…them”)
Startwiththefirstquestion.Thisquestionisverystraightforwardtoanswerbyitself.Allyouneedtodois find out what percent of the cars in Washington were damaged. Although there isn’t a given linereference,youcanstillskimthroughthetextlookingfortheleadwordsWashingtonandpercent.You’llfind these in the sixthparagraph, around lines 35–49.The text clearly states that less than1%of carssuffereddamage.Underlinethatlineandchoose(D)forquestion16.Then,becauseyoualreadyhavethe“bestevidence”underlined,whenyougettoquestion17,you’vealreadyansweredit.Justfindyourlinereferenceintheanswers,bubbleitin,andmoveon.
GeneralPairedSetsandParallelPOENotallsetsofpairedquestionswillbeaseasyasspecificpairedsets,butthey’llstillbeapproachable.Ifyouhaveaquestionthat isamainidea/generalquestionoraquestionwithoutaclear linereferenceorleadword,ParallelPOEisaveryusefulstrategy.
UsingParallelPOE,you’llbeabletoworkthroughthequestionsatthesametime!Whenyoufindyourselffacedwithasetofpairedquestions,youcanstartwiththesecondquestion(the“bestevidence”question)if(1)youaren’tsurewheretolookfortheansweror(2)thefirstquestionisageneralquestionaboutthepassage. Because the second question in the pair asks which lines provide the best evidence for thepreviousquestion,youcanuse those lines tohelpwork through theanswers for thepreviousquestion.Let’stakealook.
BestEvidenceNotsurewheretofind
theanswer?Letthe“bestevidence”lineshelp!
20. Basedonthepassage,theauthormostlikelyagreesthat“pitting”isA) acoincidencebasedongroupobservations.B) theresultofcosmicraysandnuclearfallout.C) anexampleofmasshysteriasimilartotheSalemWitchtrials.D) theresultofastreakofvandalisminthespringof1954.
21. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines12–14(“Panickedresidents…tests”)B) Lines30–32(“Assummer…shelters”)C) Lines60–64(“Theidea…guillotine”)D) Lines86–89(“Isuspect…it”)
Whenyoureadquestion20,youmighthaveaninitialfeelingof,“Well,thatcouldbefromanywhereinthe
passage.”Surecould.Nowyou’refacedwithwhatispotentiallytheworstscavengerhuntever.Insteadofwadingthroughtheentirepassage,though,andtryingtofindsomethingyouthinkanswersthequestionandthenhopeit’sincludedinthe“bestevidence”question,gotothe“bestevidence”first!ThisistheParallelPOEstrategy.
What’sgreataboutParallelPOEisthat,inthefirstinstance,theoriginalquestiondoesnotevenmatter.Thinkforamomentabouthowpairedquestionsoperate.Thecorrectanswertothefirstquestionmustbesupportedbyananswertotheevidencequestion,andthecorrectanswertotheevidencequestionmustsupportananswertothefirstquestion.Inotherwords,ifthereisanevidenceanswerthatdoesn’tsupportananswertothefirstquestion,itiswrong.Likewise,ifthereisananswertothefirstquestionthatisn’tsupportedbyanevidenceanswer,ittooiswrong.
Usethistoyouradvantage!Ratherthanworryaboutwhatthefirstquestionisaskingandwhattheanswermightbe, just startmakingconnectionsbetween the twoanswersets. Ifanevidenceanswersupportsafirst question answer, literally draw a line connecting them. You should not expect to have fourconnections.Ifyouarelucky,youwillhaveonlyoneconnection,andyouwillthereforehaveyouranswerpair.Otherwise,youmighthavetwoorthreeconnectionsandwillthen(andonlythen)worryaboutthefirstquestion.The important thing to remember is thatanyanswerchoice in thefirstquestion that isn’tphysicallyconnectedtoanevidenceanswer—andanyevidenceanswerthatisn’tconnectedtoananswerinthefirstquestion—mustbeeliminated.
Let’s take a look at how this first Parallel POE pass would look. (The paired questions have beenarrangedintwocolumnstohelpunderstandthis,andthelineshavebeenwrittenoutforyourconvenience.Thisdoesnotrepresentwhatyouwillseeontheofficialtest.)
Don’tworryaboutthequestionitselfyet.Gostraighttothe“bestevidence”lines.
• (21A)says“Panickedresidents”suspected“everythingfromcosmicraystosand-fleaeggstofalloutfromH-bombtests.”Readthroughallfouranswerchoicesforquestion20.Doyouseeanyanswersthatthoselinessupport?Notice(20B)prettymuchsaysthesamething?Drawalineconnecting(21A)with(20B).Nothingelsefromquestion20matcheswith(21A),solet’smoveonto(21B).
• (21B)saysAssummerrolledon,reportsofpittingdecreasedeverywhereandthecountrymovedontobuildingbackyardfalloutshelters.Lookingthroughtheanswersforquestion20,there’snothingthatissupportedbytheselines,sowecaneliminate(21B).Itdoesn’tmatterwhatthequestionasks;ifthere’snosupport,theanswercannotberight.
• (21C)says“TheideacamefromGustaveLeBon,aFrenchtheoristtryingtoexplainthestrangebehavioroflargegroupsduringtheFrenchRevolution,inwhichaveragecitizens
begankillinglargenumbersofpeopleviatheguillotine.”Aswith(21B),therearenoanswersinthefirstquestionthataresupportedbytheselines,so(21C)isgone.
• (21D)says“Isuspectthatmostpeoplealreadyhadthesepitsallalongandonlyattributedittothemysteriouscausewhentheyheardotherpeopledoingit”whichseemstoprettyclearlysupport(20A).Drawalinephysicallyconnecting(21D)with(20A).
Now,noticethat(C)and(D)inquestion20havenosupport?Regardlessofthequestionorwhatyoureadin the text, if the answers have no support from the “best evidence” question, they cannot be right.Eliminatethosetwo.
Yourquestionshouldlooksomethinglikethisatthispoint:
Nowyou’redowntoaverynice50/50split.Gobacktothequestion.Ofthetwopairs,whichonebestdescribespittinginawaytheauthorwouldmostlikelyagreewith?Theauthordefinitelydidnotbelieve
the pitting was caused by cosmic rays or nuclear fallout, so you can eliminate the (20B)/(21A) pair,leavingyouwiththecorrectanswerof(20A)/(21D).
On the actual test, itwouldbe too complicated todrawa full table, so all youneed todo is create acolumntotheleftofthe“bestevidence”choicesfortheanswerstothepreviousquestion.Itshouldlooksomethinglikethis:
Q20 21. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A A) Lines12–14(“Panickedresidents…tests”)B B) Lines30–32(“Assummer…shelters”)C C) Lines60–64(“Theidea…guillotine”)D D) Lines86–89(“Isuspect…it”)
ParallelPOESinceyoucan’tdrawafulltableontheactualexam,trymakingnotationsas
showninquestion21;thatis,createacolumntotheleftofthe“bestevidence”
answerchoiceslistingoutthechoicestothe
previousquestion.
MainIdea/GeneralQuestionsFormanyoftheReadingpassages,theveryfirstquestionwillaskageneralquestionaboutthepassage.Itmightaskaboutthemainideaorpurposeofthepassage,thenarrativepointofview,orashiftthatoccursthroughthepassage.RemembertheSelectaQuestionstep?Thosegeneralquestionsarenotgoodtodofirstbecauseyouhaven’treadthepassageyet,butonceyou’vedonemostoftheotherquestions,youhaveareallygoodideaoftheoverallthemesofthetext.
Let’stakealookatthefirstquestionfromthe“Windshield-PittingMystery”passage:
11. Thecentralclaimofthepassageisthat
Because this question asks about thecentralclaim of the passage, there’s no one place you can look.Generalquestionsdon’thavelinereferencesorleadwords,sothere’snowaytousethetexttopredictananswer. It’sokay, though:You’veansweredalmostallof thequestionsabout thepassage,soyouknowwhatthemainideaofthepassageis.Notonlythat,butyoualsohaveagoodsenseofwhatthetestwritersfoundmostinterestingaboutthepassage.Whilehavingthisknowledgedoesnotalwayshelp,itsurecansometimes.If thereareanswerchoices thathavenothingtodowitheither thequestionsor theanswers
you’ve seen repeatedly, you can probably eliminate them and instead choose the one that is consistentwiththosequestionsandanswers.
Let’stakealookattheanswerchoices:
A) windshieldpittingwasamajorsourceofconcernformostdriversin1954.B) windshieldpittingturnedouttobenothingbutaprank.C) widespreadfocusonaspecificeventcanmakerandomoccurrencesseem
significant.D) lackofconsensusforanevent’sexplanationcancausehysteria.
Remember:Ifit’sacentralclaim,it’samainpointofthetext.Whatcanyoueliminate?
Choice(A)mightlookgoodinitiallybecauseithasthewordswindshieldpitting,drivers,and1954,butthisisdefinitelynotacentralclaimofthepassage.
Choice(B)canbeeliminatedbecausetheonlymentionofaprankwasasapossibletheoryputforwardbysomeoneelse.
Choice(C)looksprettygood.You’vealreadyansweredseveralspecificquestionsdealingwiththisidea.
Choice (D)might look pretty good at first too.When you go back to the text, though, you see that theauthor’scentralclaimisnotaboutthelackofconsensuscausingthehysteria.That’sapartofit,butit’snotacompleteanswer.
Choice(C)isbestsupportedbythetextandalloftheotherquestionsyou’veanswered.
ChartsandGraphsTwopassagesontheReadingTestwillcontainoneortwoofwhattheCollegeBoardcallsinformationalgraphics,whicharecharts,tables,andgraphs.Thatmeansthattwoofthefourhistory/socialstudiesandscience passageswill be accompanied by one or two figures thatwill provide additional informationrelatedtothepassages.Thesepassageswillincludeafewquestionsthataskaboutthedatapresentedinthegraphics,eitheraloneorinrelationtotheinformationinthepassage.Thesefiguresmightseemlikethey’llrequiremorework,butthecharts,tables,andgraphsandthequestionsaboutthemarerelativelystraight-forward.Let’stakealookatanexample.
DatacollectedbyInsuranceInformationInstitute,http://www.iii.org/fact-statistic/auto-insurance.
Step1:Readthegraphic.Carefullylookatthetitle,axislabels,andlegend.Noticeonthisgraphwe’relookingatAverageExpenditures forAuto Insurance from2008–2012.Theyears are listed across thehorizontalaxis,andtheamount,indollars,islistedontheverticalaxis.Accordingtothelegend,wearecomparingtheentirecountrytoAlaska,NewYork,NorthCarolina,andRhodeIsland.
Step2:Readthequestion.
30. Accordingtothegraph,whichofthefollowingstatementsismostconsistentwiththedata?
Since the question asks youwhich is consistentwith the data, see if you can find specific reasons toeliminatethreeanswerthatareNOTconsistentwiththedata.AnotherpossibilityforChartsandGraphsquestionsistosimplyfindthedatapointthatanswersthequestion.
Step3:Readtheanswerchoices.
A) Autoinsuranceexpenditureshaveincreasedinallstatesfrom2008–2012.B) Ofallthestatesshownonthegraph,NewYorkhadthegreatesttotalincreaseinauto
insuranceexpenditures.C) Thestatesshownonthegraphallhaveautoinsuranceexpenditureshigherthanthe
UnitedStates’average.D) NorthCarolinadriversarebetterthanNewYorkdrivers.
Takeanotherlookatthegraph,thistimelookingforspecificreasonstokeeporeliminateanswers.
Basedonthedatashown,(B)isthecorrectanswer.
Nowyoutryone.
31. DatainthegraphindicatethatRhodeIsland’saverageexpenditureforautoinsurancewasclosesttothenationalaverageinwhichyear?A) 2009B) 2010C) 2011
D) 2012
Here’sHowtoCrackItThequestiononlyasksaboutRhodeIslandandthenationalaverage(whichindicatestheUnitedStatesline).Thatmeansyouonlyneedtoworryaboutthosetwolines.Findtheplacewherethosetwolinesaretheclosestandputyourpencilonit.NoticehowtheRhodeIslandlineisjustaboutparalleltotheUnitedStates line,exceptwhere itdipsdownbefore itgoesbackup?Thatdip iswhere the linesareclosesttogether,whichisin2009.Theansweris(A)!Asyoumayhavenoticed,therewasnoneedtoeliminatethe threewronganswerchoicesbecauseyouwereable tosimply find thedatapoint thatanswered thequestion.Sometimesitreallywillbethatsimple.Justmakesureyouhavetheinformationtosupportyouranswer.
DualPassagesOneofyourscienceorhistory/socialstudiespassageswillbeasetofdualpassages.Therewillbetwoshorterpassagesaboutonetopic.Althoughthetwopassageswillbeaboutthesametopic,therewillalsobe differences that you’ll need to pay attention to.Rather than attempting to read and understand bothpassagesatthesametime,justfollowtheBasicApproachandfocusononeatatime.
Thequestions forPassage1will comebefore the questions forPassage2, and the questions for eachpassage follow the order of the passage, just like single-passage questions. The questions about bothpassageswillfollowthequestionsforPassage2.
Two-PassageQuestionsForquestionsaskingtocompareorcontrastbothpassages,it’shelpfultoconsideronepassageatatimeratherthantryingtojugglebothpassagesatthesametime.First,findtheanswerforthefirstpassage(orthesecondpassageifthatoneiseasier)andusePOEtonarrowdowntheanswerchoices.ThenfindtheanswerintheotherpassageandusePOEtoarriveatthecorrectanswer.Thiswillsavetimeandkeepyoufromconfusingthetwopassageswhenyou’reevaluatingtheanswerchoices.AlwayskeepinmindthatthesamePOEcriteriaapply,nomatterhowtwo-passagequestionsarepresented.
• Ifaquestionisaboutwhatissupportedbybothpassages,makesurethatyoufindspecificsupportinbothpassages,andbewaryofalltheusualtrapanswers.
• Ifaquestionisaboutanissueonwhichtheauthorsofthetwopassagesdisagreeoronhowthepassagesrelatetooneanother,makesureyoufindsupportineachpassagefortheauthor’sparticularopinion.
• Ifthequestionaskshowoneauthorwouldrespondtotheotherpassage,findoutwhatwassaidinthatotherpassage,andthenfindoutexactlywhattheauthoryouareaskedaboutsaidonthatexacttopic.
Thebottom line is that if youareorganized and rememberyourbasic readingcomprehension strategy,you’llseethattwo-passagequestionsarenoharderthansingle-passagequestions!Inthefollowingdrill,you’llhaveachancetotryasetofdualpassages.Answersandexplanationscanbefoundattheendofthechapter.
Questions12–22arebasedonthefollowingpassages.
Passage1isadaptedfromLouisaTwining,“WorkhousesandWomen’sWork”©1857byTheNationalAssociationforthePromotionofSocialScience.Passage2isadaptedfromFlorenceNightingaleandWilliamRathbone,“WorkhouseNursing,theStoryofaSuccessfulExperiment”©1867byMacmillanandCo.
12. TheprimarypurposeofPassage1istoA) praiseaneffectivestructure.B) criticizeasocialgroup.C) examinethefinancesofasystem.D) advocateforanecessarychange.
13. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines13–16(“Efficientnurses…pay”)B) Lines16–19(“Oneof…it”)C) Lines22–27(“butin…week”)D) Lines28–32(“Seeinghow…law”)
14. Asusedinlines21,“maintained”mostnearlymeansA) providedfor.B) affirmed.C) healed.D) fixed.
15. Thephraseinlines34–35(“wecouldhardlyhope”)mostdirectlysuggeststhatA) anidealcandidateshouldbefoundforaposition.B) peoplewhogotohospitalsshouldbecriticalofnurses.C) allowancesshouldbemade,sincenopersonisperfect.D) animprovementisstilllikelytohavesomeflaws.
16. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines13–16(“Efficientnurses…pay”)B) Lines19–22(“Ofcourse…parish”)C) Lines29–32(“itwould…law”)D) Lines35–38(“fromwhat…plan”)
17. ThefinalsentenceofPassage1haswhicheffect?A) Itemphasizesthatthecurrentsituationisunpleasant.B) Itsharestheauthor’sdespairoverthecircumstances.C) Itcastsanentirelyoptimisticlightonaproposal.D) Itevokesthegenerallylowopinionheldforacertaingroup.
18. ItcanbemostdirectlyinferredfromthesecondparagraphofPassage2(lines46–56)thatthefirstyearoftheexperimentdescribedinthepassagewasunusualinA) havingweatherthatcausedanuncharacteristicamountofillness.B) theoverallnumberofpeoplewhorequiredmedicaltreatment.C) thateffectivemedicaltreatmentexceededstatisticalexpectations.D) thenumberofpeoplewhodiedfromdisease.
19. TheauthorofPassage2referencesa“carefulclassifiedlistofcases”(line64)inordertoA) specifywhatwillberequiredofallworkhousesinthefuture,iftheexperiment
continues.B) explainamissingelementthatwouldhaveensuredanoutcome.C) revealaninconsistencywhichmademoreaccurateanalysisimpossible.D) detailtheextenttowhichrecordscanbekeptoveralongperiod.
20. Asusedinline69,thephrase“characterofseasons”mostnearlymeansA) changesinmorality.B) weatherpatterns.C) theoverallhealthduringaperiod.D) theunpredictablenatureofhumanbehavior.
21. TheauthorofPassage1wouldmostlikelyrespondtothephraseinlines46–47(“Withtheexception…class”)ofPassage2byA) expressingsurpriseatanunexpectedresultthatisinconsistentwithprior
observations.B) acknowledgingthatanidealsituationmaynotbepracticaltoattain.C) notingthatinterventionearlierinlifemayhavechangedanoutcome.D) suggestingthatthedatamaynotbeentirelyrepresentative.
22. Whichchoicebestdescribestherelationshipbetweenthetwopassages?A) Passage2describesascenariothataddressessomeelementsofthesituationshown
inPassage1.B) Passage2discussespotentialresultsoftheoverallproblemreviewedinPassage1.C) Passage2underscoresthefutilityofattemptstoresolvetheconcernsofPassage1.D) Passage2resolvestheissuesbroughttolightinPassage1.
DUAL-PASSAGEDRILLANSWERSANDEXPLANATIONS12. D Becausethis isageneralquestionfollowedbya“bestevidence”question,ParallelPOElets
youusetheanswerchoicesforthenextquestiontohelpwiththisone.Remember:Youcanlookat the lines given in the “best evidence” question to see if they support any of these answerchoices.Noneof thechoices for thenextquestionseemtosupport (A), soyoucaneliminate(A).Choice(B)mightinitiallyseemtobesupportedby(B)fromthenextquestion,sokeepthatpair. Choice (C) might have a connection with (D) from the next question, as it mentionsmattersofexpense, sokeep thatpair aswell.Choice (D) is supportedby (C) from thenextquestion. Now consider your remaining pairs. The passage discusses the evils of theemploymentofpaupernurses,andthatinnocaseshouldtheybeleftwiththesolechargeandresponsibilityofsick [patients],as theycontinuallyareatpresent; thepassage isprimarilyconcernedwithdescribingasystemthatneedstobechanged.Thepassageisnotcriticizingasocial group or focusing specifically on financial matters. This leaves (D) as the correctanswer,automaticallymaking(C)thecorrectanswerforthe“bestevidence”question.
13. C Becausethisisa“bestevidence”questionfollowingageneralquestion,ParallelPOEletsyouusetheanswerchoicesforthisquestiontohelpwiththepreviousone.Remember:Youcanlookat the lines given in the “best evidence” question to see if they support any of the answerchoicesforthepreviousquestion.Choice(A)doesnotsupportanyoftheanswerchoicesfromthepreviousquestion,soyoucaneliminate(A).Choice(B)inthisquestionseemstosupport(B)inthepreviousquestion,sincethelinesrefertoawomanwho’sproudofbeinginjail,sokeep thatpair.Choice(C) in thisquestionsupports (D) in thepreviousquestion,as the linesshowaproblemthatclearlyneedstobechanged.Choice(D)inthisquestionseemstosupport(C) from thepreviousquestion, as itmentionsmattersofexpenseand finances of a system.Now you’re down to three pairs, so go back to the question,which asks about theprimarypurposeofthepassage.Thepassagediscussestheevilsoftheemploymentofpaupernurses,and that in no case should they be left with the sole charge and responsibility of sick[patients], as they continually are at present, the passage is primarily concerned withdescribingasystemthatneedstobechanged.Thepassagedoesnotcriticizeasocialgrouporfocusspecificallyonfinancialmatters.This leaves(D)as thecorrectanswer toquestion12,automaticallymaking(C)therightanswerforthis“bestevidence”question.
14. A Careful reading is necessary in order to dissect the context of the wordmaintained in thepassage.Thepassagedrawsacontrastbetweenpauperandefficient nurses.Those refers topaupernurses, since innocaseshould theybe leftwith thesolecharge…ofsick [people],which the passage indicates immediately after referring to the evils of the employment ofpaupernurses.Sinceapauperis“onewhoreliesoncharity,”paupernursescanbeinferredtorelyoncharity.Thus,sincethesepaupernursesmustbemaintainedatthecostoftheparish,maintainedcanbeinferredtomeanatleast“givenassistancewithbasicneeds.”Choice(A)iscorrect because it matches the predicted answer. Choice (B) is a secondary meaning ofmaintained,butitdoesnotmatchthepredictedanswer;eliminateit.Choice(C)istempting,asthe passage discussesnurses, but it’s still incorrect because it does notmatch the predictedanswer.Choice(D)alsodoesn’tmatchthepredictedanswer,soeliminate(D).
15. D Thephrasewe could hardly hope refers towhetherapaidnurse would beall [the author]coulddesireforsoimportantapost, indicatingthattheauthordoesnotbelieveapaidnursewoulddoaperfectjob.Theauthorcontinuestosaythatthereasonforthisjudgmentiswhatweknow of the paid nurses in hospitals, implying that paid nurses are known to have flaws.Finally,theauthorstatesthatatanyratetherewouldbeabetterchanceofaneffectivesystemwithapaidnurse.Thus,thecorrectanswershouldindicatethatwhileapaidnursewouldbeanimprovement,theauthorstillexpectstheretobeproblems.Choice(A)isincorrect,asidealistheoppositeofthepredictedanswer.Choice(B)isincorrectbecausetheauthordiscussespaidnursesinhospitalsinordertomakeapointaboutwhatcouldbeexpectedfromapaidnurseingeneral, not about hospitals themselves, and critical is too extreme.Choice (C) is incorrectbecauseitdoesnotmatchthatthereisevidenceofaproblemwithpaidnursesinhospitals,andthephrasewecouldhardlyhopedoesnot indicate thatallpeoplehaveflaws.Choice(D) iscorrectbecauseitmatchestheprediction.
16. D When youmade your prediction for the previous question, you should have underlined thatsucha personwouldbe…allwedesire…wecould hardly hope, fromwhatwe knowof thepaidnurses inhospitals…butbetter chanceof efficiencyandcharacter thanpresentplan.Therefore,(D)iscorrect.
17. A In the final sentence of Passage 1, the author acknowledges that a solution has flaws but isnonetheless a preferable solution. By using the phrasingwe could hardly hope, and at anyrate…better…than…thepresentplan,theauthorattemptstogainsympathyfortheperspectivethatthecurrentsituationissonegativethatevenaflawedsolutionisanimprovement.Choice(A)iscorrectbecauseitmatchestheprediction.Choice(B)isincorrectbecausetheauthorisprovidingapotentialsolution,whichdoesn’tmatchdespair.Choice(C)isalsoincorrect,sinceoptimisticistheoppositeofthepredictedanswer,andentirelyisextremelanguage.Choice(D)isincorrectbecausetheauthorisnottryingtocriticizeacertaingroup,butrathershowthattheoverallcircumstancesrequireevenaflawedsolution.
18. B ThesecondparagraphofPassage2indicatesthattheseasonwasveryunhealthy,whichmeansthat more people than usual became sick during a particular period. Eliminate (A), as theweatherisnotsupportedasthecauseofsickness.Choice(B)matchestheprediction,sokeepit.Eliminate(C)becausethepassageindicatesthatitwasimpossible…tojudgetheresultbystatistics. Choice (D) may be true, but it is still incorrect because the third paragraph ofPassage 2 implies only that theproportionof deathsmay have been unusually high, not thenumberofpeoplewhorequiredmedicaltreatment.Choice(B)istheanswer.
19. C TheauthorofPassage2statesthatItwasimpossible…tojudgetheresultbystatistics,andthatevenhadtherebeennoexceptionaldisturbingelement,thereisadefectinthestatisticsofworkhousehospitals.Thus,theauthorindicatesthattherewereotherreasonsstatisticalresultscould not be drawn, but that even without those other reasons, workhouse hospitals lack acarefulclassifiedlistofcases,whichwouldbenecessaryforstatisticalanalysis.Choices(A)and(D)areincorrectbecausetheydonotmatchtheprediction.Choice(B)isalsoincorrect;thepassagestates that therewereseveralreasons for thelackofevidenceofsuccessor failure,andtheseason[being]veryunhealthymaystillhavemadeanalysisimpossible.Choice(C)iscorrect:Whiletheauthorstatesthattherewereotherreasonsthattheresultscouldnotbejudged
bystatistics,adefectinthestatistics…affectsallinferencesfromthem.
20. C Passage2referstoaseasonasveryunhealthyaspartofthereasonthatstatisticscouldn’tbejudgedaccurately.ThereferencetothecharacterofseasonsinthethirdparagraphofPassage2serves a similar purpose by listing reasons that statistical judgments are difficult tomake ingeneral.When comparedwith the earlier reference to an unhealthy season, the character ofseasons refers most clearly to the health of the population during a certain period of time.Eliminate(A)and(B),whichdonotmatchtheprediction.Choice(D)isincorrectbecausethepredictedanswerreferstothehealthofpeople,nottheirbehavior;eliminate(D).Choice(C)matchesthepredictionandisthecorrectanswer.
21. B Thephrasewiththeexceptionof thefailureof thenursestakenfromthepauperclassverybrieflyindicatesthatthepaupernursesincludedintheexperimentmadeinPassage2werenotsuccessful. The author of Passage 1 states that it is desirable, if possible, to employ [thepaupernurses],andthattheonlyway…[such]employment…couldbe[successful]…wouldbeundertheconstantsupervisionortrainednurses.Thequalifyingphrase,ifpossible, indicatesthattheauthorofPassage2wouldpreferthatthepaupernursesbeinvolvedinanewsystembutisnotcertainthiswouldbepossible.Choice(A)isincorrectbecausetheauthorofPassage1indicatedpriorobservations,whichwere negative toward the pauper nurses. Choice (B) iscorrectbecauseitmatchestheprediction.Choice(C)isincorrect;whileitcouldbetrue,itisnotdirectlysupportedbytheinformationinPassage1.Choice(D)isincorrectbecauseitisnotsupportedbyPassage1andreliesontheunrelatedsurroundinginformationinPassage2.
22. A Passage1describesanoverallproblem,andPassage2describesaspecificattempt tosolvetheproblem.Choice(A)iscorrectbecauseitmatchestheprediction.Choice(B)isincorrectbecause it does notmatch the prediction, and (C) is wrong because futility is too extreme.Choice(D)canbeeliminatedbecauseresolvesisextremeaswell.
Summary◦ Forpairedquestions,makesureyou’refollowingtherightstrategy.
• Specific paired questions simply require you to follow the Basic Approach, making sureyou’veunderlinedtheevidenceforyourpredictioninthetext.
• General paired questions will be much more straightforward if you use Parallel POE toconsiderthe“bestevidence”intandemwiththepreviousquestion.
◦ For dual passages, doquestions about the first passage first, questions about the secondpassagesecond,anddualquestionslast.Rememberthatevenwithdualquestions,youmustfindsupportinthepassages.
◦ Savemainideaorgeneralquestionsuntiltheendofthepassage.POEwillbemuchmoreefficientonceyou’vedonealloftheotherquestions.
◦ Don’tgetboggeddownbyhardortime-consumingquestions!Ifyoufindyourselfstuckorrunningshortontime,useLOTDandmoveon.
Chapter5ReadingDrillsUseyournewreadingcomprehensionand test-takingskillson these twoReadingdrills,whichcontainpassages on science and literature topics. Then, check your responses against the answers andexplanationsprovidedattheendofthechapter.
Questions1–10arebasedonthefollowingpassage.
ThispassageisadaptedfromCharlesAnderson,“ConflictMineralsfromtheDemocraticRepublicoftheCongo—TinProcessingPlants,aCriticalPartoftheTinSupplyChain.”©2015byU.S.GeologicalSurvey.
A) expensive.B) practical.C) complicated.D) synthetic.
2. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines14–18(“Crushed…tin”)B) Lines38–40(“Electrolytic…tin”)C) Lines58–61(“Becausetin…storage”)D) Lines65–66(“Thetin…opaque”)
3. TheoverallstructureofthepassagecouldbestbedescribedasA) acompleteanalysisofanaturallyoccurringelement.B) anoverviewofthestepsandresultsofaprocess.C) anintroductionwrittenforageologycourse.D) anexplanationofthesolutiontoaproblem.
4. ThemostlikelyapplicationoftinproducedbymeansofelectrolyticprocessingwouldbeA) platingforcommonlyproducedcannedgoods,tobewidelydistributed.B) miniaturefigurinesdesignedtobepaintedanddisplayed.C) smallamountsofmaterialintendedforscientificanalysis.D) soldersoldworldwideaspartofacampaigntomarketlead-freeproducts.
5. Betweenthefirstandsecondparagraphs,thefocusshiftsfromA) meticulousattentiontodetailtobroad,assumptivegeneralizations.B) scientificanalysisofthepropertiesandusesofamaterialtoindustrialprocesses.C) detaileddescriptionofaseriesofstepstoimplementationofaresult.D) overviewofaspecificcycletoitsroleintheminingindustry.
6. WhatcanmostreasonablybeinferredabouttheSafeDrinkingWaterActfromthepassage?A) Itspecifiedthenatureandpercentageofthecomponentsofsolder.B) Itmayhaveimpactedwhatelementsacompanychosetouseinmakingsolder.C) Itpromotedtinoverleadforallapplications.D) Itpromptedshiftsinthemanufactureanddistributionofcannedgoods.
7. TheauthorindicatesthatthedemandfortininpartexistsbecauseA) tincanbefoundinnature.B) tinofnearly100%puritycanbeproduced.C) tinisthebestconductorofelectricity.D) oftin’simpactonanindividual’shealth.
8. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–2(“Tinis…cassiterite”)B) Lines38–40(“Electrolytic…tin”)C) Lines42–44(“Solder…connection”)D) Lines58–61(“Becausetin…storage”)
9. Asusedinline66,“opaque”mostnearlymeansA) dark.B) wide.C) impenetrableD) dense.
10. Thesentenceinlines79–81(“Companieschanged…business”)primarilyservestoA) indicateacontinuationofanexistingchain.B) describethemanyusesforaproduct.C) showthesoledifficultyinansweringaquestion.D) supportanearlierstatementthroughanexample.
Questions1–11arebasedonthefollowingpassage.
Thispassageisanexcerptfromthe1854bookWaldenbyHenryDavidThoreau,whichdetailsThoreau’sexperienceslivinginacabinalonefortwoyears.
1. ThemainnarrativepointofviewofthepassageisofA) amanadjustingtolifeinabigcityaftergrowinguponafarm.B) adiscussionofvisitorstoasmallhouseawayfromcitylife.C) asailordiscussingthepondonwhichhegrewupandhowitaffectedhis
friendships.D) amandiscussingthepotentialofbigthoughtsandtheirneedtobeexpressed.
2. Thepassagesuggestedwhichofthefollowingabouttheauthor?A) Heenjoyedlivinginthecountrynearapond.B) Hehadmorevisitorstohishomeinthecountrythanatanyothertimeinhislife.C) Hefeltthathavingmorethanthreepeopleinhishousewastoomany.D) Heneededtothrowdinnerpartiestoenticegueststocomefromtowntohishome.
3. Whichchoiceprovidesthebestevidencefortheanswertothepreviousanswer?A) Lines7–11(“Ihadthree…forthemall”)B) Lines33–35(“Ihavefound…oppositeside”)C) Lines72–73(“Youneed…yougive”)D) Lines75–76(“Ihadmore…inmylife”)
4. Asusedinline11,“economized”mostnearlymeansA) wasted.B) usedefficiently.C) squandered.D) purchased.
5. Itcanbeinferredfromthepassagethat“bigthoughts”(line21)mustA) becomeviolentbeforesettlingdown.B) bouncearoundandbreakoutofone’shead.C) bemulledoverandformulatedbeforebeingheard.D) havetimetomovearoundbeforebeingheard.
6. Inthecontextofthepassage,thephrase“aswhenyouthrowtwostonesintocalmwatersonearthattheybreakeachother’sundulations”(lines37–39)isbestdescribedasA) areferencetotheauthor’schildhooddayswhenhethrewstonesintoalake.B) ananalogyusedtoelaborateonapreviousstatement.C) awaytoexpandonthereasonsnationalboundariesarealwayschanging.D) areasonthattheauthorandhiscompanionhadtocontinuallymovetheirchairstobe
heard.
7. Asusedinline27,“plow”mostnearlymeansA) push.B) furrow.C) cultivate.D) walk.
8. Whathappenswhentheauthordoesnothaveenoughfoodforhisguests?A) Heshares.B) Heturnsthemaway.C) Hebuysmorefood.D) Theyrefrainfromeating.
9. ThepassagesuggeststhathousekeepersmostlikelyA) arestuckintheirwaysandunabletochange.B) feelthattraditionsshouldnotchange.C) believethereisacertainprotocolthatmustbefollowedwhenhostingguests.
D) feelthatpuddingandbreadarenotasuitablemeal.
10. Whatdoestheauthormeanwhenhesaidthat“onlythefinestsedimentwasdeposited”(lines84–85)onhim?A) Hewaslivingfarfromtownandhisvisitorswereofahighercaliber.B) Hewascoveredinafinedustwhilelivinginthewoods.C) Thepondnearhishomefrequentlyflooded,leavingsedimentinhis“best”room.D) Manypeoplecametoseehimaboutthedirtybusinessoftrivialmatters.
11. Whatchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines48–50(“apriceless…order”)B) Lines70–72(“thoughmany…old”)C) Lines75–77(“Ihadmore…some”)D) Line79(“Butfewer…business”)
CHAPTERDRILLANSWERSANDEXPLANATIONS
ReadingDrill11. B Becausethis isageneralquestionfollowedbya“bestevidence”question,ParallelPOElets
youusetheanswerchoicesforthenextquestiontohelpwiththisone.Remembertolookatthelinesgiveninthe“bestevidence”questionandseeiftheysupportanyoftheseanswerchoices.Choice(A)initiallylookslikeitcouldbesupportedby(B)fromthenextquestion,sokeepthatpairaswell.Choice(B)inthisquestionissupportedby(C)inthenextquestion,sokeepthatpair. Neither (C) nor (D) in this question has support in the “best evidence” question, soeliminate those two.Whenyouconsideryour remainingpairsof choicesmorecarefully,yousee that the author refers to the process of electrolytic processing as expensive, not the tinitself.Therefore,youcaneliminate(A),whichalsoeliminates(B)fromthenextquestion.Theanswerhereis(B).
2. C Becausethisisa“bestevidence”questionfollowingageneralquestion,ParallelPOEletsyouusetheanswerchoicesforthisquestiontohelpwiththepreviousone.Remembertolookatthelinesgiveninthe“bestevidence”questiontoseeiftheysupportanyoftheseanswerchoices.Choice (A)doesnot support anyof the answer choices in thepreviousquestion, soyoucaneliminate(A).Choice(B)initiallylookslikeitcouldsupport(A)inthepreviousquestion,sokeep that pair. Choice (C) supports (B) in the previous question, so keep that pair aswell.Choice(D)doesnotsupportanyoftheanswerstothepreviousquestion,soyoucaneliminate(D).Whenyouconsideryourremainingpairsofchoicesmorecarefully,youseethattheauthorreferstotheprocessofelectrolyticprocessingasexpensive,not the tin itself.Therefore,youcaneliminate(B),whichalsoeliminates(A)fromthepreviousquestion.Choice(C)iscorrect.
3. B Thepassagediscussesthenatureoftin,theproceduresofminingfortin,theusesoftin,andthesupplychainof tin.While thenatureof tin isdiscussedinextremedetail, thesupplychain isdescribed as complex, and the passage provides only a broad overview of some of theobstaclesindeterminingtheexactchain.Thus,thepassagereviewsseveralelementsoftininvaryingdegreesofdetail.Choice(A)isincorrectbecausetheanalysisof thesupplychainisnotcomplete.Choice (B)matches thepredictionand is thereforecorrect.Choice (C) isalsoincorrect:While the passage could be used for a geology course, it does not provide anyinformationtodescribethepassage.Choice(D)canbeeliminatedbecauseitdoesnotmatchtheprediction.
4. C According to the passage, electrolytic processing is more expensive, but produces up to99.9999percenttin,which indicates that tinproduced in this fashionwouldbe lesscommon(since it is more expensive), and appeals most to those who required a purer form of tin.Choice(A)isincorrectbecausecommonlyproduceditemsdonotmatchthepredictedanswer.Choice (B)canbeeliminatedbecause there isno indication that the figurineswouldbenefitfromapurerformoftin.Choice(C)iscorrectbecauseitmatchesboththesmallquantityandthe appeal of a purer formof tin.Choice (D) is incorrect; an item soldworldwide does notmatchthepredictedanswer.
5. C Thefirstparagraphdiscusseshowtinisfoundinnature,mined,andprocessedintoanindustrialform. The second paragraph discusses the uses of tin. Choice (A) is incorrect becauseassumptive generalizations do not match the specific numbers provided in the secondparagraph.Choice(B)canbeeliminatedbecauseindustrialprocesseswouldbeabetterfitforthediscussioninthefirstparagraphaboutrefiningtin;thesecondparagraphmainlydetailstheusesfortin.Choice(C)maybevague,butitmatchesthepredictionandisthereforethecorrectanswer.Choice(D)isincorrectbecauseitdoesnotmatchtheprediction.
6. B ThepassagestatesthatSolderhasbeenmadefromleadandtin,butsincetheSafeDrinkingWaterAct, tinhasbecome theprimarymetal insolder.Thissuggests that theSafeDrinkingWater Act may have caused the change from solder being made with both lead and tin toprimarily tin.Choice (A) is incorrect because specified is extreme. Similarly, eliminate (C)because all applications is too extreme. Choice (D) does notmatch the prediction, so it isincorrect.Choice(B)isthecorrectanswer,asitmatchestheprediction.
7. D Accordingtothepassage,Becausetinisnotharmfultohumans,it isapreferredmethodofcanning and preserving food. Choices (A) and (B) can be eliminated because they do notmatchthepredictedanswer.Choice(C)istempting,asthepassageindicatesademandfortininsolder, but the best is extreme and unsupported by the passage. Choice (D) is the correctanswerbecausetheimpactonanindividual’shealthcanbenotharmful.
8. D Basedon thepreviousquestion, tinhasahighdemandbecause it isnotharmful tohumans.Choices (A), (B), and (C) are incorrect because they do not match the previous answer’sprediction.Only(D)matchesthepredictedanswer.
9. C According to the passage, companies…may not describe which of their plants use whichstartingmaterials,plants…mayormaynotconsumeand(or)produceallofthetinmaterialsreported, and companies that were reported to have been tin suppliers could not beconfirmedassuch,amongotherdescriptionsofwhat results inanextremelydifficult—ifnotimpossible—trailtofollow.Therefore,aphrasetouseinplaceofopaqueis“verydifficulttounderstand.”Choices(A),(B),and(D)areincorrectbecausetheydonotmatchtheprediction.Only(C)matchesthepredictedanswer,asimpenetrablecanmean“inaccessibletoknowledge”orsomethingthatcan’tbeknown.
10. D Thefinalparagraphdiscussesthecomplexnatureofthetinsupplychainandlistsanumberofreasons why the tin supply chain is difficult—if not impossible—to follow. The sentencecompanieschangednames,werereferredtoimprecisely,changedownership,orwentoutofbusiness provides another example to support the idea that the tin supply chain is complex.Choices(A)and(B)donotmatchthepredictionandarethereforeincorrect.Choice(C)maybetempting, but sole is too extreme; eliminate (C). Choice (D) matches the predicted answerbecausetheearlierstatementisthatthetinsupplychainiscomplex.Theansweris(D).
ReadingDrill21. B Themainnarrativepointofviewinthispassageisfromamanwhoislivinginahousenexttoa
pond(Ihavefounditasingularluxurytotalkacrossthepond),whichisnearthewoods(the
pinewoodbehindmyhouse).Choice (A) is incorrectbecause thenarrator isnot in thecity.Choice(C)isincorrectbecausethereisnoevidencethattheauthorwasasailor.Choice(D)isalso incorrect:Although the author does discuss thoughts in the third paragraph, it is not themainsubjectofthepassage.Therefore,(B)isthecorrectanswer.
2. B Becausethisisageneralpairedquestion,youcanusetheanswerchoicesinthenextquestiontohelpwiththisquestion.Remember,thecorrectanswerforquestion3mustsupportthecorrectanswerforthisquestion.Usethechoicesfromquestion3toseewhichoftheseanswerchoicesyoucankeeporeliminate.Choice(A)inquestion3mightinitiallyseemtosupport(C)forthisquestion, soconnect those twoanswer choices.Choice (B) inquestion3canconnect to (A)here, sodraw that line.Choice (C) inquestion3doesnot support anyof thechoices in thisquestion, so you can eliminate (C). Choice (D) in question 3 supports (B) in this question.Because thisquestion’s (D)hadno support fromquestion3, youcan eliminate (D).Nowgoback and reread the question to make further POE decisions. The 2(A)-3(B) set does notaddresstheauthor’senjoymentoflivingnearthepond,soeliminateit.The2(C)-3(A)pairdoesnot answer the question, so eliminate that one aswell. The remaining set of 2(B) and 3(D)answersthequestion,sothoseareyourcorrectanswers.
3. D When solving general paired questions, match the line references to the answer choicesavailableinthepreviousquestion.Inthiscase,thereareseveralpossiblematches.Choice(A)inthisquestionseemstorelateto(C)inquestion2,butonfurtherinspection,thislinereferencedoes not support this choice in a way that answers the previous question, so it can beeliminated.Choice(B)seemstorelatetoquestion2’s(A),butitdoesnotaddresstheauthor’senjoymentoflivingnearthepond,soeliminateit.Choice(C)referstothefoodthattheauthorprepares but does not support the reference in question 2’s (D) and is therefore incorrect.Choice(D)doessupportquestion2’s(B)andisthecorrectanswer.
4. B Theauthornotesthatiftherearemorethanthreepeopleintheroom,theyeconomizedthespacebystanding,showingthattheyweremakingthemostoftheroomavailablebyusingamethodthat allowsmore people to exist in the same amount of space.He further notes, I have hadtwenty-fiveorthirtysouls,withtheirbodies,atonceundermyroof,andyetweoftenpartedwithoutbeingawarethatwehadcomeveryneartooneanother.Thisagainshowsthatthereweremanypeopleinasmallspace.Choices(A),(C),and(D)donotmatchthepredictionandcanbeeliminated,making(B)correct.
5. D Theauthorsaysthatbigthoughtsmusthaveroomtomovearoundbeforebeingheard.Hesaysthatheenjoystalkingacrossthepondbecausethereisenoughroomforthoughts tobeheard.Thereisnoevidenceinthepassagethatthebigthoughtsneedtobeviolent,soeliminate(A).Eliminate (B) because the author does not state that big thoughts need to break out of thereceiver’shead,onlythattheycouldiftheyarenotgivenenoughtimetodevelop.Choice(C)isincorrectbecauseitisnotsupportedbythetext;theauthorisnotliterallysayingthatthoughtsneedmoretimetoreachthehearer.Choice(D)matchesthetextmostcloselyandisthecorrectanswer.
6. B Thephrase in thequestion isused toprovideacommonexperiencebywhich theauthorcangivemoredetailtohisexplanationofwhathappenswhenspeakinginsidehishouse.Wordsdo
notliterallybumpintooneanother.Theauthorhasmadenoreferencetohischildhoodinthispassage,soeliminate(A).Whilenationalboundariesarementionedinthisparagraph,theyarejust another analogy by which the author is describing his experience; therefore, (C) isincorrect.Thereasonthattheauthormoveshischairisduetotheconversation,nottheanalogybywhichtheauthoristryingtobringclaritytohisideas;thus,(D)isincorrect.Choice(B)mostcloselymatchesthepredictionfromthetext,soitiscorrect.
7. A Theauthornotes that the ideasneed tobouncearoundandsettle,or theywillplow andpushtheirwayoutof the listener’shead.Choice (A) is thecorrectanswerbecause itmatches thepredictionfromthetext;theotheranswerchoicesdonot.
8. D Theauthorstatesthatwhenmorethanafewguestsarepresent,theytreateatingasaforsakenhabitandpracticeabstinence.Choice(A)isincorrectbecausetheauthorshareshisfoodonlywhenthereisenoughtofeedeachguestadequately.Choice(B)isincorrectbecausethereisnomention of the author ever turning away a guest, and (C) is incorrect because there is nomentionoftheauthorpurchasingfoodinthispassage.Choice(D)bestmatchesthepredictionfromthetextandisthereforethecorrectanswer.
9. B Thepassagementionsthattheauthorwasunabletofeedlargegroupsofvisitorstohishome,and that insuchcasesallguests, including theauthor, refrained fromeating.Hementions theeasebywhichhehasestablishedanewcustom.Healsostatesthathousekeepersmaydoubttheeasebywhichthesocialconventionwaschanged.Thispredictionmostcloselymatches(B),soit is the correct answer.Choice (A) is incorrect because the authormakesno such statementabout housekeepers. Choice (C) is incorrect because the author does not state that thehousekeepers have a certain way in which to serve guests, only that they would doubtestablishing new and better customs in place of the old. Choice (D) is incorrect becausealthoughtheauthorispreparingpuddingandbreadforaguest,thereisnomentionofwhatthehousekeeperswouldthinkofthemeal.
10. A Theauthormentionsthatbecausehishousewaslocatedfarfromthetown,hehadfewervisitorscoming to discuss trivial matters; therefore, (D) is incorrect. The sentence that discussessedimentisfigurative,soanyliteralreferencetodirtordustcanbeeliminated:getridof(B)and(C).Choice(A)bestmatchestheinformationinthelastparagraphofthepassage,inwhichtheauthoraddressesthenumberofvisitorshehasreceivedandhowfewerguestscametoseehimabouttrivialbusiness.Therefore,(A)isthecorrectanswer.
11. D Remember,withspecificpairedquestions,aslongasyouusethetexttosupportyouranswerfor thefirstquestion,youhaveanactual two-for-onedeal.Youused thereferenceBut fewercame to seemeon trivial business, to answer question 10, so you know the answer to thisquestionis(D)!Done.
PartIIIHowtoCracktheWritingandLanguageTest6 IntroductiontoWritingandLanguageStrategy7 Punctuation8 Words9 Questions
Chapter6IntroductiontoWritingandLanguageStrategyTheWritingandLanguageTestconsistsof44multiple-choicequestionsthatyou’llhave35minutestocomplete.Thequestionsaredesignedtotestyourknowledgeofgrammaticalandstylistictopics.Inthischapter, we’ll introduce you to the format of Writing and Language Test, the types of questions andpassagesyou’llencounter,andtheoverallstrategiesyouneedtoacethissection.
CANYOUREALLYTESTWRITINGONAMULTIPLE-CHOICEEXAM?Wewouldsayno,butETSandtheCollegeBoardseemtothinktheanswerisyes.Tothatend,youwillhave 35 minutes to answer 44 multiple-choice questions that ask about a variety of grammatical andstylistictopics.Ifyouliketoreadand/orwrite,theSATmayfrustrateyouabitbecauseitmayseemtoboilwritingdown toacoupleofdull rules.Butasyouwill see,wewilluse thenext fewchapters tosuggestamethodthatkeepsthingssimpleforpro-andantigrammariansalike.
WHEREDIDALLOFTHEQUESTIONSGO?OnethingthatcanseemalittlestrangeabouttheWritingandLanguageTestisthatmostofthequestionsarenottechnically,well,questions.Instead,mostofthequestionslooksomethinglikethis:
Thehistoryof 1 languagealthoughitmaysoundlikeaboringsubject,isatreasuretroveofhistorical,cultural,andpsychologicalinsights.
1.A) NOCHANGEB) language,althoughitmaysoundlikeaboringsubjectC) language,althoughitmaysound,likeaboringsubject,D) language,althoughitmaysoundlikeaboringsubject,
Howareyousupposedtochooseananswerwhenthere’snoquestion?
Well,actually,whatyou’llfindthroughoutthischapterandthenexttwochaptersisthatyou’regivenalotofinformationinthislistofanswerchoices.
Lookatthesepairs,andyou’llseejustwhatwemean.Asyoureadthroughthesepairsofanswerchoices,thinkaboutwhateachquestionisprobablytesting.
i. A) couldofB) couldhave
ii. A) tall,dark,andhandsomeB) tall,darkandhandsome
iii. A) lettheminB) letSisterSusieandBrotherJohnin
iv. A) WearrivedinParisonaSunday.Thenwetookthe train toNantes.ThenwetookthetraintoBordeaux.
B) WearrivedinParisonaSunday.ThenwetookthetraintoBordeaux.ThenwetookthetraintoNantes.
Ifyouwereabletoseethedifferencesintheseanswerchoices,you’realreadymorethanhalfwaythere.Now,noticehowthedifferences in theseanswerscanreveal thequestion that is lurkingin theheartofeachlistofanswerchoices.
i. Thedifferencebetweentheword“of”and“have”meansthatthisquestionisasking,Isthecorrectform“couldof”or“couldhave”?
ii. Thedifferencebetweenhavingacommaaftertheword“dark”andnothavingonetheremeansthatthisquestionisasking,Howmanycommasdoesthissentenceneed,andwheredotheybelong?
iii. Thedifferencebetween“them”and“SisterandSusieandBrotherJohn”meansthatthisquestionisasking,Is“them”adequatelyspecific,ordoyouneedtorefertopeoplebyname?
iv. Thedifferencebetweentheorderofthesesentencesasks,Whatordershouldthesentencesbein?
Therefore, what we have noticed in these pairs of answer choices is something that may seem fairlysimplebutwhichisessentialtosuccessontheSAT.
THEANSWERCHOICESASKTHEQUESTIONSAtsomepointinEnglishclass,you’vealmostcertainlyhadtodoanexercisecalled“peerediting.”Inthisexercise,youare taskedwith“editing” theworkofoneofyour fellowstudents.But thiscanbe reallytough,becausewhatexactlydoes itmean to“edit”anentireessayorpaperwhenyouaren’tgivenanydirections?It’sespeciallytoughwhenyoustartgettingintothesubtletiesofwritingandlanguage,namely,whetherapieceofgrammarisdefinitelywrongorcouldmerelybeimproved.
Forexample,lookatthesetwosentences:
Itwasabeautifuldayoutsidebirdsweresingingcheerfulsongs.
Itwasabeautifuldayoutside;birdsweresingingcheerfulsongs.
You’dhave topick the secondone in thiscasebecause the firsthasagrammaticalerror: it’sa run-onsentence.Orforthenon-grammariansoutthere,youhavetobreakthatthingup.
Now,lookatthesenexttwosentences:
Theweatherwasjustright,soIdecidedtoplaysoccer.
JustrightwashowIwoulddescribetheweather,soadecisionofsoccer-playingwasmadebyme.
Inthiscase,thefirstsentenceisobviouslybetterthanthesecond,butthesecondtechnicallydoesn’thaveanygrammaticalerrorsinit.Thefirstmaybebetter,butthesecondisn’texactlywrong.
Whatmadeeachofthesepairsofsentencesrelativelyeasytodealwith,though,isthefactthatyoucouldcomparethesentencestooneanother.Indoingso,younotedthedifferencesbetweenthosesentences,and
youpickedthebetteransweraccordingly.
Let’sseehowthislooksinarealSATsituation.
Languageisaliving 2 documentshowshowpeoplethinkandcommunicate.
2.A) NOCHANGEB) documentitshowsC) documentthatshowsD) document,whichshowing
Here’sHowtoCrackItFirst,lookatwhat’schangingintheanswerchoices.Theworddocumentremainsthesameineach,butwhatcomesafteritchangeseachtime.Thisquestion,then,seemstobeasking,Whichwordswillbestlinkthetwoideasinthesentence?
Choices (A) and (D) make the sentence incomplete, so eliminate them. Choice (B) creates a run-onsentence,so thatshouldalsobeeliminated. It looks likeonly(C)appropriately links the ideaswithoutaddingnewerrors.
Notice that the entire process startedwith asking, “What’s changing in the answer choices?”With thatquestion,wefiguredoutwhatwasbeingtested,andweusedPOEtodotherest.
Let’stryanother.
Acommunity’sverysoul,wemightsay,iscommunicatedthrough 3 theirlanguage.
3.A) NOCHANGEB) they’relanguage.C) theirlanguages.D) itslanguage.
Here’sHowtoCrackIt
Asalways,startbyfiguringoutwhatischangingintheanswerchoices.Itlookslikethemainchangeisbetween the words their, they’re, and its, with a minor change between the words language andlanguages.Assuch, thisquestionseems tobeasking,What is theappropriatepronoun touse in thiscontext,andjusthowmany“languages”arewetalkingabout?
Startwhereveriseasiest.Inthiscase,itcanbealittlebitdifficulttosayforsurewhetherthesentenceistalkingaboutonelanguageoraboutabunchoflanguages.Instead,workwiththepronoun.Whatdoesitreferbackto?Inthissentence,itseemsthatthepronounrefersbacktoacommunity,whichisasingularnoun(eventhoughitdescribesalotofpeople).Therefore,theonlypossibleanswerthatcouldworkis(D),whichcontainsthesingularpronounits.
Noticehowit is irrelevantas towhether thequestionis talkingaboutonelanguageormanylanguages.Sometimesfixingoneproblemwillmakeothersirrelevant!
LEARNFROMTHEANSWERCHOICESLet’sthinkaboutthepreviousquestionabitmore.IfsomeonesaidtoyouAcommunity’sverysoul,wemightsay,iscommunicatedthroughtheirlanguage,youmightnotnecessarilyhearthataswrong.That’sbecausethewaywespeakisoftenverydifferentfromthewaywewrite.OntheSAT,however,thetestwritersaremoreconcernedwithhowwewriteandthestrictersetofrulesthatgoalongwithwriting.
Therefore,theanswerchoicesnotonlyindicatewhataparticularquestionistesting,butcanalsorevealmistakesthatyoumightnothaveotherwiseseen(intheoriginalsentence)orheard(inyourhead).Inthepreviousquestion,forexample,wemightnothavenotedthemistakeatall ifwehadn’t lookedatwhatwaschangingintheanswerchoices.
Tryanotherexample.
4 Forallintensivepurposes,anysocial,cultural,orhistoricalstudymuststartwithananalysisoflanguage.
4.A) NOCHANGEB) Forallintentsandpurposes,C) Forallintent’sandpurpose’s,D) Forallintensivepurpose’s,
Here’sHowtoCrackItAsalways,startbycheckingwhat’schangingintheanswerchoices.Inthiscase,thisstepisespecially
importantbecauseyoucan’treallyheartheerror.Peoplemisusethisidiomallthetimebecausetheysorarelyseeitwritten,andallfouroftheanswerchoicessoundbasicallythesame.So,forthisquestion,checkingtheanswerchoicesrevealsanerrorthatyoumightnothaveotherwiseseen.
NowusePOE.There’snogoodreasontohaveapostrophesanywhere(thereareneithercontractionsnorpossessions),soeliminate(C)and(D).Then,ifyou’restillnotsure,takeaguess.Thecorrectformoftheidiomis(B).
Noticethat lookingat theanswerchoicesrevealedtheproblemthatyoumightnothaveotherwisebeenabletoseeorhear.POEtookyoutherestoftheway.
POEDOESTHEBIGWORKOnceyouhaveasenseofwhatthequestionistesting,POEcangetyoucloserandclosertotheanswer.POEisespeciallyhelpfulwhenyou’redealingwithsentencesthathavelotsofissues,likethisone:
Itmayseemthathowpeoplespeakisdistinctfromhow 5 theyareacting;however,there’ssomethingthatmosthistorianswilltellyouiswrong.
5.A) NOCHANGEB) theyact,however,there’ssomethingC) theyareacting,however,that’ssomethingD) theyact;however,that’ssomething
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.Here,therearethreethingschanging:actandareacting,that’s and there’s, and a comma versus a semicolon. This is a lot of differences, which means thisquestionisahugePOEopportunity!Startwiththedifferenceyoufindeasiestandworkbackwardfromthere.
Becausethesemicolonisnotcommonlyused,savethepunctuationpartforlast.Youmaybeabletogettherightanswerwithouthavingtodealwiththepunctuationatall.Startwiththedifferencebetweenthat’sandthere’s.Thesentencedoesnotmentionaplace,sothesentencecan’tcontainthere’s,eliminating(A)and(B).Now,choosebetweenthelasttwo:theyactismoreconciseandmoreconsistentwiththerestofthesentencethantheyareacting,whichmakes(D)betterthan(C).Inthisinstance,youfoundthecorrectanswerwithouthavingtodealwithallthemessinessinthequestion!
ALLOFTHEQUESTIONSCAN’TBEWRONGALLOFTHETIMENowthatyouknowthestrategy,tryamoredifficultquestion.
6 Yourknowledgeofgrammarandvocabularymaybeshaky,butyoucanlearnalotfromsomebasictenetsoflinguistics.
6.A) NOCHANGEB) You’reknowledgeofgrammarorvocabularymightbeshaky,C) Yourknowledgeofgrammarandvocabularymightbeshakily,D) You’reknowledgeofgrammarandvocabularymightbeshaky,
Here’sHowtoCrackItAs always, check the answer choices first. In this case, here’s what’s changing: The answers areswitchingbetweenyourandyou’re,andandor,andshakyandshakily.Dotheeasypartsfirst!
Firstofall, there’sno reason to insert thewordshakilyhere.Youcan’t say that someonehas“shakilyknowledge”ofsomething,soeliminate(C).Then,theknowledgebelongstoyou,soitisyourknowledge,notyouareknowledge,thuseliminating(B)and(D).Thisleavesonly(A).
Remember,NOCHANGE is right sometimes! If you’ve done the other steps in the process and haveeliminatedalloftheotherchoices,goaheadandpick(A)!
HOWTOACETHEWRITINGANDLANGUAGETEST:ASTRATEGYHere’sastep-by-stepbreakdownoftheprocesswe’vebeenfollowing:
Step1: Checkwhat’schangingintheanswerchoices.Step2: Figureoutwhatthequestionistestingandletthedifferencesintheanswerchoicesreveal
potentialerrors.
Step3: UseProcessofElimination.Step4: Ifyoucan’teliminatethreeanswerchoices,picktheshortestonethatismostconsistent
withtherestofthesentence.
ThenextfewchapterswillcoversomeofthemoretechnicalissuesrelatedtotheWritingandLanguageTest,but this strategywillbeused throughout.Try thedrill on thenextpage toget someof thebasicsdown.
WritingandLanguageDrill1The purpose of this drill is to get a basic idea ofwhat each question is testing fromonly the answerchoices.Checkyouranswersonthispage.
1.A) NOCHANGEB) babies’favoritebottlesC) baby’sfavoritebottle’sD) babies’favoritebottles’
What’schangingintheanswerchoices?
Whatisthisquestiontesting?
2.A) NOCHANGEB) didC) doesD) havedone
What’schangingintheanswerchoices?
Whatisthisquestiontesting?
3.A) NOCHANGEB) AlthoughC) WhileD) Because
What’schangingintheanswerchoices?
Whatisthisquestiontesting?
4.A) NOCHANGEB) wasnotablefortheir
C) werenotableforitsD) werenotablefortheir
What’schangingintheanswerchoices?
Whatisthisquestiontesting?
5.A) NOCHANGEB) beautiful,asinsuperpretty.C) beautiful,likeeasyontheeyes.D) beautiful.
What’schangingintheanswerchoices?
Whatisthisquestiontesting?
WRITINGANDLANGUAGEDRILL1ANSWERKEY1. Apostrophes;apostrophesandwheretheygo2. Verbs;verbtenseandnumber3. Words;transitionwords(direction)4. Was/wereandtheir/its;verbnumberandpronounnumber5. Numberofwords;conciseness
Summary◦ TheWritingandLanguageTestontheSATis35minuteslongandcontains44questions.
◦ ThequestionsontheWritingandLanguageTestarenotintraditionalquestionform.Instead,you’llbepresentedwithaseriesofpassageswithdifferentportionsof itunderlined,andyour jobis todeterminewhethertheunderlinedportioniscorrectorifitshouldbereplacedwithoneofthegivenchoices.
◦ Thefirststepisalwaystodeterminewhat’schangingintheanswerchoices.Theynotonlytellyouwhat a particular question is testing, but also revealmistakes that youmight not have otherwiseseen.
◦ UsePOEtogetridofincorrectanswersandnarrowdownyouroptions.Ifyoucan’teliminatethreechoices,picktheshortestonethatismostconsistentwiththerestofthesentence.
Chapter7PunctuationPunctuationisthefocusofmanyquestionsontheWritingandLanguageTest.Buthowdoyouknowwhento use the punctuationmarks that are being tested? This chapterwill answer that question aswell ashighlightsomeoftheSAT’srulesforusingpunctuationandthestrategiesyoucanusetooutsmartthetestwriters.
WAIT,THESATWANTSMETOKNOWHOWTOUSEASEMICOLON?KurtVonnegutoncewrote,“Hereisalessonincreativewriting.Firstrule:Donotusesemicolons…Allthey do is show you’ve been to college.”Unfortunately, this does not apply to the SAT. For the SAT,you’llneedtoknowhowtousethesemicolonandafewothertypesofweirdpunctuation.Thischaptercoversavarietyofpunctuationyouneed toknowhow touseon theWritingandLanguageTest.Learnthesefewsimplerules,andyou’llbeallsetonthepunctuationquestions.
Firstandforemost,sticktothestrategy!
Startbyasking,“What’schangingintheanswerchoices?”
If you see punctuation marks—commas, periods, apostrophes, semicolons, colons—changing, then thequestionistestingpunctuation.Asyouworktheproblem,makesuretoaskthebigquestion:
Doesthispunctuationneedtobehere?
Theparticularpunctuationmarkyouareusing,nomatterwhatitis,musthaveaspecificrolewithinthesentence.Youwouldn’tuseaquestionmarkwithoutaquestion,wouldyou?Nope!Well,allpunctuationworksthatway,andinthischapterwe’llgiveyouexamplesofspecificinstancesinwhichyouwoulduseaparticulartypeofpunctuation.Otherwise,letthewordsdotheirthingunobstructed!
STOP,GO,ANDTHEVERTICALLINETESTLet’s get theweirdonesout of theway first.Everyoneknows that a period ends a sentence, but oncethingsgetmorecomplicated,evenaparticularlynerdygrammariancangetlost.Becauseofthisconfusion,we’vecreatedachartthatsummarizesthedifferentsituationsinwhichyoumightusewhattheSATcalls“end-of-sentence”and“middle-of-sentence”punctuation.WecallthemSTOP,HALF-STOP,andGO.
Whenyouarelinkingideas,youmustuseoneofthefollowing:
STOP• Period• Semicolon• Comma+FANBOYS
• Questionmark• ExclamationMark
HALF-STOP• Colon• Longdash
GO• Comma• Nopunctuation
FANBOYSstandsforFor,And,Nor,But,Or,Yet,
andSo.
STOPpunctuationcanlinkonlycompleteideas.
HALF-STOPpunctuationmustbeprecededbyacompleteidea.
GOpunctuationcanlinkanythingexcepttwocompleteideas.
Let’sseehowthesework.Hereisacompleteidea:
SamanthastudiedfortheSAT.
Noticethatwe’vealreadyusedoneformofSTOPpunctuationattheendofthissentence:aperiod.
Now,ifwewanttoaddasecondcompleteidea,we’llkeeptheperiod.
SamanthastudiedfortheSAT.Sheendedupdoingreallywellonthetest.
Inthiscase,theperiodislinkingthesetwocompleteideas.ButthenicethingaboutSTOPpunctuationisthatyoucanreallyuseanyofthepunctuationinthelisttodothesamething,sowecouldalsosaythis:
SamanthastudiedfortheSAT;sheendedupdoingreallywellonthetest.
What the listofSTOPpunctuationshowsus is thatessentially, aperiodanda semicolonare the samething.WecouldsaythesamefortheuseofacommaplusoneoftheFANBOYS.
SamanthastudiedfortheSAT,andsheendedupdoingreallywellonthetest.
YoucanalsouseHALF-STOPpunctuationtoseparatetwocompleteideas,soyoucouldsay
SamanthastudiedfortheSAT:sheendedupdoingreallywellonthetest.
or
SamanthastudiedfortheSAT—sheendedupdoingreallywellonthetest.
There’s a subtle difference, however, between STOP and HALF-STOP punctuation: For STOPpunctuation,bothideashavetobecomplete,butforHALF-STOPpunctuation,onlythefirstonedoes.
Let’sseewhat this lookslike.Ifyouwant tolinkacompleteideaandanincompleteidea,youcanuseHALF-STOPpunctuationaslongasthecompleteideacomesfirst.Forexample,
SamanthastudiedfortheSAT:allthreesectionsofit.
or
SamanthastudiedfortheSAT:thesilliesttestinalltheland.
WhenyouuseHALF-STOPpunctuation,therehastobeacompleteideabeforethepunctuation.So,theseexampleswouldn’tbecorrect:
Samanthastudiedfor:theSAT,theACT,andeveryAPtestinbetween.
TheSAT—Samanthastudiedforitandwasgladshedid.
Whenyouarenotlinkingtwocompleteideas,youcanuseGOpunctuation.Soyoucouldsay,forinstance,
SamanthastudiedfortheSAT,theACT,andeveryAPtestinbetween.
or
SamanthastudiedfortheSAT,allthreesectionsofit.
Thesearethethreetypesofmid-sentenceorend-of-sentencepunctuation:STOP,HALF-STOP,andGO.You’llnoticethatthereisabitofoverlapbetweentheconcepts,buttheSATcouldn’tpossiblymakeyougetintotheminutiaofchoosingbetween,say,aperiodandasemicolon.Allyouneedtobeabletodoisfigureoutwhichofthebigthreecategories(STOP,HALF-STOP,andGO)you’llneed.
Let’sseewhatthislookslikeincontext.
Jonahstudiedeverydayforthebig 1 testhewastakingtheSATthatSaturday.
1.A) NOCHANGEB) test,hewastakingC) test,hewastaking,
D) test;hewastaking
Here’sHowtoCrackItAs always, check what’s changing in the answer choices. In this case, the only thing changing is thepunctuation;thewordsstaythesame.Noticethetypesofpunctuationthatarechanging:STOPandGO.
Now,whenyouseeSTOPpunctuationchangingintheanswerchoices,youcandoalittlesomethingweliketocalltheVerticalLineTest.
Drawalinewhereyouseethepunctuationchanging—inthiscase,betweenthewordstestandhe.Then,readuptotheverticalline:Jonahstudiedeverydayforthebigtest.That’scomplete.Now,readaftertheverticalline:hewastakingtheSATthatSaturday.That’salsocomplete.
So,think;you’vegottwocompleteideashere.Whatkindofpunctuationdoyouneed?STOPorHALF-STOP.ItlookslikeSTOPistheonlyoneavailable,sochoose(D).
Let’stryanother.
Itwasveryimportantforhimtodo 2 well.Highscoresinallthesubjects.
2.A) NOCHANGEB) well;highC) well:highD) well,hewantedhigh
Here’sHowtoCrackItChecktheanswerchoices.What’schanging?It looks like thepunctuation ischanging,andsomeof thatpunctuation is STOP.Use theVertical Line Test.Draw a vertical linewhere you see the punctuation:betweenwellandhighorwellandhe.
What’sbeforetheverticalline?Itwasveryimportantforhimtodowelliscomplete.Then,highscoresinallthesubjectsisnot.Therefore,becauseyouhaveonecompleteidea(thefirst)andoneincompleteidea(thesecond),youcan’tuseSTOPpunctuation,thuseliminating(A)and(B).
Now,what’sdifferentbetween the last two?Choice (C) containsHALF-STOPpunctuation,whichcanwork,sokeepthat.Choice(D)addssomewords,withwhichthesecondideabecomeshewantedhighscoresinallthesubjects,whichiscomplete.Thatmakestwocompleteideasseparatedbyacomma,butwhatdoyouneedwhenseparating twocomplete ideas?STOPpunctuation!Eliminate (D)!Only(C) is
left.
Let’sseeonemore.
WheneverJonahhadafree 3 moment—hewasstudying.
3.A) NOCHANGEB) moment;heC) moment,he,D) moment,he
Here’sHowtoCrackItThepunctuationischangingintheanswerchoices,andthere’ssomeSTOPpunctuation,sousetheVerticalLineTest.Putthelinebetweenmomentandhe.Thefirst idea,WheneverJonahhadafreemoment, isincomplete,and thesecond idea,hewasstudying, iscomplete.Therefore,youcan’tuseSTOP(whichneeds twocomplete ideas)orHALF-STOP(whichneedsacomplete ideabefore thepunctuation), thuseliminating (A)and (B).Then,because there isnogood reason toputacommaafter thewordhe, thecorrectanswermustbe(D).
ASLIGHTPAUSEFORCOMMASCommascanbealittletricky.Inquestion3,wenarroweditdowntotwoanswerchoices,(C)and(D),afterhavingcompletedtheVerticalLineTest.Butthenhowdoyoudecidewhethertokeepacommainornot? It seems a little arbitrary to say that you use a comma “every time youwant to pause,” so let’sreversethatandmakeitalittlemoreconcrete.
Ifyoucan’tciteareasontouseacomma,don’tuseone.
OntheSAT,thereareonlyfourreasonstouseacomma:• inSTOPpunctuation,withoneoftheFANBOYS• inGOpunctuation,toseparateincompleteideasfromotherideas• inalistofthreeormorethings• inasentencecontainingunnecessaryinformation
We’vealreadyseenexamplesofthefirsttwoscenarios,solet’slookattheothertwo.
Trythisone.
Histop-choiceschoolswere 4 Harvard,YaleandPrinceton.
4.A) NOCHANGEB) Harvard,Yale,andPrinceton.C) Harvard,Yale,and,Princeton.D) HarvardYaleandPrinceton.
Here’sHowtoCrackItFirst, checkwhat’s changing in the answer choices. It looks like the commas in this list are changing.Becausethere’snotanyobviousSTOPorHALF-STOPpunctuation,theVerticalLineTestwon’tdomuchgood.
IthelpstoknowherethattheruleontheSATistoplaceacommaaftereveryiteminaseries.Thinkofitthisway.There’sapotentialmisunderstandinginthissentence:
Iwenttotheparkwithmyparents,mycatVioletandmydogStuart.
Withoutacomma,itsuresoundslikethisguyhassomeinterestingparents.Ifthere’snocomma,howdoweknowthatthissentenceisn’tsupposedtosayhisparentsaremycatVioletandmydogStuart?Theonlywaytoremovetheambiguityistoaddacommalikethis:
Iwenttotheparkwithmyparents,mycatViolet,andmydogStuart.
Keepthatinmindasyoutrytocrackquestion4.Here,Harvard,Yale,andPrincetonformalist,sotheyshouldbesetoffbycommas,astheyarein(B).
Let’stryanother.
5 Jonah,everyoneseemedfairlycertain,wasgoingtogetintooneofthoseschools.
5.
A) NOCHANGEB) JonaheveryoneseemedfairlycertainC) Jonah,everyoneseemedfairlycertainD) Jonaheveryoneseemedfairlycertain,
Here’sHowtoCrackItFirst, check what’s changing in the answer choices: just the commas. And those commas seem to becircling around the words everyone seemed fairly certain. When you’ve got a few commas circlingaroundaword,phrase,orclause like this, thequestion isusually testingnecessaryversusunnecessaryinformation.
Agoodwaytotestwhethertheideaisnecessarytothemeaningofthesentenceistotakeitout.Readtheoriginalsentenceagain.Nowreadthisone:Jonahwasgoingtogetintooneofthoseschools.
Is the sentence still complete?Yes.Has themeaningof the sentencechanged?No,we just lost a littleextrathing.Therefore,theideaisunnecessarytothemeaningofthesentenceandshouldbesetoffwithcommas,asitisin(A).
Let’stryafewmore.Trytofigureoutwhetherthewordorideainitalicsisnecessarytothemeaningofthesentence,andwhetherornotcommasneedtosurroundtheitalics.Theanswersareonthispage.
1. ThestudentwiththebestGPAwillbeadmittedtothebestcollege.2. EdwardwantstogotoPomonaCollegewhichisareallygoodschool.3. Thecarthatwaspaintedreddroveoffatahundredmilesanhour.4. CharlesChesnuttwhowrotealotofgreatstorieswasalsoalawyer.5. PhiladelphiaFlyersgoalieSteveMasonisanunderappreciatedplayer.
Nowlet’sputitalltogetherinthisquestion.
Everyone 6 hoped,hewouldgetin,afterhisbrotherandtwosistershadgonetotheirfirst-choiceschools.
6.A) NOCHANGEB) hoped,hewouldgetin,afterhisbrother,andtwosistershadC) hoped,hewouldgetinafterhisbrother,and,twosistershadD) hopedhewouldgetinafterhisbrotherandtwosistershad
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.Therearevaryingnumbersofcommasinvaryingplaces.Remember,theruleofthumbwithcommasisthatifyoucan’tciteareasontouseacomma,don’tuseone.
Itlookslikehewouldgetinisbeingsetoffbycommas.Determinewhetherit’snecessaryorunnecessaryinformation. Read the original sentence, and then read the sentence again without that piece ofinformation:Everyonehopedafterhisbrotherandtwosistershadgonetotheirfirst-choiceschools.Itlookslikethesentencehaschangedinmeaningandisnotreallycompleteanymore.Therefore,thatbitofinformation isnecessary to themeaningof thesentence,so itdoesn’tneedcommas.Therearenogoodreasonstoputcommasaroundorinthephraseafterhisbrotherandtwosisters.
In the end, there aren’t reasons to put commas anywhere in this sentence. The correct answer is (D).SometimesSATwill test“unnecessarypunctuation”explicitly,somakesureyouhaveagoodreasontousecommaswhenyouusethem!
YOURGOINGTOBETESTEDONAPOSTROPHE’S(ANDINTERNETSPELLINGISATERRIBLEGUIDE!)Likecommas,apostropheshaveonlyaverylimitedsetofapplications.Apostrophesarealittletrickier,though,becauseyoucan’treallyheartheminspeech,sopeoplemisusethemallthetime.Thinkabouttheheaderofthissection.Theapostrophesarewrongthere.Here’sthecorrectwayofpunctuatingit:You’regoingtobetestedonapostrophes.Canyouhearthedifference?Neithercanwe.
Therefore,aswithcommas,ifyoucan’tciteareasontouseanapostrophe,don’tuseone.ThereareonlytworeasonstouseanapostropheontheSAT:
• Possessivenouns(NOTpronouns)• Contractions
Let’sseesomeexamples.
Someofthosevery 7 selectiveschools’requirereallyhighscore’s.
7.A) NOCHANGEB) selectiveschool’srequirereallyhighscores’.C) selectiveschoolsrequirereallyhighscore’s.
D) selectiveschoolsrequirereallyhighscores.
Here’sHowtoCrackItCheckwhat’s changing in the answer choices. In this case, thewords are all staying the same,but theapostrophesarechanging.Remember,don’tuseapostrophesatallifyoucan’tciteagoodreasontodoso.
Doesanythingbelongtoschoolsorscore?No!Aretheyformingcontractionslikeschoolisorscoreis?No! Therefore, there’s no reason to use apostrophes, and the only possible answer is (D), whichdispenseswiththeapostrophesaltogether.
Asinthepreviousquestion,there’snoneedforanypunctuation,andinaquestionlikethis,you’rebeingtestedonwhetheryoucanspotunnecessarypunctuation.
Butsometimestheapostropheswillbenecessary.Lookatthefollowingexample.
8 It’stoughtogetintoyou’retop-choiceschools.
8.A) NOCHANGEB) ItstoughtogetintoyourC) Itstoughtogetintoyou’reD) It’stoughtogetintoyour
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.Themainchangeinvolvesapostrophes,particularlyonthewordsits/it’sandyour/you’re.
Thefirstword,its/it’s,needsanapostrophe:Itcreatesthecontractionitis.Therefore,because thisoneneeds an apostrophe, get rid of (B) and (C).As for theother, thisword is possessive (as in, the top-choiceschoolsbelonging toyou),but remember,possessivenounsneedanapostrophe,butpossessivepronounsdon’t.Therefore,becauseyouisapronoun,thiswordshouldbespelledyour,asitisin(D).
Phew!Theseapostrophescangetalittletricky,solet’stryafewmore.Onthese(asonmanypartsoftheSAT),you’llfindthatusingyourearandsoundingthingsoutdoesn’treallyhelpallthatmuch.
Highlight the option thatworks.Thebig question is, apostrophes or no apostrophes?You can find the
answersonthispage.
1. Tinas/Tina’sbosssaidshes/she’sallowedtotakethenextfewdays/day’soff.2. Ifyour/you’renotcomingtomyparty,its/it’sreallyfinewithme.3. There/they’rearereallynogoodreasons/reason’sforyour/you’rebadattitude.4. Well/we’llgetbacktoyouassoonasyour/you’reapplicationisreceived.5. Its/it’shis/his’guacamole,andhesaidwecant/can’thaveanybecauseits/it’snotours/our’s.
CONCLUSIONWe’venowcovered all of thepunctuationyouwill ever need toknowon theSAT. It’s reallynot thatmuch, and you probably knew a lot of it already. In general, checkingwhat’s changing in the answerchoicescanhelprevealmistakesthatyoumaynothavenoticedotherwise,andPOEcanhelpyounarrowdownyouroptions.
Punctuationrulesareeasytolearn,asisthebiggestruleofallaboutpunctuation.
Knowwhyyouareusingpunctuation,whetherthatpunctuationisSTOP,HALF-STOP,GO,commas,orapostrophes.Ifyoucan’tcitereasonstousethesepunctuationmarks,don’tusethem!
Tryouttheseskillsonthedrillonthenextpage.
AnswerstoQuestionsonthispage:
1. NECESSARYtothemeaningofthesentence(nocommas).Ifyouremovetheitalicizedpart,thesentenceisnotadequatelyspecific.
2. UNNECESSARYtothemeaningofthesentence(commas).Ifyouremovetheitalicizedpart,thesentenceisstillcompleteanddoesnotchangemeaning.
3. NECESSARYtothemeaningofthesentence(nocommas).Ifyouremovetheitalicizedpart,thesentenceisnotadequatelyspecific.
4. UNNECESSARYtothemeaningofthesentence(commas).Ifyouremovetheitalicizedpart,thesentenceisstillcompleteanddoesnotchangemeaning.
5. NECESSARYtothemeaningofthesentence(nocommas).Ifyouremovetheitalicizedpart,thesentenceisnolongercomplete.
AnswerstoQuestionsonthispage:
1. Tina’s,she’s,days2. you’re,it’s3. There,reasons,your4. We’ll,your5. It’s,his,can’t,it’s,ours
WritingandLanguageDrill2Usewhatyou’velearnedinthischapterinthedrillquestionsthatfollow.Answerscanbefoundonthispage.Time:7–8minutes
Moreandmoreofourlivesaremechanized,andatsomepoint,wehavetostartwondering,what’sthelimitofthatmechanization?Manyfactoryworkersinthe19thcenturythoughttheirjobs 1 weresafebutweknownowthattheywerewrong.Manypeople 2 intoday’sworldbelievetherejobsaresafe,buthowsafearethosejobsreally?
Studiesaboundthataskwhethermanormachineisbetteratparticulartasks,andtheresultsarenotalwayssoobvious.Sure,amachineisobviously 3 betteratsay,weldinghugepiecesofsteeltogether,butwhatwouldyousayifsomeonetoldyoupeoplearemorelikelytoopenuptoamachinethantoapsychologist?Orthatamachinecouldwriteaquicker,moreefficientnewsstorythananexperiencedreportercould?
1.A) NOCHANGEB) weresafe,butweknowC) weresafe;butweknowD) weresafe.Butweknow
2.A) NOCHANGEB) intodaysworldbelievetheirjobsC) intodaysworldbelievethey’rejobsD) intoday’sworldbelievetheirjobs
3.A) NOCHANGEB) betterat,sayweldingC) betterat,say,weldingD) betteratsaywelding
Thesequestionsmayseemoverlypessimistic(oroverlyoptimisticdependingon 4 yourpointofview);however,somerecentstudieshavebeentrulyremarkable.TakeEllie,a
computerprogramusedprimarilytodiagnosepatientswith 5 depression,PTSDandothermooddisorders.Manypatientsfounditeasiertotalkto“Ellie”than 6 toarealperson:shedidn’treactinsomeofthoseseeminglyjudgmentalwaysthatapersonwould,andhervoice 7neverbrokeontopofthatshecouldhelppsychologiststodiagnosementalillnessesbetterthanhumanobservationcould.Shecoulddetectfacialmovementsorvoicetonesthatapersonmighthavenotheardorignored.
4.A) NOCHANGEB) yourpointofview),however,C) you’repointofview),however,D) you’repointofview);however,
5.A) NOCHANGEB) depression,PTSD,andotherC) depression,PTSD,and,otherD) depression,PTSD,andother,
6.A) NOCHANGEB) toarealperson,sheC) toarealperson;butsheD) toarealpersonshe
7.A) NOCHANGEB) neverbroke,ontopofthat,C) neverbroke.Ontopofthat,D) neverbroke;ontop,ofthat,
WhetherEllieisthewayofthefutureisyettobedetermined.Wecan’tknowrightnow,butthereisnoquestionthatsheraisessomeinterestingquestions,notonlyabout 8 theworkofpsychologists’,butalsoaboutallofwhatwethinkaredefinitivelyhumanactivities.
Ontheothersideofthediscussion,however,there’ssomeevidencethathumansmayhavetheupperhand.Insomeofthemorebasic 9 tasksthoselearnedbeforetheageofabout10humanshaveahugeupperhand.Computerscandothecomplexthinking,butonethingwith
whichtheyhavealotoftroubleis,paradoxically,simplicity.Sure,acomputer 10 cantellyourwasher’sanddryer’swhataperfectwashinganddryingcycleis,butcanitfoldyourlaundry?YourGPScantellyouthefastestroutetothenextstate,butcanittellyoutheprettiestwaytogoorthebestrestaurantsalongtheway?Notwithouthumans!
8.A) NOCHANGEB) psychologistsworkC) theworkofpsychologistsD) theworkofpsychologist’s
9.A) NOCHANGEB) tasksthoselearnedbeforetheageofabout10,humansC) tasks,thoselearnedbeforetheageofabout10humansD) tasks,thoselearnedbeforetheageofabout10,humans
10.A) NOCHANGEB) cantellyourwasheranddryerwhatC) cantellyou’rewashersanddryersD) cantellyou’rewasheranddryer
Whilethebattleofmanagainstmachinerages 11 on.Thequestionswillpersist.Nomatterwhowins,though,humanswillalmostassuredlyfindwaystoadapt:that’ssomethingwe’vebeendoingforthousandsofyears,whichissomethingthatnocomputercansay.
11.A) NOCHANGEB) on;theC) on—theD) on,the
WRITINGANDLANGUAGEDRILL2:ANSWERSANDEXPLANATIONS1. B Thefirstchangeintheanswerchoicesis thepunctuationafter thewordsafe.The ideaMany
factoryworkersinthe19thcenturythoughttheirjobsweresafeisacompleteidea.Theideathatfollows,weknownowthattheywerewrong,isalsoacompleteidea.Twocompleteideasmust be separated by STOP punctuation.Choice (A) uses no punctuation between the ideas;eliminate (A). Choices (C) and (D) use STOP punctuation followed by the conjunction but,which makes the second part of the sentence an incomplete idea. Choice (B) uses thecombinationofacommaandtheconjunctionbut,whichtogetherfunctionasSTOPpunctuation;itisthecorrectanswer.
2. D Thefirstchangeintheanswerchoicesistheremovaloftheapostropheinthewordtoday’s,sothequestionistestingpossession.Todeterminewhetherthewordispossessiveandrequiresanapostrophe,considerthewordthatfollows,world.Becausethepassagediscussestheworldoftoday,today’sispossessive,andtheformwiththeapostropheiscorrect.Eliminate(B)and(C).Thenextdecisiontobemadeisbetweenthereandtheir.Becausethewordreferstothejobsbelonging to the people, the possessive pronoun their is consistent with themeaning of thesentence.Therefore,(D)isthecorrectanswer.
3. C Noticethattheplacementofcommasischangingintheanswerchoices.Thisindicatesthatthequestion is testing comma rules. In the sentence, theword say has ameaning similar to “forexample.”Thismakesthewordsayunnecessaryinformation.Tomakethecommasconsistentwiththismeaning,commasbeforeandafterthewordarenecessary.Choice(C)iscorrect.
4. A The first change in the answer choices is between your and you’re. Your is a possessivepronoun,whileyou’re is a contraction for theyouare.The sentence requires thepossessiveformoftheword,notthecontraction.Eliminate(C)and(D).Thenextchangeisthepunctuationafter the close of the parentheses. Since parentheses indicate unnecessary information, youshouldcheckthepunctuationbyreadingthesentencewithouttheparentheticalinformation.ThephrasesThesequestionsmayseemoverlypessimisticandHowever,somerecentstudieshavebeen trulyremarkable arebothcomplete ideas.STOPpunctuation isnecessary, soeliminate(B).Choice(A)isthecorrectanswer.
5. B Noticethattheplacementofcommasischangingintheanswerchoices.Therefore,thisquestionistestingcommarules.Theunderlinedportionispartofalist.Theruleforcommauseinalististohaveacommaaftereveryiteminthelist.Theitemsinthelistherearedepression,PTSD,andothermooddisorders.Therefore,acommaisneededafterdepressionandafterPTSD,butnotafterotherorand.Thecorrectansweris(B).
6. A Thefirstchangeintheanswerchoicesisthepunctuationafterperson.Theideaprecedingthepunctuation is complete, and the idea that follows is also complete. The answer must havepunctuationthatisconsistentwithtwocompleteideas.Choice(D)hasnopunctuation;eliminate(D).Acommawithoutoneof theFANBOYSisnotSTOPpunctuation;eliminate(B).Choice
(C)usesSTOPpunctuationfollowedbytheconjunctionbut,whichmakesthesecondpartofthesentenceanincompleteidea.Eliminate(C).Choice(A)isthecorrectanswer.
7. C Notice the punctuation changing in the answer choices. The idea ending with broke is acomplete idea.Theidea thatfollows,beginningwithontopofthat, isalsoacomplete idea.LookforanswerchoiceswithSTOPpunctuation.Choice(A)hasnopunctuation;eliminate(A).Choice(B)hasacomma,butacommawithoutoneof theFANBOYSisnotable toseparatecomplete ideas;eliminate (B).Choice (C)hasaperiod,and (D)hasa semicolon,whicharebothacceptableformsofpunctuationforseparatingcompleteideas.However,(D)includesanunnecessarycommaaftertop,soeliminate(D).Thecorrectansweris(C).
8. C Notice the wording and the use of an apostrophe changing in the answer choices, whichindicatesthatthequestionistestingpossession.Whenusingthephrasetheworkof,possessionisalreadyaccountedfor,andanapostropheisnotneededinpsychologists.Eliminate(A)and(D).When using the phrase psychologists work, the apostrophe is necessary; eliminate (B).Choice(C)isthecorrectanswer.
9. D Noticetheplacementofcommaschangingintheanswerchoices;thisquestionistestingcommarules. The commas in the answer choices are placed after the word tasks and/or after thenumber10.Thephrasethoselearnedbeforetheageofabout10 isunnecessary information.Theanswerchoiceconsistentwithunnecessaryinformationmusthavecommasbeforeandafterthephrase.Therefore,(D)isthecorrectanswer.
10. B Thefirstchangein theanswerchoices isbetweenyourandyou’re, so thequestion is testingpossession. Your is a possessive pronoun, while you’re is a contraction for you are. Thepossessiveformisconsistentwiththemeaningofthesentence.Eliminate(C)and(D).Choice(A)includesapostrophesonthewordswashersanddryers,whichimpliespossession.Thisisnotconsistentwiththemeaningofthesentence.Eliminate(A).Choice(B)iscorrect.
11. D Notice the punctuation changing in the answer choices. The idea preceding the punctuationchange,Whilethebattleofmanagainstmachinerageson,isnotacompleteidea.Therefore,eliminateanyanswerchoicesusingpunctuationconsistentwithcompleteideas.Eliminate(A)and (B). A dash must follow a complete idea, so eliminate (C). Choice (D) is the correctanswer.
Summary◦ RememberSTOP,HALF-STOP,andGOpunctuation.
• STOPpunctuationcanlinkonlycompleteideas.• HALF-STOPpunctuationmustbeprecededbyacompleteidea.• GOpunctuationcanlinkanythingexcepttwocompleteideas.
◦ WhenyouseeSTOPpunctuationchangingintheanswerchoices,usetheVerticalLineTest.
◦ OntheSAT,thereareonlyfourreasonstouseacomma:• STOPpunctuation(withoneoftheFANBOYS)• GOpunctuation• aftereveryiteminalist• tosetoffunnecessaryinformation
◦ OntheSAT,thereareonlytworeasonstouseanapostrophe:• possessivenouns(NOTpronouns)• contractions
◦ Know why you are using punctuation, whether that punctuation is STOP, HALF-STOP, GO,commas,orapostrophes.Ifyoucan’tcitereasonstousethesepunctuationmarks,don’tusethem!
Chapter8WordsIn addition to testing punctuation, theWriting and Language Testwill focus onwords—mainly nouns,pronouns, and verbs.Whilewewill discuss a few of these grammatical concepts along theway, thischapterwillboil thesemanyconceptsdowntothreemainterms:consistency,precision,andconcision.With lessminutia toremember,youwillbeable toworkthroughWordsquestionswithconfidenceandease.
THEWORDSCHANGE,BUTTHESONGREMAINSTHESAMEIn the lastchapter,welookedatwhat todowhentheSATis testingpunctuation. In thischapter,we’regoingtolookatwhattodowhentheSATistestingwords—mainlyverbs,nouns,andpronouns.
Ourbasicstrategy,however,hasremainedthesame.Aswesawintheprevioustwochapters,whenfacedwithanSATWritingandLanguagequestion,weshouldalways
Checkwhat’schangingintheanswerchoicesandusePOE.
AchieveGrammarGreatness
Whileyoudon’tneedtobeagrammarexpertto
dowellontheW<est,youmaywanttobrushuponyourgrammarterms,especiallyifyou’refeelingabitrusty.PickupacopyofGrammarSmartfora
quickrefresher!
Asyouwillnotice,throughoutthischapter,wetalkalotaboutcertainpartsofspeech,butwedon’treallyusealotofgrammarterms.That’sbecausewefindthatontheSAT,thecorrectanswersacrossalotofdifferent parts of speech can be summed up more succinctly with three basic terms: consistency,precision,andconcision.
Youdon’tneedtoknowatonofgrammarifyoucanrememberthesethreebasicrules.
CONSISTENCY:Correctanswersareconsistentwiththerestofthesentenceandthepassage.
PRECISION:Correctanswersareaspreciseaspossible.
CONCISION:Barringothererrors,correctanswersareasconciseaspossible.
Let’slookatsomeexamplesofeach.
Consistency
Thespeakersofwhathascometobeknownas 1 AppalachianEnglishhasusedaformofEnglishthatfewcanexplain.
1.A) NOCHANGEB) AppalachianEnglishusesC) AppalachianEnglishuseD) AppalachianEnglishusing
Here’sHowtoCrackItFirst,asalways,checkwhat’schangingintheanswerchoices.Inthiscase,AppalachianEnglishstaysthesame,but theformsof theverb touse change.Therefore,because theverbschange,youknow that thequestionistestingverbs.
Whenyouseeverbschangingintheanswerchoices,thefirstthingtocheckisthesubjectofthesentence.Is the verb consistentwith the subject? In this case, it’s not.The subject of this sentence is speakers,whichisplural.Therefore,(A)and(B)havetobeeliminated,and(D)createsanincompleteidea.Only(C)canworkinthecontext.
Thus,whenyouseeverbschangingintheanswerchoices,checkthesubjectfirst.Subjectsandverbsneedtobeconsistentwitheachother.
Takealookatanother.
ManyscholarsbelieveAppalachianpronunciationcomesfromScots-Irishimmigration,but2 sometheorizesthatthisdialectofEnglishmaybeclosertowhatLondonersspokeinElizabethantimes.
2.A) NOCHANGEB) sometheorizedC) somehavetheorizedD) sometheorize
Here’sHowtoCrackIt
Check what’s changing in the answer choices. The word some remains consistent, but the verbs arechanging.Rememberfromthefirstquestionthatwheneveryouseeverbschanging,makesuretheverbisconsistentwith thesubject.Because thesubjectof this sentence issome,youcaneliminate (A),whichisn’tconsistent.
Then,becausealloftheotherchoicesareconsistentwiththesubject,makesuretheyareconsistentwiththe other verbs. It looks like all the other verbs in this sentence—believe, comes,maybe—are in thepresenttense,sotheunderlinedverbshouldbeaswell,asitisin(D).Choices(B)and(C)couldworkinsomecontexts,butnotthisone.
Asyoucansee,verbsareallaboutconsistency.
Whenyouseeverbschangingintheanswerchoices,makesurethoseverbsare
• CONSISTENTwiththeirsubjects• CONSISTENTwithotherverbsinthesentenceandsurroundingsentences
Let’stryonethathasalittlebitofeverything.
Tryingtounderstandthesechanges 3 demonstratethatalthoughwealltechnicallyspeakEnglish,wespeakverydifferentlanguagesindeed.
3.A) NOCHANGEB) demonstratethatalthoughwealltechnicallyspokeEnglish,wespeakC) demonstratesthatalthoughwealltechnicallyspeakEnglish,wemighthavebeen
speakingD) demonstratesthatalthoughwealltechnicallyspeakEnglish,wespeak
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.Itlookslikelotsofverbs!
First, determine whether demonstrate or demonstrates is consistent with the subject. That subject isTrying,whichissingular,thuseliminating(A)and(B).
Then, you have to choose between speak and might have been speaking. Since both of these are
consistentwiththesubjectwe,trytopicktheonethatismostconsistentwithotherverbs.Theonlyotherverbsaredemonstratesandspeak,bothofwhichare in thepresent tenseanddon’tuse theoddmighthavebeenform.Therefore,ifchoosingbetween(C)and(D),(D)isdefinitelybetter.
Consistencyappliesacrossthetest.Let’sseeanotherquestioninwhichtheideaofConsistencymighthelpus.
Appalachian-Englishspeakersand 4 theirfamilycommunicateinawaythatshowsjusthowinfluentialdiversitycanbeonthelanguagewespeak.
4.A) NOCHANGEB) they’refamiliescommunicateC) theirfamiliescommunicateD) theirfamilycommunicates
Here’sHowtoCrackItCheck the answer choices first. It looks like pretty much everything is changing here: they’re/their,families/family,andcommunicate/communicates.
Thereisn’tagoodreasontouseanapostrophe,sogetridof(B).Then, theverbchanges,socheckthesubject. That subject is Appalachian-English speakers and their family/families, which is pluralregardlessofthewordfamilyorfamilies.Keeptheverbconsistentwiththepluralsubjectandeliminate(D).
Then, you have to choose between family and families, two nouns. Like verbs, nouns are all aboutconsistency.Whenyouseenounschangingintheanswerchoices,makesuretheyareconsistentwiththeothernounsinthesentence.Inthiscase,thesentenceistalkingaboutAppalachian-Englishspeakers,allofthem,soitmustbetalkingaboutalloftheirfamiliesaswell.Manyspeakersmustmeanmanyfamilies,as(C)suggests.
Nounconsistencycanshowupinotherwaysaswell.Takealookatquestion5.
ThelanguageoftheWestVirginiansinAppalachiaisalmostnothinglike 5 NewYorkersorevenotherWestVirginians.
5.A) NOCHANGEB) thelanguageofNewYorker’sorevenotherWestVirginian’s.C) thatofNewYorkersorevenotherWestVirginians.D) peoplefromNewYorkorfromWestVirginia.
Here’sHowtoCrackItLookatwhat’schangingintheanswerchoices.Itlookslikethemainchangeisbetweenthenouns—NewYorkersorevenotherWestVirginiansandthelanguage.Yousawin the lastproblemthatwhennounsarechangingintheanswerchoices,youwanttomakesurethosenounsareconsistentwithothernounsinthesentence.
In this case, the nouns are being compared. The language of Appalachia is being compared with thelanguageofNewYorkersandWestVirginians.Choices(A)and(D)suggest that the language isbeingcomparedwiththepeople,sothoseareinconsistent.Then,(B)containssomeunnecessaryapostrophes,soonly(C)isleft.
TheSATcalls thisconcept“faultycomparison,”butwedon’thavetoknowthatname.Instead,wecanjust remember that nouns have to be consistent with other nouns.When the answer choices show achangeinnouns,lookforthesentence’sothernouns.They’llprovidetheclue!
ScholarstodayarenotsurewhethertocallitapurelyEuropeandialector 6 auniquelyAmericanone.
6.A) NOCHANGEB) uniquelyAmerican.C) auniqueone.D) American.
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.There’safairlysignificantchangebetweenAmericanandAmericanone.As in theprevious sentence,makesure this isconsistent.Thepartof the sentence rightbeforetheunderlinedportionreferstoaEuropeandialect,somakethepartofthesentenceconsistent:anAmericandialect,notmerelyAmerican,asin(B)and(D).
Nowyou’redownto(A)and(C).Thedifferenceherecomesbetween thewordsunique anduniquely
American.Whileit’simportanttobeconcisewhenpossible,youneedtomakesurefirstandforemostthatyou are being precise. Choice (A) is more precise than (C) because it has a clearer relation to theEuropeandialectwithwhichitisbeingcontrasted.Therefore,(A)isthecorrectanswerinthatitisthemostconsistentwiththerestofthesentenceandthemostpreciseoftheremainingpossibleanswers.
Consistency
• Whentheverbsarechangingintheanswerchoices,makesurethoseverbsareconsistentwiththeirsubjectsandwithotherverbs.
• Whenthenounsarechangingintheanswerchoices,makesurethosenounsareconsistentwiththeothernounsinthesentenceandtheparagraph.
PrecisionConsistency is probably the most important thing on the SAT, but precision is a close second. Onceyou’vemadesurethattheunderlinedportionisconsistentwiththerestofthesentence,thenmakesurethattheunderlinedportionisaspreciseaspossible.Perfectgrammarisonething,butitwon’tmattermuchifnooneknowswhatthewriteristalkingabout!
Let’shearthatonemoretime.
Once you are sure that a word or phrase is consistent with the non-underlined portion of thesentence,makethatwordorphraseaspreciseasyoucan.
Really, 7 mostarecollectionsofmanyinfluences,buttheAppalachiandialectseemsunique.
7.A) NOCHANGEB) mostofthemC) mostAmericans
D) mostAmericandialects
Here’sHowtoCrackItCheckwhat’schangingintheanswerchoices.Thechangescouldbesummedupwiththequestion“mostwhat?”We’vegotfourdifferentoptions,sousethemainguidingprinciplesofconsistencyandprecision.
First of all, there’s a comparison in this sentence between different kinds of dialects, so (C) can beeliminatedbecausethatexplicitlychangesthecomparisontosomethingelseinconsistent.
Then,beaspreciseaspossible.Choices(A)and(B)areverysimilarinthattheysaymost,buttheydon’tspecifywhat thatmost refers to. Even though these are grammatically consistent with the rest of thesentence,they’renotquitepreciseenough,whichmakes(D)alotbetter.
Asquestion7shows,pronounscanbeabitofachallenge.Theycanappearinotherwisegrammaticallycorrectsentences.Still,precisioniskeywhenyou’redealingwithpronouns.Seewhatyoucandowiththesesentences.Highlightthepotentiallyimprecisepronounsandrewritethesentences.Answerscanbefoundonthispage.
1. Certaindialectshaveobvioussources,butthatdoesn’tmakeitanyeasiertounderstand.
2. Eachofusspeakswithanaccentbecauseofwheretheyarefrom.
3. Wordchoiceandpronunciationit’susuallyeasytohearinsomeone’saccent.
4. Everyoneusessomekindofdialectwordsintheireverydayspeech.
5. Movies,TV,theInternet:itmaybedestroyingdifferentiateddialectsinthemodernworld.
Precisioncanshowupinsomeotherwaysaswell.Havealookatthisquestion.
TheAppalachianregion’s 8 isolationhasledtosomehypothesesfrommajorurbancentersthatitsdialecthasremainedintactfromthedaysofitsearliestsettlers.
8.A) NOCHANGEB) isolationhasledtosomehypothesesthatitsdialectfrommajorurbancentershas
remainedintactC) isolationfrommajorurbancentershasledtosomehypothesesthatitsdialecthas
remainedintactD) isolationhasledtosomehypothesesthatitsdialecthasremainedintactfrommajor
urbancenters
Here’sHowtoCrackItCheckwhat’s changing in the answer choices. This step is crucial here because there are no obviousgrammaticalerrors,sotheanswerchoicesareessentialtofiguringoutexactlywhatthequestionisaskingyoutodo.
Intheend,theonlydifferenceamongtheanswerchoicesisthatthephrasefrommajorurbancentersisindifferentplaces.Intheend,youwilljustneedtoputthatphraseinthemostpreciseplace,hopefullyrightnexttowhateveritismodifying.
Inthiscase,choosefromamonghypotheses,dialect,isolation,andintact.Whichofthesewouldhavethemost precise need for the phrase from major urban centers? Because urban centers seems to havesomethingtodowithplace,eliminate(A),hypotheses,and(D),intact,whichdon’thaveanythingtodowithplace.Then, because thepassage as awholehas talked about the remotenessof theAppalachiandialect,youcansayforsurethatitisnotadialect frommajorurbancenters,eliminating(B).All thatremains,then,is(C),whichcompletesthephraseisolationfrommajorurbancenters,whichisthemostpreciseanswer.
Nowpracticewithsomemoreofthesemodifiers.Rewriteeachofsentencessothatthemodifiermakestheprecisesensethatitshould.Checkyouranswersagainstthoseonthispage.
1. Withallitsinsandouts,manypeoplefindlanguageatoughthingtostudy.2. Dialectsarereallyfascinatingtoanyonewhowantstostudythemofaparticularlanguage.3. Onceopenedup,youcanfindendlessmysteriesinthestudyoflanguage.4. IfirstlearnedabouttheAppalachiandialectfromaprofessorincollegeatage19.5. Franklyprettyboring,Donalddidn’tpaymuchattentioninhislinguisticsclass.
ConcisionEverhearthesaying“lessismore”?Concisionhasitsadvantages.Forexample,ifyouweretoaskfordirections,whichanswerwouldyouratherreceive?
TurnrightatMainStreetandwalkfourblocks.
or
Sincethisstreet,ElmStreet,isfacinginanortherlydirection,andyourdestinationisduenortheast,goeastwhenyouarriveattheintersectionofElmandMain.Goingeastwillentailmakingaright turn in quite that easterly direction. After having made this turn and arrived on theperpendicularstreet…
Thefirstone,obviously.
That’sbecauseconcision iskeywhenyouwant tocommunicatemeaning.Really,as longaseverything
elseisinorder—aslongasthegrammarandpunctuationaregoodtogo—thecorrectanswerwillalmostalwaysbetheshortest.
Let’sseeanexample.
ItispreciselythisisolationthathasledmanyscholarstobelievethatAppalachianEnglishis9 alikeandsimilartotheEnglishspokeninShakespeare’stime.
9.A) NOCHANGEB) similarC) likelysimilarD) similarlyalike
Here’sHowtoCrackItCheckwhat’schanging in theanswerchoices. In thiscase, thewordsimilar appears inall theanswerchoices, and in some it is pairedwith theword alike. Typically, if you see a list of answer choiceswherein one answer is short and the rest mean the same thing but are longer, the question is testingconciseness.
What,afterall,isthedifferencebetweenthewordssimilarandalike?Therereallyisn’tone,sothere’snouseinsayingbothofthem,asin(A),orpairingthemawkwardly,asin(D).Infact,theshortestanswerchoice,(B),doeseverythingtheotherchoicesdo,butitdoessointhefewestwords.Therefore,(B)isthecorrectanswer.
Let’sseeonemore.
10 Whateverthecasemaybe,Appalachianisafascinatingdialect,andwecanonlyhopethatitpersistsagainsttheonslaughtofmassmedia.
10.A) NOCHANGEB) Whoop-de-doo,AppalachianC) Allthingsconsidered,AppalachianD) Appalachian
Here’sHowtoCrackItAs always, checkwhat’s changing in the answer choices. The changes could be summed up like this:There’sabunchofstuffbefore thewordAppalachian.Doesanyof thatstuffcontribute inasignificantwaytothesentence?No.DoesthewordAppalachianalonehelpthesentencetofulfillitsbasicpurpose?Yes.Therefore,thecorrectansweris(D).
Aswe have seen in this chapter,when SAT is testingwords (any time thewords are changing in theanswerchoices),makesurethatthosewordsare
• Consistent.Verbs,nouns,andpronounsshouldagreewithinsentencesandpassages.• Precise.Thewritingshouldcommunicatespecificideasandevents.• Concise.Wheneverythingelseiscorrect,theshortestanswerchoiceiscorrect.
AnswerstoQuestionsonthispage:
1. itistheproblem.Certaindialectshaveobvioussources,butthatdoesn’tmakethosedialectsanyeasiertounderstand.
2. theyistheproblem.Eachofusspeakswithanaccentbecauseofwhereheorsheisfrom.3. it’sistheproblem.Changeit’stoare!Word-choiceandpronunciationareusuallyeasytohearin
someone’saccent.4. theiristheproblem.Everyoneusessomekindofdialectwordsinhisorhereverydayspeech.5. itistheproblem.Movies,TV,theInternet:allthreemaybedestroyingdifferentiateddialectsin
themodernworld.
AnswerstoQuestionsonthispage:
1. Manypeoplefindlanguageatoughthingtostudybecauseofallitsinsandouts.2. Dialectsofaparticularlanguagearereallyfascinatingtoanyonewhowantstostudythem.3. Onceopenedup,themysteriesofalanguagecanbeendless.4. IfirstlearnedabouttheAppalachiandialectfromacollegeprofessorwhenIwas19yearsold.5. Donalddidn’tpaymuchattentioninhislinguisticsclass,whichhefound,frankly,prettyboring.
WritingandLanguageDrill3Answerscanbefoundonthispage.
Time:7–8minutes
WarandPeace(1869)is 1 well-knownandfamousmainlyforitslength.Notmanyreaders,especiallyinthemodernday, 2 hasthetimeorthepatiencetoworkthroughLeoTolstoy’s1,400pages,countlesscharacters,andplottwists. 3 Theyaremissingamajoropportunity,notonlybecausethenovelismorefunthanitspagecountsuggests,butalsobecauseitmarkstheendofaparticularmomentinhistory.
1.A) NOCHANGEB) famousandwell-knownC) famouslywell-knownD) well-known
2.A) NOCHANGEB) haveC) arehavingD) dohave
3.A) NOCHANGEB) ThosereadersC) ManyofthemD) Some
CzechnovelistMilanKunderacitedTolstoyasthelastnovelistwhocould 4 bepossessingthesumofhisera’shumanknowledge.Thismayseemlikeanoddclaim.Somepeoplemaybeveryintelligent,othersmaybeknow-it-alls,butisitreallypossibletoknoweverything?AbooklikeWarandPeacemakesthecasethatitispossibletoknowitall,oratleastthatitwaspossible, 5 alongsideTolstoy’sothergreatnovelsandnon-fictionwritings.Shakespeare 6seemedtohaveanemotionalvocabularythatwasadvancedforhisage,butTolstoylivedin 7aneraoffactsanddiscoveries,andhisnovelsshowthefruitsofhisvaststudy.Itisfrankly
conceivablethatamanwithTolstoy’sleisure,intelligence,andcuriosity 8 learnsabouthisage’smostcurrentfindingsinliterature,politics,religion,andscience.
4.A) NOCHANGEB) ofhadC) possessD) possessed
5. Ifthepunctuationwereadjustedaccordingly,thebestplacementfortheunderlinedportionwouldbeA) whereitisnow.B) atthebeginningofthesentence.C) afterthewordthat.D) afterthewordleast.
6.A) NOCHANGEB) seemshavingC) hasD) seeminglyhas
7.A) NOCHANGEB) anera,C) ahistoricaltimeperiod,D) one,
8.A) NOCHANGEB) hadbeenlearningC) couldhavelearnedD) arelearning
TheveryfactthatsuchanachievementisimpossiblenowshowsusjusthowmuchthingshavechangedsinceTolstoy’sdeathin1910. 9 Thiswastheyear,infact,thatVirginiaWoolfcitedinheroft-quotedremark,“Onorabout1910humancharacterchanged.”Ifweatleast
entertaintheideathatsheiscorrect,wecanbegintoseewhyshewouldbewillingtomakesuchagrandioseremark.After1910,thetwentiethcenturystartedinearnest.Knowledgebecamemorecomplexasitbecamemorespecialized,andalthoughairplanesseemedtomaketheworldasmallerplace,thedifferencesamongalltheplacesinthatsmallworldtrulyemerged.
9. ThewriterisconsideringdeletingthephrasesinceTolstoy’sdeathin1910andendingthesentencewithaperiodafterthewordchanged.Shouldthephrasebekeptordeleted?A) Kept,becauseitcontributestotheessay’sbiographicalsketchoftheauthorofWar
andPeace.B) Kept,becauseitintroducesatopicofdiscussionthatiscontinuedthroughoutthe
paragraph.C) Deleted,becausetheremainderoftheparagraphdescribestheinsignificanceof
Tolstoy’sdeath.D) Deleted,becausetheparagraphasawholeisfocusedontheachievementsof
anotherauthor.
WarandPeaceisthegreatdocumentofthatpre-1910era,ofamomentwhenthegreatscientistswerealso 10 intophilosophyandwhenthegreatmathematicianswerealsothegreattheologians.Agreatdiscoveryinonefieldcouldalsobe 11 another.Althoughitwascertainlyremarkable,itwasalsopossibleforamanlikeTolstoytohaveafundamentalgraspofallthatunitedthemanybranchesofknowledge.Tolstoy’sachievementisimpossibletoday,butitisawonderfulreminderofthevalueofintellectualcuriosityandcosmopolitanism.Nomatterhowbrilliantandrefinedwemaybecome,wecanalwaysstandtoberemindedthatthereisaworldoutsideofourimmediatecircle.
10.A) NOCHANGEB) fascinatedwithphilosophicalinquiryC) interestedinphilosophyD) thegreatphilosophers
11.A) NOCHANGEB) anotherfield.C) agreatdiscoveryforanother.D) thesamethingelsewhere.
WRITINGANDLANGUAGEDRILL3:ANSWERSANDEXPLANATIONS1. D Notice that the length of the phrase is changing in the answer choices. Some of the answer
choiceshaveextrawords,which indicates that thequestion is testingconcision.Because thewords famousandwell-known are synonyms, itwouldbe redundant touseboth.Choose themostconciseanswer,whicheliminatesthisredundancy.Choice(D)iscorrect.
2. B Sincetheverbischangingintheanswerchoices,thequestionistestingsubject-verbagreement.First, find the subject.Readers is the subjectof the sentence,which isplural.Theverbwillneedtobeconsistentwiththatsubject.Eliminate(A).Theremainingoptionsareallplural,butonly(B)isconciseandconsistentwiththemeaningofthesentence,whichmakesitthecorrectanswer.
3. B When the use of pronouns changes in the answer choices, the question is usually testingprecision. It isunclearwhomanyof them, they,andsome are.Only (B)precisely identifiesreadersasthesubject.
4. C Notice that verb tense is changing in the answer choices. The word could precedes theunderlinedportion,soinordertobeconsistentwiththesentence,theverbshouldbeinitsbaseform.Eliminate(A)and(D).Otherwise,couldcanbefollowedbyhave,notof.Eliminate(B).Choice(C)isthecorrectanswer.
5. B The question asks for the best placement of the underlined portion, which is a reference toTolstoy’sothernovelsandwritings.Therefore,itsbestplacementisnexttothementionofoneofhisnovels:WarandPeace.Oftheanswerchoices,(B)doesthisthebest.
6. A Notice that verb tense changing in the answer choices. The subject of the sentence isShakespeare,aplaywrightfromthepast.Therefore,toremainconsistentwiththesentence,usepasttense.Eliminate(B),(C),and(D)becausetheyuseverbsinthepresenttense.Choice(A)iscorrect.
7. A The description of Tolstoy’s time is changing in the answer choices. The sentence refers toTolstoy’svaststudy.Theonlyanswerchoicethatisconsistentwiththeideaofavaststudyis(A),whichisthecorrectanswer.
8. C Again, notice that verb tense changing in the answer choices. The sentence here refers toTolstoy,awriterfromthepast.Therefore,toremainconsistentwiththesentence,usepasttense.Eliminate(A)and(D).BecausethesentenceisremarkingonTolstoy’sabilitytolearnsomuch,theuseofthewordcouldismostconsistentwiththemeaningofthesentence.Choice(C)isthecorrectanswer.
9. B Thequestionaskswhether thephrasesinceTolstoy’sdeath shouldbedeleted.Thephrase isconsistentwiththecontentoftheparagraphandpreciselyidentifiesthetimeperiodinquestion.Thephraseshouldbekept.Eliminate(C)and(D).Thephrasedoesmoretointroducethetime
periodasatopicofdiscussionthantodescribeTolstoyhimself,soeliminate(A).Thecorrectansweris(B).
10. D Notice thewordingchanging in theanswerchoices.Thegreatscientistswerealso thegreatphilosophers is theonlychoice that isconsistentwith thesecondhalfof thesentence,whichsays the great mathematicians were also the great theologians. Choice (D) is the correctanswer.
11. C Again,noticethewordingchangingintheanswerchoices.Inthesentence,itisnotclearwhatthe underlined portion, the pronoun another, is referring back to. Choice (C) clarifies thisconfusion and is consistent with the idea in the previous sentence that scientists were alsophilosophersandmathematicianswerealsotheologians.Thecorrectansweris(C).
Summary◦ OnWritingandLanguagequestions,thefirststepisalwaystocheckwhat’schangingintheanswer
choicesandthenusePOE.
◦ Thecorrectanswersacrossmanydifferentpartsofspeechcanbesummedupsuccinctlywiththreebasicterms:consistency,precision,andconcision.Youdon’tneedtoknowatonofgrammarifyoucanrememberthesethreebasicrules:• Correctanswersareconsistentwiththerestofthesentenceandthepassage.• Correctanswersareaspreciseaspossible.• Barringothererrors,correctanswersareasconciseaspossible.
◦ Whenyouseeverbschangingintheanswerchoices,makesurethoseverbsareconsistentwiththeirsubjectsaswellaswithotherverbsinthesentenceandsurroundingsentences.
◦ Whenthenounsarechangingintheanswerchoices,makesurethosenounsareconsistentwiththeothernounsinthesentenceandtheparagraph.
◦ Once you are sure that a word or phrase is consistent with the non-underlined portion of thesentence,makethatwordorphraseaspreciseasyoucan.
◦ Concisioniskeywhenyouwanttocommunicatemeaning.Aslongasthegrammarandpunctuationaregoodtogo,thecorrectanswerwillalmostalwaysbetheshortest.
Chapter9QuestionsMostofthequestionsyouwillseeontheWritingandLanguageTestarenotinquestionform,buteverynow and then youwill be presentedwith a traditionalmultiple-choice question. It’s important to readthesecarefully soyouknowexactlywhat isbeingaskedanddonot jump toconclusions.This chaptercoverssometypicalquestionsyoumightseeandstrategiesyoucanusetoapproachandsimplifythem.
ANDTHENSATWASLIKE,“HEY,CANIASKYOUAQUESTION?”Asyouhave seen, “questions”on theWritingandLanguageTest aren’tquestionsat all,grammaticallyspeaking.They’rejust listsofanswerchoices,andyoustart theprocessofansweringthembyaskingaquestionofyourown:“What’schangingintheanswerchoices?”
Because you need to move quickly through this test, you may fall into the habit of not checking forquestions.Evenwhenyoudoreadthequestions,youmayreadthemtoohastilytounderstandwhatyouarebeingasked.Well,weareheretotellyouthatneitheroftheseapproacheswillwork.
Themost important thingaboutWritingandLanguagequestions is thatyounotice thosequestionsandthenanswerthosequestions.
Thismayseemlikejustabout themostobviousadviceyou’veeverbeengiven,butyou’dbesurprisedhowmuchlesspreciseyourbrainiswhenyou’reworkingquickly.
Here’sanexample.Dothesenext10questionsasquicklyasyoucan.
1. 2+1=
2. 1+2=
3. 3+1=
4. 3+2≠
5. 1+2=
6. 2−1<
7. 2±2=
8. 3+1=
9. 3+2=
10. 3+3≠
Nowcheckyouranswers.
1. 3
2. 3
3. 4
4. Anythingbut5
5. 3
6. Anynumbergreaterthan1(butnot1!)
7. 0or4
8. 4
9. 5
10. Anythingbut6
Now,it’sverypossiblethatyougotatleastoneofthosequestionswrong.Whathappened?It’snotthatthequestionsaredifficult.Infact,thequestionsareaboutaseasyascanbe.Sowhydidyougetsomeofthemwrong?Youwereprobablymovingtooquicklytonoticethatthesignschangedafewtimes.
ThisisalotliketheWritingandLanguageTest.Youmightmisssomeoftheeasiestquestionsonthetestbynotreadingcarefullyenough.
As you will see throughout this chapter, most of the questions will test concepts with which we arealreadyfamiliar.
WORDSANDPUNCTUATIONINREVERSEMany of the concepts you learned in the chapters on punctuation andwords showup explicitly in thequestions,butusuallythere’ssomekindoftwist.
Here’sanexample.
Mostpeoplearefamiliarwiththeideaofagenderpay 1 gap.Whatmostpeopledon’trealizeisjusthowpersistentthatpaygaphasbeen.
1. WhichofthefollowingalternativestotheunderlinedportionwouldNOTbeacceptable?A) gap;whatB) gap:whatC) gap,however,D) gap,but
Here’sHowtoCrackIt
Firstandforemost,it’simportanttonoticethequestion.ThisoneisaskingforthealternativethatwouldNOTbeacceptable,soyou’llneedtofindananswerthatdoesn’twork.
Now go through the steps. What’s changing in the answer choices? STOP, HALF-STOP, and GOpunctuation.UsetheVerticalLineTestbetweenthewordsgapandwhat.Theideabeforetheline,Mostpeoplearefamiliarwiththeideaofagenderpaygap,iscomplete.Theideaaftertheline,whatmostpeopledon’trealizeisjusthowpersistentthatpaygaphasbeen,isalsocomplete.Therefore,youneedeitherSTOPorHALF-STOPpunctuation.
Choices(A)and(B)definitelyprovidethepunctuationyouwant.Choice(D)doesn’t looklikeitdoes,but remember!But is one of the FANBOYS, and comma + FANBOYS is one of the forms of STOPpunctuation!Therefore,theonlychoicethatdoesn’tworkinthiscontextis(C),soitisthealternativethatwouldNOTbeacceptable.
NoticehowimportantthatwordNOTwasinthisquestion.Ifyoumissedit,youmighthavethoughtthequestionhadthreecorrectanswers!
Let’stryanother.
The 2 sizeofthegapmayhavenarrowed,butwestillhavealongwaytogo.
2. WhichofthefollowingsubstitutionswouldbeLEASTacceptable?A) magnitudeB) proportionC) vastnessD) immensity
Here’sHowtoCrackItAgain,payattentiontowhatthequestionisasking.YouneedtofindtheoptionthatisLEASTacceptable,so eliminate any answer choice thatworks. In this case, youneed something similar inmeaning to theword size as it is used in this sentence. All four words mean something similar to size in differentcontexts,butyouwantsomethingthatreferstojusthowlargethegapis,so(A),(C),and(D)wouldallwork.
Choice(B)doesgiveasynonymforthewordsize,butitmeanssomethingmorelike“dimensions”than“largeness,”soitistheLEASTacceptableofthesubstitutions.
Let’slookatanotherquestionthatdealswithsomeofthetopicswe’veseenearlier.
Theproblemhascertainlygainedagooddealoftractioninpublicdebates.Thefactthatithasgainedsuchtractionmakesuswonderwhyisn’ttheremoresignificantactiontocombatthegenderpaygap. 3
3. Whichofthefollowinggivesthebestwaytocombinethesetwosentences?A) Theproblemhascertainlygainedagooddealoftractioninpublicdebates;thefact
thatithasgainedsuchtractionmakesuswonderwhyisn’ttheremoresignificantactiontocombatthegenderpaygap.
B) Theproblemhascertainlygainedagooddealoftractioninpublicdebates,whichraisesthequestionofwhymoreisn’tbeingdonetocombatthegap.
C) Theproblemhascertainlygainedagooddealoftractioninpublicdebates:thisfactofmorepublicattentionraisesaseriousquestionofwhymoreisn’tbeingdonetoclosethatgap.
D) Theproblemhascertainlygainedagooddealoftractioninpublicdebates.Whyisn’tmorebeingdonetocombatthegap?
Here’sHowtoCrackItThequestionasksyoutocombinethetwosentences.Youreyeswereprobablydrawnimmediatelyto(D),whichisthemostconciseofthechoices.There’sjustoneproblem:(D)doesn’tanswerthequestion!Thequestionaskstocombinethesentences,andwhile(D)shortensthem,itdoesn’tcombinethem.
Therefore,(B)istheanswer.Itcombinesthesentencesandshortensthemabit,unlike(A)and(C),whichcombinethesentencesbutdon’treallydomuchbeyondchangingthepunctuation.
Questionslikequestion3arewhy…
ThemostimportantthingtorememberaboutWritingandLanguagequestionsisthatyoumustnoticethosequestionsandthenanswerthosequestions.
PRECISIONQUESTIONSNotallquestionswillbejustapplicationsofpunctuationandwords.Somequestionswillaskyoutodomorespecific things.Remember the three termswekeptrepeatingin thepreviouschapter:consistency,precision, and concision.We’ll startwith the precision-related questions. Evenwhen precision is not
askedaboutdirectly,orwhenitismixedwithconsistencyorconcision,rememberthis:
Answerthequestioninthemostprecisewaypossible.Readliterally!
Let’stryone.
Thequestionofunequalpayforwomendrawsonmanyotherbroadersocialissues. 4
4. Thewriterisconsideringdeletingthephraseofunequalpayforwomenfromtheprecedingsentence.Shouldthisphrasebekeptordeleted?A) Kept,becauseremovingitwouldremoveacrucialpieceofinformationfromthis
partofthesentence.B) Kept,becauseitremindsthereaderofsocialinjusticeinthemodernworld.C) Deleted,becauseitwronglyimpliesthatthereisadisparitybetweenwhatwomen
andmenarepaid.D) Deleted,becauseitgivesinformationthathasnobearingonthisparticulartext.
Here’sHowtoCrackItThisquestionaskswhethertokeepordeletethephraseofunequalpayforwomen.Withoutthatphrase,the sentence reads,Thequestiondrawsonmanyotherbroader social issues.Becausenothing in thissentenceoranyofthepreviousonesspecifieswhatthisquestionmightbe,keepthephrase.Beaspreciseaspossible!
As(A)says,youwanttokeepthephrasebecauseitiscrucialtoclarifyingpreciselywhatthequestionis.Choice(B)isabittoograndioseareasontokeepthephrase,especiallywhenthewholepassageisabouttheparticularinjusticeofthegenderpaygap.Choice(A)isthecorrectanswer.
Let’stryanother.
Thegenderdisparitiespersistinareasotherthanpay.Itisakindofopensecret,forinstance,thatwomenhavehadtherighttovoteintheUnitedStatesforlessthanacentury. 5 ThereisalonghistoryofmisogynywrittenintotheveryculturalandsocialfabricoftheUnitedStates.
5. Atthispoint,thewriterisconsideringaddingthefollowingtruestatement:
Theyearthatwomen’ssuffragebecamelegalintheUnitedStateswasalsotheyearthattheAmericanFootballLeaguewasformedundertheleadershipofJimThorpe.
Shouldthewritermakethisadditionhere?A) Yes,becauseitgivesabroadercontexttotheachievementofwomen’ssuffrage.B) Yes,becauseithelpstoeasesomeofthepoliticalrhetoricintherestofthepassage.C) No,becauseitdoesnotcontributeinasignificantwaytothediscussionofthe
genderpaygap.D) No,becausethequestionofgenderpayisirrelevantwhenallfootballplayersare
men.
Here’sHowtoCrackItTheproposedsentencedoescontainaninterestingbitofinformation,butthatpieceofinformationhasnoclearplaceineitherthesefewsentencesorthepassageasawhole.Therefore,itshouldnotbeadded,andyoucaneliminate(A)and(B).
Then,becausethetopicofthestatementdoesnotplayasignificantroleinthepassage,itshouldnotbeadded for the reason stated in (C).While (D)may be true in away, it does not relate to the role thesentencemightplayinthepassageasawhole.Readliterally,andanswerasliterallyandpreciselyasyoucan.
CONSISTENCYQUESTIONSJust as questions should be answered as precisely as possible, they should also be answered withinformationthatisconsistentwithwhat’sinthepassage.
Whenansweringconsistencyquestions,keepthisgeneralruleinmind:
WritingandLanguagepassagesshouldbejudgedonwhattheydosay,notonwhattheycould say.Whendealingwithstyle,tone,andfocus,makesuretoworkwiththewordsandphrasesthepassagehasalreadyused.
Let’slookattwoquestionsthatdealwiththeideaofconsistency.
[1]Oneneedlooknofurtherthantotheideaofthe“traditional”family.[2]Theshift,however,hasyettoproduceasubstantiveincreaseinhowwomen,whoarenownearlyaslikelytoworkasmen,arepaid.[3]Inthisidea,thefatherofthefamilyearnsthefamilywage
6 andgivesthechildrenhislastname.[4]Withsuchanideabolsteringwhatmanyconsidertobethegoalinherentinthe“Americandream,”itisnowonderthatwomenintheworkplaceshouldhaveasomewhatdegradedposition.[5]Shiftingsocialandeconomicroles,however,havebeguntochangehowpeoplethinkaboutgenderroleswithinthefamily. 7
6. Whichofthefollowingchoiceswouldbestcompletethedistinctiondescribedinthissentenceandtheparagraphasawhole?A) NOCHANGEB) whilethemothertendstothechildrenandthehome.C) thoughhisinterestinmasculinethingslikesportsmayvary.D) butwillonlybeabletoachieveawagecommensuratewithhisskillsandeducation.
7. Thebestplacementforsentence2wouldbeA) whereitisnow.B) beforesentence1.C) aftersentence4.D) aftersentence5.
Here’sHowtoCrackItLookatquestion6first.Inthiscase,thequestiontellsyouexactlywhattolookfor:somethingthatwouldcomplete thedistinction in the sentence, adistinctionmadebetweenwhat is expectedof amanandawomanina“traditional”family.Choices(A),(C),and(D)maybetrueinsomedefinitionsofwhatthat“traditional”familyis,butnoneofthoseanswersfulfillsthebasicdemandsofthequestion.Only(B)doessobydescribingwhatisexpectedofamotherincontrasttowhatisexpectedofafather,asdescribedearlierinthesentence.
Forquestion7,youneedtofindsomeveryliteralwaytomakesentence2consistentwiththerestoftheparagraph.Lookforwordsandphrases thatwill linksentence2 toothersentences.Remember, it’snotwhatthepassagecouldsay;it’swhatthepassagedoessay.Sentence2,weshouldnote,startswith theshift,thusclearlyreferringtoashiftthathasbeenmentionedbeforeit.Assuch,sentence2belongsaftersentence5,whichdiscussesshiftingsocialandeconomicroles.
Asyoucansee,thesequestionscanbeansweredcorrectlyifyoutakethespecificstepsdiscussedhere.Make sure you read the questions carefully and that you answer those questions as precisely andconsistentlyasyoucan.
ThesamegoesforchartsandgraphsontheWritingandLanguageTest.Don’t let thestrangenessofthechartsthrowyouoff!Justreadthegraphswithasmuchprecisionasyoucanandchoosethemostpreciseanswerspossible.
Let’shavealookatone.
Evenaswomen’srolesinhigh-levelpositions,suchasCongress,haveincreasedalmostfive-foldsince1981, 8 thepaythatwomenreceiverelativetomenhasincreasedbyonlyapproximately33%.
8. Whichofthefollowingchoicesgivesinformationconsistentwiththegraph?A) NOCHANGEB) women’swageshaveincreasedbyover80%.C) thewagesofwomeninCongresshavedecreased.D) theeffortsofwomeninCongresstoraisewageshavefailed.
Here’sHowtoCrackIt
Thequestionasksyoutofindwhichchoiceagreeswiththegraph.Itlookslike“WomeninCongress”goesup significantlywhere “Women’s Pay” remains relatively consistent. The only choice that reflects thattrendis(A).Choice(B)misreads thegraph,and(C)and(D)can’tbesupportedonewayor theother.Choice(A)isthereforethecorrectanswer.
Ingeneral,graphsontheSATReadingandWritingandLanguageTestsareverystraightforward,andthefundamentalquestiontheyaskis,“Canyoureadagraph?”TheseareeasypointsaslongasyoureadthegraphscarefullyandusePOE.
CONCLUSIONAsyouhaveseeninthischapter,theSATcanaskalotofdifferentkindsofquestions,butyou’renotgoingto have anything really crazy thrown at you. The most important rules to remember, aside from thepunctuationrules,areconsistencyandprecision. Ifyouchooseanswers thatarepreciseandconsistentwithotherinformationinthepassage,youshouldbegoodtogo.Justbesuretoanswerthequestion!
WritingandLanguageDrill4Answerscanbefoundonthispage.Time:7–8minutes
[1]
1 GenreinHollywoodmoviesisaconstantbutinconstantthing.Horror,Western,andSci-Fimoviesaremadeeveryyear,butthenumberofmoviesproducedineachgenrefluctuatesannually.Forexample,asthenumberofWesternshasstayedatorbelowabout25peryearsincethe1960s,thenumberofZombieandVampirefilms 2 hasrisen,withZombiefilmsincreasingnearlysix-fold.
1. Whichofthefollowingchoiceswouldbestintroducetheessaybypointingtothevariabilityininterestindifferenttypesofmovies?A) NOCHANGEB) WhilemanymoviegenresarestaplesinHollywood,thepopularityofthesegenres
haschangedovertime.C) EveryoneknowsthatthehighestformofHollywoodfilmisthedrama.D) There’salotthatyoumaynotknowabouthowfilmsaremadeinHollywood.
2. Whichofthefollowinggivesinformationconsistentwiththegraph?A) NOCHANGEB) hasrisen,withVampirefilmsincreasingnearlysix-fold.C) hasdeclined,withZombiefilmproductiondecreasingbyasixth.D) hasdeclined,withVampirefilmproductiondecreasingbyasixth.
[2]
Whilethesayinggoesthatthere’s“noaccountingforthepublic’staste,” 3 lotsofpeoplelikelotsofdifferentthings.WhyshouldthenumberofWesternshaveremainedrelativelylowwhilethenumberofZombiefilmshasskyrocketed?Maybeweshouldaskthequestionanotherway:whatdopeopletodaygetfromZombiefilmsthattheydon’tfromWesterns?
3. Whichofthefollowingchoiceswouldofferthemosteffectivetransitionbetweenthepreviousparagraphandthecurrentone?A) NOCHANGEB) thesetrendsnonethelessinviteustotry.C) alotofpeopledon’tevencareaboutZombiemovies.D) sciencehasnotyetshownthatzombiesexist.
[3]
Westernsdominatedthe1920s.Zombiefilmshavedominatedthe1990sand2000s.Beginningwiththesefactsalone,wecanstarttoseewhythesefilmsmighthavebeenpopularindifferenteras. 4 The1920s,forinstance,wasanAmericanmomentofcrusade. 5 Onlyatoughsheriff,thekindonemightgetinanold-westtown,couldfindtheperfectbalancebetweenjusticeand 6 brutality.Thus,iftheworldcouldnotbecontainedbylawandorder,atleastherewasanimaginaryspacethatcouldbeintheWest.
4. Thewriterisconsideringdeletingthephraseindifferenterasandendingthesentencewithaperiodafterthewordpopular.Shouldthephrasebekeptordeleted?A) Kept,becausethemeaningofthesentencechangeswithoutthephrase.B) Kept,becauseitisinterestingtothinkabouthistoryandfilmtogether.C) Deleted,becausetheessayismoreconcernedwiththegenres’popularityacross
timeperiods.D) Deleted,becausetheessayisalreadydullandcouldstandtohavesomewords
removed.
5. Atthispoint,thewriterwantstoinsertanideathatwillsupporttheideagiveninthe
previoussentence(“The1920s…crusade”).Whichofthefollowingtruestatementswouldofferthatsupport?A) ThesewerecrusadesaltogetherdistinctfromthoseconductedbytheCatholic
Churchstartingin1095.B) TheUnitedStatesisstillinterestedincrusadetoday,soit’shardtoseewhythey
don’tmakeasmanyWesternsanymore.C) LedbyWoodrowWilson’splanforaU.S.-ledLeagueofNations,theworld,reeling
fromWorldWarI,wantedjusticeamongtheoutlaws.D) Thestockmarketwouldn’tcrashforanothernineyears,atwhichpointpeople
wouldreallyfreakout.
6. WhichofthefollowingalternativestotheunderlinedportionwouldNOTbeacceptable?A) brutality,andifB) brutality:ifC) brutality;thus,ifD) brutality,thus,if
[4]
Itmayseemthatgenreconventionsneverchange.Becausetheyneverchange,itprobablyseemslikeaWesterntodayfollowsthesamesetofrulesasaWesternfrom100yearsago. 7WhattheriseinZombiefilmsshows,however,isthatthegenresthemselveschange,andtheyprovidedifferentthingstodifferenteras. 8 Thisisnottosaythatonegenreisbetterthantheother—thatit’sbetter,forinstance,towatchatoughcowboyfightoffagangofcattlerustlers—butitistosaythatthesegenresholdalotmorethantheirmereentertainmentvalue.
7. Whichofthefollowinggivesthemosteffectivewaytocombinetheprevioustwosentences,reproducedbelow?
Itmayseemthatgenreconventionsneverchange.Becausetheyneverchange,itprobablyseemslikeaWesterntodayfollowsthesamesetofrulesasaWesternfrom100yearsago.
A) (keepthesentencesastheyare)B) Itmayseemthatgenreconventionsneverchange;becauseofit,itcouldbeargued
thataWesterntodayfollowsthesamesetofrulesasaWesternfrom100yearsago.C) Itmayseemthatgenreconventionsneverchange:aWesterntodayfollowsthesame
setofrulesasaWesternfrom100yearsago.D) BecauseWesternstodayfollowthesamesetofrulesastheydid100yearsago,it
seemstomostoutsideobserversthatgenreconventionsneverchange.
8. Atthispoint,theauthorisconsideringaddingthefollowingtruestatement:
Forwhatit’sworth,mypersonalfavoriteisJacquesTourneur’sIMarriedaZombie,whichisbasedlooselyonJaneEyre.
Shouldthewritermakethisadditionhere?A) Yes,becausetheessayasawholeisfilledwiththesekindsofexamplesand
personalpreferences.B) Yes,becausetheauthor’squirkychoiceshowsthathehasanoff-beatperspective.C) No,becausetheauthor’sstrangechoicedisqualifieshimfromdiscussingpopular
taste.D) No,becausetheessayasawholeisnotprimarilyfocusedontheauthor’spersonal
preferences.
[5]
The1990sand2000s,dominatedastheyarebyZombiefilms,showthatcontemporaryconflictsarenotsofaraway.Althoughwenowhavetheworldattheclickofabutton,Zombiefilmsshowthatwearenotallthatinterestedinthatworld.Instead,weareinterestedinandsuspiciousofthepeoplearoundus.Whethercoworkersorfellowstudents,thepeoplearoundus,especiallywhen 9 viewedasamass,canseemalmost“dead.”Andthereasonsforthisarefairlyobvious:ourprivateoronlinepersonalitieshavebecomesorobustthatthe“realworld”outsidecannothelpbutseemdullorclaustrophobicbycomparison. 10
9. WhichofthefollowingalternativestotheunderlinedportionwouldbeLEASTacceptable?A) takenB) espiedC) seenD) regarded
10. Thewriterisconsideringreplacingthewordrobustintheprecedingsentencewiththewordhealthy.Shouldthewritermakethechangeorkeepthesentenceasitis?A) Makethechange,becausethewordrobustisnotfamiliartomanyreaders.B) Makethechange,becausethewordhealthyprovidesamoreaccuraterepresentation
ofpeople’smedicalconditions.C) Keepthesentenceasitis,becausethewordhealthychangesthemeaninginaway
inconsistentwiththepassageasawhole.D) Keepthesentenceasitis,becausethewordrobustkeepsthelevelofvocabulary
withinthepassageatanappropriatelyhighlevel.
Question 11 asksaboutthepreviouspassageasawhole.
Thinkaboutthepreviouspassageasawholeasyouanswerquestion11.
11. Thebestplacementforparagraph5wouldbeA) whereitisnow.B) beforeparagraph1.C) afterparagraph2.D) afterparagraph3.
WRITINGANDLANGUAGEDRILL4:ANSWERSANDEXPLANATIONS1. B Thequestionasksforthechoicethatpointsoutthepotentialconfusioninhowtounderstandthe
roleofgenre.Choice(A)impliesthataparadoxmightexistbutdoesnotpointitout;eliminate(A).Choices(C)and(D)donotdiscussgenreandarethereforeunrelated,soeliminate(C)and(D).Choice(B)isthecorrectanswer.
2. A Hereyouneedtofindtheanswerchoicethatisconsistentwiththegraph.Thegraphshowshowthenumbersofvampireandzombiefilmshaveincreasedsince1950.Choices(C)and(D)arenotconsistentwiththisinformation;eliminatethem.Zombiefilmshaveincreaseddramatically,fromabout10in1960toabout55in2000,whilevampiremovieswentfromabout15toabout40.Becausevampiremoviesdidnotincreasenearlysix-fold,eliminate(B).Choice(A)isthecorrectanswer.
3. B The question asks you to identify the correct transition between the paragraph about trendsinvolvingWestern,zombie,andvampiremoviesandthecurrentparagraph.Choice(A)doesnotaddress either paragraph, so eliminate (A). Choice (C)mentions zombiemovies, but not inrelation to the trends, so eliminate (C). Choice (D)mentions zombies but not in relation tomovies; get rid of (D). Choice (B) mentions the trends and introduces a discussion, and isthereforethecorrectanswer.
4. A Thequestionasksaboutdeletingthephraseindifferenteras.Thetopicoftheparagraphiswhydifferent genres dominated in different time periods, so the phrase is necessary to keep thissentenceconsistentwith theparagraph.Eliminate(C)and(D).Thephrase is important to themeaningofthesentence.Choice(A)iscorrect.
5. C Hereyou’relookingforthestatementthatsupportstheideaofAmericancrusade.Choice(A)containsanunrelated reference to theCatholicChurch; eliminate (A).Choice (B) relates theinformation to today,which is not the time period in question, so eliminate (B).Choice (D)contains unrelated information about the stock market crash that happened years later, soeliminate (D).Choice (C)mentions the postwarcrusadementioned in the previous sentenceandisthecorrectanswer.
6. D You’re looking for an alternate form of punctuation that would not be acceptable. Since theoriginalunderlinedportioncontainsaperiod,theideasbeforeandafterthepunctuationmustbecomplete.Therefore, replacing aperiodwith a comma-conjunctionpair orwith a semicolonwouldbeacceptable.Eliminate(A)and(C).Choice(B)makesuseofthecolon,whichcanbeusedbetweentwocompleteideas.Choice(B)isacceptable,soeliminate(B).Choice(D)usesacommawithoutoneoftheFANBOYSinplaceofstoppunctuation,sothisisincorrect.Choice(D)isthecorrectanswer.
7. C Thequestionasksforthemosteffectivewaytocombinethesentences.Because(A)repeatsthephrase never change, eliminate (A), as it is not concise. Choice (B) includes the phrasebecauseofit,buttheuseoftheambiguouspronounitnullifiesthischoiceaswell.Choice(D)
addsthephrasetooutsideobservers,whichisneithernecessarynorconcise.Thus,(C)isthemostconciseoptionandisthecorrectanswer.
8. D This question asks whether a statement about the author’s personal favorite zombie movieshould be included in the paragraph. The essay is about the overall trends and changesregardingmoviegenres,notsomeone’spersonalpreferences.Becauseitisnotconsistentwiththe topicof thepassage, donot add the sentence.Eliminate (A) and (B).The reason fornotadding thesentence isnot related to thechoiceofmovie,but rather to theunrelatedfocusonpersonalpreference.Thecorrectansweris(D).
9. B Hereyou’relookingfortheoptionthatisleastacceptablewhenusedinplaceofviewedinthephraseviewedasamass.Taken,seen,andregardedwouldallhaveameaningconsistentwiththe intendedmeaning in the sentence.Espied,while related to theverbsview and see, has adifferent meaning. Espy means “to spot” or “to catch sight of” something, which is notconsistentwiththemeaningoftheotherverbshere.Eliminate(A),(C),and(D).Choice(B)isthecorrectanswer.
10. C Thequestionasksifrobustshouldbechangedtohealthytodescribeonlinepersonalities.Thesentencedescribestheexcitementofonlinepersonalitiesasthereasonpeoplefeelreallifeisdull.Healthywouldnotmakethesamepoint,andthemeaningwouldnotbeconsistentwiththerestoftheparagraph.Keeprobust.Eliminate(A)and(B).Thereasonforkeepingtheoriginalwordhasnothingtodowiththelevelofdifficultyofthevocabulary,justtheconsistentmeaningofthepassage.Eliminate(D).Choice(C)iscorrect.
11. D Thisquestionsasksabouttheplacementoftheparagraph,whichdiscusseshowcontemporaryconflictsofthe1990sand2000srelatetothepopularityofparticulargenres.Thisissimilartoparagraph3,whichdiscusseshowtheAmericancrusaderelatedtothepopularityofWesternsin the 1920s. Therefore, paragraph 5 should be placed after paragraph 3.Choice (D) is thecorrectanswer.
Summary◦ ThemostimportantthingtorememberaboutWritingandLanguagequestionsisthatyoumustnotice
thosequestionsandthenanswerthosequestions.Don’tmissoutonsomeoftheeasiestpointsonthewholetestbynotreadingcarefullyenough.
◦ Alwaysanswerquestionsinthemostprecisewaypossible.
◦ When answering consistency questions, keep this general rule in mind: Writing and Languagepassages should be judgedonwhat theydo say, not onwhat they could say.When dealingwithstyle,tone,andfocus,workwiththewordsandphrasesthepassagehasalreadyused.
◦ TherewillbechartsorgraphsontheWritingandLanguageTest,butdon’t let thatthrowyouoff.Justreadthegraphswithasmuchprecisionasyouwouldapassageandchoosethemostpreciseanswerspossible.
PartIVHowtoCracktheMathTest10 SATMath:TheBigPicture11 FunwithFundamentals12 Algebra:CrackingtheSystem13 OtherAlgebraStrategies14 AdvancedArithmetic15 FunctionsandGraphs16 Geometry17 Grid-Ins
AFEWWORDSABOUTSATMATHAswe’vementionedbefore,theSATisn’tyourtypicalschooltest.ThisalsogoesfortheMathsectionsofthe SAT. There are two types of questions that you’ll run into: multiple-choice and student-producedresponsequestions.We’vealreadydiscussedmultiple-choicequestions,solet’stalkaboutthesestrangequestions known as student-produced response questions. These questions are the only non-multiple-choice questions on the SAT other than the essay. Instead of selecting the correct answer from amongseveralchoices,youwillhavetofindtheansweronyourownandmarkitinagrid(whichiswhywecallthemGrid-Ins).TheGrid-InquestionsontheSATwillbedrawnfromarithmetic,algebra,andgeometry,just likethemultiple-choicemathquestions.However, thegrid-informathasspecialcharacteristics,sowewilltreatthesequestionsabitdifferently.You’lllearnmoreaboutthemlaterinthisbook.
WhatDoestheSATMathTestMeasure?ETS and theCollegeBoard say that theMathTest covers “allmathematical practices,”with a strongfocus on problem solving, using tools appropriately, and using structure to manipulate expressions.Fortunatelyforyou,thereisnowayonetestcancoverallmathematicalconcepts.TheSATMathTestisactuallyabrieftestofarithmetic,algebra,andabitofgeometry—whenwesaya“bit,”wemeanit.Thereareonly6geometryquestionsatmostonthetest.We’llshowyouwhichgeometryconceptsareimportant.WewillalsogiveyouthetoolsyouneedtodowellontheMathTestasawhole,andtheskills tousethosetoolsappropriately.
OrderofDifficultyThe questions in both sections of theMathTest (NoCalculator andCalculator), including theGrid-Inquestions,arearrangedinalooseorderofdifficulty.Theearlierquestionsaregenerallyeasierandthelastfewareharder,butthelevelofdifficultymayjumparoundalittle.Also,“hard”ontheSATmeansthat a higher percentage of students tend to get itwrong, often due to careless errors or lack of time.Becausedifficultylevelscangoupanddownabit,don’tworrytoomuchabouthowhardthetestwritersthinkaquestionis.Focusinsteadonthequestionsthatareeasiestforyou,anddoyourbesttogetthoserightbeforemovingontothetougherones,nomatterwheretheyappear.
YouDon’tHavetoFinishWe’veallbeentaughtinschoolthatwhenyoutakeatest,youhavetofinishit.Ifyouansweredonlytwo-thirdsofthequestionsonahighschoolmathtest,youprobablywouldn’tgetaverygoodgrade.Butaswe’vealreadyseen,theSATisnotatalllikethetestsyoutakeinschool.Moststudentsdon’tknowaboutthedifference,sotheymakethemistakeofdoingalloftheproblemsonbothMathsectionsoftheSAT.
Becausetheyhaveonlyalimitedamountoftimetoanswerallthequestions,moststudentsrushthroughthequestionstheythinkareeasytogettotheharderonesassoonaspossible.Atfirst,itseemsreasonabletosavemoretimeforthemorechallengingquestions,butthinkabouthowthetestisscoredforaminute.Allcorrectanswersareworththesameamount,nomatterhowdifficulttheyareorhowlongtheytaketoanswer. Sowhen students rush through aMath Test, they’re actually spending less time on the easierquestions(whichtheyhaveagoodchanceofgettingright),justsotheycanspendmoretimeontheharder
questions(whichtheyhaveverylittlechanceofgettingright).Doesthismakesense?Ofcoursenot.
Here is thesecret:On theMathTest,youdon’thave toanswereveryquestion ineachsection. In fact,unlessyouareaimingforatopscore,youshouldintentionallyskipsomeharderquestionsineachsection.MoststudentscanraisetheirMathscoresbyconcentratingoncorrectlyansweringallofthequestionsthattheyfindeasyandmedium.Inotherwords…
SlowDown!Most students do considerably better on the Math Test when they slow down and spend less timeworrying about the more complex questions (and more time working carefully on the morestraightforward ones). Haste causes careless errors, and careless errors can ruin your score. In mostcases, you can actually raise your score by answering fewer questions.That doesn’t sound like a badidea,doesit?Ifyou’reshootingforan800,you’llhavetoanswereveryquestioncorrectly.Butifyourtargetis550,youshouldignorethehardestquestionsineachsectionanduseyourlimitedtimewisely.
QuickNoteRemember,thisisnotamathtestinschool!Itisnotscoredonthesamescaleyourmathteacheruses.Youdon’tneedto
getallthequestionsrighttogetanabove-average
score.
CalculatorsCalculators are permitted (but not required) on Section 4 of the SAT. You should definitely take acalculatortothetest.Itwillbeextremelyhelpfultoyouonmanyquestions,aslongasyouknowhowandwhen to use it and don’t get carried away. In this book, questions that would likely appear in theCalculatorsectionwillhaveacalculatorsymbolnexttothem.If thereisnosymbolbyaquestion,it ismorelikelytobefoundintheNoCalculatorsectionofthetest.We’lltellyoumoreaboutcalculatorsaswegoalong,aswellasteachyouhowtomanagewithoutit.
ThePrincetonReviewApproachWe’regoingtogiveyouthetoolsyouneedtohandletheeasierquestionsontheMathsection,alongwithseveralgreattechniquestohelpyoucracksomeofthemoredifficultones.Butyoumustconcentratefirston getting the easier questions correct.Don’tworry about the questions you find difficult on theMathsectionsuntilyou’velearnedtoworkcarefullyandaccuratelyontheeasierquestions.
Whenitdoescometimetolookatsomeoftheharderquestions,useProcessofEliminationtohelpyouavoidtrapanswersandtonarrowdownyourchoices ifyouhavetoguess.Justasyoudid in theothersectionsofthetest,you’lllearntousePOEtoimproveyouroddsoffindingtheanswerbygettingridofanswerchoicesthatcan’tpossiblybecorrect.
Generally speaking, each chapter in this section beginswith the basics and then graduallymoves intomoreadvancedprinciplesandtechniques.Ifyoufindyourselfgettinglosttowardtheendofthechapter,
Chapter10SATMath:TheBigPictureIn this chapter,we’ll see a fewwaysyoucaneliminatebadanswer choices, avoid traps, improve theoddsifyouhavetoguess,andmaximizeyourMathscore.We’llalsoteachyouhowtobestmakeuseofyourcalculator,whenitispermitted,andhowtogetalongwithoutit.
25. Joyplantsthreerowsofcorninhergarden.Therowonthesouthedgeofthegardenreceivesmoresunlightthantherowonthenorthedgeofthegarden.Therefore,thecornonthenorthedgeofthegardenis30%shorterthanthatonthesouth.Ifthecornonthesouthedgeofthegardenis50inchestall,howtallisthecornonthenorthedgeofthegarden,ininches?
THEBIGPICTUREIntheReadingsectionofthisbook,youlearnedaboutvariouswaystoeliminatewronganswersonhardquestions. Well, that idea comes into play on the SATMath Test as well. This chapter provides anoverviewofthestrategiesyoushouldknowtomaximizeyourMathscore,aswellassometipsonhowtouseyourcalculatorwisely(andhowtoworkwithoutit!).
BallparkingOnewaytoeliminateanswersontheMathTestisbylookingforonesthatarethewrongsize,orthatarenot “in the ballpark.”We call this strategyBallparking. Although you can use your calculator on thefollowingquestion,youcanalsoeliminatewithoutdoinganycalculations.
A) 30B) 33C) 35D) 65
Here’sHowtoCrackItThequestionstatesthatthecornonthenorthedgeisshorterthanthecornonthesouthedge,whichis50inchestall.Youareaskedtofindtheheightofthecornonthenorthedge,sothecorrectanswermustbelessthan50.Eliminate(D),whichistoohigh.Often,oneormoreofthebadanswersonthesequestionsistheresultyouwouldgetifyouappliedthepercentagetothewrongvalue.Tofindtherightanswer,take30%of50bymultiplying0.3by50toget15,thensubtractthatfrom50.Thecornonthenorthedgewouldbe35inchestall,whichis(C).
ReadtheFullQuestionYouneverknowwhataquestionisgoingtoaskyoutodo,somakesuretoalwaysReadtheFullQuestionbeforesolving.Underlinewhatyouareactuallysolvingforandanykeywordsyouthinkyoumightforgetaboutasyousolvethequestion.Then,trytoBallparkbeforeyousolve.
7. If16x−2=30,whatisthevalueof8x−4?A) 12B) 15C) 16D) 28
MasterSATMathAcingthemathsectionallcomesdowntostrategy,includingoneslikeRead
theFullQuestion(RTFQ).Formorestrategiesandtips,checkoutthevideosavailableintheyouronline
PremiumPortal.
Here’sHowtoCrackItFirst,seeifyoucaneliminateanswersbyBallparking,whichcanalsoworkonalgebraquestions.Togofrom 16x to 8x, you would just divide by 2. Dividing 30 by 2 gives you 15, so 28 is way too big.Eliminateit.Thecorrectanswerisnotlikelytobe15,either,becausethatignoresthe–2andthe–4inthequestion.
Tosolvethisone,add2toeachsideoftheequationtoget16x=32.Dividebothsidesby2,whichgivesyou8x=16.Butdon’tstopthere!Thefullquestionasksfor8x−4,so(C)isatrapanswer.Youhavetotakethelaststepandsubtract4frombothsidestofindthat8x−4=12,whichis(A).
OnePieceataTimeWhendealingwith complicatedmathproblems, take it one little piece at a time.We call this strategyBite-SizedPieces.Ifyoutrytodomorethanonestepatatime,especiallyifyoudoitinyourhead,youarelikelytomakemistakesorfallfortrapanswers.Aftereachsteptakealookattheanswerchoicesanddeterminewhetheryoucaneliminateany.
Trythefollowingquestion.
9. Apaperairplaneisthrownfromthetopofahillandtravelshorizontallyat9feetpersecond.Iftheplanedescends1footforevery3feettravelledhorizontally,howmanyfeethastheplanedescendedafter5secondsoftravel?A) 3B) 10C) 15D) 20
Here’sHowtoCrackItThereareafewthingsgoingonhere.Theplaneistravelinghorizontally,anditisalsodescending.Startbyfiguringouthowfarittravelshorizontally.Itmovesinthatdirectionat9feetpersecondfor5seconds,soitmoveshorizontally9×5=45feet.Itdescends1footforevery3traveledhorizontally.Ifitgoes45feethorizontally,itwilldescendmorethan3feet,soeliminate(A).Nowfigureouthowmany“3feet”arein45feet—foreachoneofthem,theplanewilldescend1foot.45÷3=15,sotheplanedescends15feet,(C).
Youmayalsohavenoticed thatall thenumbers in thequestionareodd.Thismakes itunlikely that theanswer would be 10 or 20, which are even. If you see things like that, use them as opportunities toeliminate.
Here’sanotherexample.
6. (5jk2+5j2−2j2k)−(jk2+2j2k+5j2)
Whichofthefollowingisequivalenttotheexpressionabove?A) 4jk2
B) 4jk2−4j2kC) 5j2k4−10j4kD) 8j2k3+7j2k−5j2
Here’sHowtoCrackItStart with one tiny piece of this ugly-looking question. The first set of parentheses startswith a termcontaining jk2. Check in the second set of parentheses for the same combination of variables andexponents.Thefirsttermtherematches,sothefirststeptotakeis5jk2−jk2=4jk2.Therearenoothertermswithjk2,sothecorrectanswermustcontain4jk2.Eliminate(C)and(D).Nowyouhaveafifty-fiftychanceofgettingitright,soyoucanguessandgo,oryoucandoonemoresteptodetermineiftheansweris (A)or (B).Thedifferencebetween the twoanswers is the−4j2k term,so focuson the terms in the
expressionthatcontainj2k.Inthefirstsetofparentheses,youhave−2j2k,andthenyousubtractthe2j2kterminthesecondsetofparentheses.−2j2k−2j2k=−4j2k,sothecorrectansweris(B).
WriteStuffDownAsyousolvequestionsinsmallpieces,writedownthesteps.Don’tkeeptrackofthingsinyourhead—yourtestbookletisthereforyournotes.Ifafigureisgiven,writetheinformationfromthequestionrightonit.
Here’sanexample.
12.
Lineslandmextendfromtwosidesoftheregularhexagonasshownabove.IfA=120,whatisthevalueofB,indegrees?A) 30B) 60C) 90D) 140
Here’sHowtoCrackItSometimesBallparkingcanevenhelpongeometryquestions.Notallpicturesaredrawntoscale,sodon’tassumethefigureisexact.Youcan,however,usewhatthequestiontellsyouaboutthefiguretoestimate
angles,linelengths,areas,andpointsongraphsinthexy-plane.
Ifthepreviousfigureisdrawntoscale,theanglewithmeasurementBappearstobeacute,making(A)or(B)agoodbet.Thequestionsaysthehexagonis“regular,”whichmeansthatalltheinteriorangleshavethesamemeasure,andthedrawinglookslikethisisthecase.StartbymarkingtheanglethatisA°as120°onthefigure.Thisanglelookslike120°,soBcan’tpossiblyequal90°or140°.Eliminate(C)and(D).TofindtheexactvalueofB,youneedtofindthemeasureof theangleopposite it,whichisoneof theanglesfromthetriangle.Theangleoftheupper-leftcornerofthetriangleisformedbydrawingastraightlinefromtheanglethatisA°,or120°.Thereare180°inastraight line,so theupper-leftcornerof thetrianglemeasures180−120=60°.Labelthismeasureonthefigureaswell.Thefactthatthehexagonisregularmeans that all the interior angles are 120°, so label the angle next to the bottom corner of thetriangle.Sincethiscornerofthetriangleisformedinthesamewayastheupper-leftcorner,thebottomcorneralsomeasures60°.Labelit.Thereare180°inatriangle,sotheupper-rightangleisalso60°.TheanglemeasuringB°isoppositethis,soBis60°and(B)iscorrect.
Bythetimeyou’redone,yourfigureshouldlooklikethis:
THECALCULATORAs you already know, theMath Test is divided into a shorter section in which calculator use is notpermitted(Section3)andalongersectioninwhichitispermitted(Section4).Thisaffectsthewayyoudothequestionsineachofthesesections.TheNoCalculatorsectionwillleanmoretowardfluencyandunderstandingofmathematicalconcepts,butthatdoesn’tmeanyouwon’thavetocalculateanything.OntheCalculator section, using the calculator is not always helpful. In this book, if you see a calculator
symbolnexttoaquestion,itmeansyoumayuseyourcalculatorasneededtoarriveattheanswer.Ifthereisnocalculatorsymbolnexttoaquestion,leavethatcalculatoralone!Therestofthischapterwillgiveyougeneralinformationabouthowtouseyourcalculatorwhenyoucanandwhattodowhenyoucan’t.OtherMathchapterswillprovideinformationaboutusingyourcalculatorinspecificsituations.Evenifyounowuseacalculatorregularlyinyourmathclassatschool,youshouldstillreadthischapterandtheotherMathchapterscarefullyandpracticethetechniqueswedescribe.
Section3:NoCalculatorETS and the College Board say that the purpose of the No Calculator section is to test your“fluency”and“conceptualunderstanding”ofmath topics.Whileyoumayhave to rearrange someterms and do some manipulation to answer questions correctly, you won’t be expected to doanythingtoocrazy,likecalculate tothreedecimalplaces—sohavenofear!
You’llneed to takeyourowncalculator to the testingcenter.Makesure thatyourcalculator iseitherascientific or a graphing calculator and can perform the order of operations correctly. To test yourcalculator,trythefollowingproblem,typingitinexactlyaswrittenwithouthittingtheENTERor“=”keyuntiltheend:3+4×6=.Thecalculatorshouldgiveyou27.Ifitgivesyou42,it’snotagoodcalculatortouse.
Section4:CalculatorAcalculatorcanbeanobstacleattimes.Thetestwritershavedesignedthissectionofthetestinthehopesofassessingyour“appropriateuseoftools,”andtheyfreelyadmitthatacalculatorcanslowyoudownon someof thequestions.So, by allmeans, use that calculator if youneed it to avoidmakingcarelesserrors,butdon’tforgetthatusingyourbrainandpencilcanbeafasterwaytogettotherightanswer.
Manystudentsalreadyownagraphingcalculator.Ifyouhaveone,great;ifyoudon’t,don’tsweatit.AgraphingcalculatorisnotnecessaryfortheSAT,thoughitmayhelpsimplifycertaingraphingproblems.
Ifyoudodecidetouseagraphingcalculator,keepinmindthatitcannothaveaQWERTY-stylekeyboard(like theTI-95).Mostof thegraphingcalculatorshave typingcapabilities,butbecause theydon’thavetypewriter-stylekeyboards,theyareperfectlylegal.
Also,youcannotusethecalculatoronyourphone.Infact,ontestday,youwillhavetoturnyourphoneoffandputitunderneathyourseat.
TheonlydangerinusingacalculatorontheSATisthatyoumaybetemptedtouseitinsituationsinwhichitwon’thelpyou.Somestudentsbelievethattheircalculatorwillsolvemanydifficultiestheyhavewithmath.Itwon’t.
Thistypeofthinkingmayevenoccasionallycausestudentstomissaproblemtheymighthaveotherwiseansweredcorrectlyontheirown.Rememberthatyourcalculatorisonlyassmartasyouare.Butifyoupracticeandusealittlecaution,youwillfindthatyourcalculatorwillhelpyouagreatdeal.
WhataCalculatorIsGoodatDoingHereisacompletelistofwhatacalculatorisgoodatontheSAT:
• arithmetic• decimals• fractions• squareroots• percentages• graphs(ifitisagraphingcalculator)
We’lldiscussthecalculator’sroleinmostoftheseareasinthenextfewchapters.
CalculatorArithmeticAdding,subtracting,multiplying,anddividingintegersanddecimalsiseasyonacalculator.But,youneedtobe carefulwhenyoukey in thenumbers.Acalculatorwill onlygiveyouan incorrect answer to anarithmeticcalculationifyoupressthewrongkeys.
Themainthingtorememberaboutacalculatoristhatitcan’thelpyoufindtheanswertoaquestionyoudon’tunderstand. Ifyouwouldn’tknowhowtosolveaparticularproblemusingpencilandpaper,youwon’tknowhowtosolveitusingacalculatoreither.Yourcalculatorwillhelpyou,butitwon’ttaketheplaceofasolidunderstandingofbasicSATmathematics.
CalculatorsDon’tThinkforYou
Acalculatorcrunchesnumbersandoftensavesyouagreatdealoftimeandeffort,butitisnotasubstituteforyour
problem-solvingskills.
UseYourPaperFirstWhetherornotcalculatoruseispermitted,thefirststepshouldbetosetuptheproblemorequationonpaper; thiswill keep you fromgetting lost or confused.This is especially importantwhen solving theprobleminvolvesanumberofseparatesteps.Thebasicideaistousetheextraspaceinyourtestbooklettomakeaplan,andthenuseyourcalculatortoexecuteit.
Workingon scratchpaper firstwill alsogive you a recordofwhat youhavedone if you changeyourmind,runintotrouble,orloseyourplace.Ifyousuddenlyfindthatyouneedtotryadifferentapproachtoaproblem,youmaynothavetogoallthewaybacktothebeginning.Thiswillalsomakeiteasierforyoutocheckyourwork,ifyouhavetimetodoso.
WriteThingsDownYoupaidforthetest
booklet,somakethemostofit.Keeptrackofyourprogressthrougheach
problembywritingdowneachstep.
Don’tusethememoryfunctiononyourcalculator(ifithasone).Becauseyoucanuseyourtestbookletasscratchpaper,youdon’tneedtojugglenumberswithinthecalculatoritself.Insteadofstoringtheresultofacalculationinthecalculator,writeitonyourscratchpaper,clearyourcalculator,andmovetothenextstepoftheproblem.Acalculator’smemoryisfleeting;scratchpaperisforever.
OrderofOperationsIn thenextchapter,wewilldiscuss theproperorderofoperationswhensolvingequations that requireseveral operations to be performed. Be sure you understand this information, because it applies tocalculators as much as it does to pencil-and-paper computations. Youmay remember PEMDAS fromschool.PEMDASistheorderofoperations.You’lllearnmoreaboutitandseehowquestionsontheSATrequireyoutoknowtheorderofoperations.Youmustalwaysperformcalculationsintheproperorder.
FractionsMost scientific calculators have buttons that will automatically simplify fractions or convert fractionsfromdecimals.(Forinstance,ontheTI-81,TI-83,andTI-84,hitting“Math”andthenselectingthefirstoption,“Answer Fraction,”willgiveyouthelastanswercalculatedasafractioninthelowestterms.)Findoutifyourcalculatorhasthisfunction!Ifitdoes,youcanuseittosimplifymessyfractionsontheCalculatorsection.Thisfunctionisalsoveryusefulwhenyougetananswerasadecimal,buttheanswerchoicesgivenareallfractions.FortheNoCalculatorsection,youwillhavetobeabletodothesethingsbyhand,sopracticetheseskillsinthenextchapter.(ForGrid-Inquestions,itisnotnecessarytoreduceafraction to itssimplest formif it fits in thegrid,andthedecimalequivalentwillalsobeacceptedasacorrectanswer.)
BatteriesChangethebatteriesonyourcalculatoraweekbeforetheSATsothatyouknowyourcalculatorwon’trunoutofpowerhalfwaythroughthetest.Youcanalsobringextrabatterieswithyou,justincase.Althoughitisn’tverylikelythatthebatterieswillrunoutonyourcalculatoronthedayofthetest,itcouldhappen—soyouwanttobeprepared.
FINALWORDSONTHECALCULATORRememberthatthetestwritersaretryingtotestyourabilitytouseyourcalculatorwisely.Assuch,theyhavepurposelycreatedmanyquestionsinwhichthecalculatorisworthless.(Therearequestionsthatareso wordy and deceptive that reading carefully is a much more important skill than properly using acalculator.)SobesuretoReadtheFullQuestion—theremaybesomeserioussurprisesinthere.Finally,rememberthatonSection3youwon’tbeabletouseitatall.Practiceyourmathskillssothatyoucan
Summary◦ Lookforwaystoeliminateanswerchoicesthataretoobigortoosmall.Ballparkingcanhelpyou
find the right answerwithout extensive paper-and-pencil calculationswhen calculator use is notallowed.Evenwhenyoucanuseyourcalculator,Ballparkingcanhelpyouavoidtrapanswersandimproveyourchancesofgettingthequestionrightifyouhavetoguess.
◦ WhenBallparkinganswersongeometryquestions,useabitofcaution.Thefiguresarenotalwaysdrawntoscale.Usethegiveninformationtodetermineifyoucantrustyourfigurebeforeusingittoeliminateanswers.
◦ Afteryou’vesetuptheproblemonthepage,youshoulddefinitelyusethecalculatorwhenallowedtoavoidcarelessmistakesfromdoingmathinyourhead.
◦ Take your own calculator when you take the test. You don’t need a fancy one.Make sure yourcalculatordoesn’tbeeporhaveatypewriter-stylekeyboard.
◦ Evenifyoualreadyuseacalculatorregularly,youshouldstillpracticewithitbeforethetest.
◦ Becarefulwhenyoukeyinnumbersonyourcalculator.Checkeachnumberonthedisplayasyoukeyitin.Clearyourworkafteryoufinisheachproblemoraftereachseparatestep.
◦ Acalculatorcan’thelpyoufindtheanswertoaquestionyoudon’tunderstand.(It’sonlyassmartasyouare!)Besuretouseyourcalculatorasatool,notacrutch.
◦ Setup theproblemor equationonpaper first.Bydoing so, youwill eliminate thepossibilityofgettinglostorconfused.
◦ Don’tusethememoryfunctiononyourcalculator(ifithasone).Scratchpaperworksbetter.
◦ Whetheryouareusingyourcalculatororpaperandpencil,youmustalwaysperformcalculationsintheproperorder.
◦ Ifyourcalculator runsonbatteries,makesure ithas freshonesat test time!Change themaweekbefore.
◦ MakesureyourmathskillsaresolidsoyoucantacklequestionsintheNoCalculatorsectionwithconfidence.
Chapter11FunwithFundamentalsAlthoughwe’llshowyouwhichmathematicalconceptsaremostimportanttoknowfortheSAT,thisbookreliesonyourknowledgeofbasicmathconcepts.Ifyou’realittlerusty,though,thischapterisforyou.Readonforaquickreviewofthemathfundamentalsyou’llneedtoknowbeforeyoucontinue.
THEBUILDINGBLOCKSAsyougo through this book, youmight discover that you’re having troublewith stuff you thought youalreadyknew—like fractions or square roots. If this happens, it’s probably a good idea to review thefundamentals.That’swherethischaptercomesin.Ourdrillsandexampleswillrefreshyourmemoryifyou’vegottenrusty.AlwayskeepinmindthatthemathtestedontheSATisdifferentfromthemathtaughtinschool.Ifyouwanttoraiseyourscore,don’twastetimestudyingmaththattheSATnevertests.
Let’stalkfirstaboutwhatyoushouldexpecttoseeonthetest.
THEMATHBREAKDOWNTheSATincludestwoscoredMathsections:oneonwhichcalculatoruseisallowedandoneonwhichitis not. The No Calculator section, or Section 3, is 25 minutes long and includes 20 questions. TheCalculatorsection,orSection4,is55minuteslongandincludes38questions.
NoNeedtoKnowHereareafewthingsyou
won’tneedtoknowtoanswerSATmathquestions:
calculus,logarithms,matrices,andgeometricproofs.Essentially,theSATtestsawholelotofalgebraandsome
arithmetic,statistics,andgeometry.
AccordingtoETSandtheCollegeBoard,theMathquestionsontheSATfallintothefollowingcleverlynamedcategories:
1. HeartofAlgebra2. PassporttoAdvancedMath3. ProblemSolvingandDataAnalysis4. AdditionalTopics
Thefirstthreewillgiveyousomeofyourtestsubscores,butthenamesofallfourcategoriesdon’treallymeananything.Thisiswhatwillreallybetested:
1. AlgebraIandII2. Arithmetic/Probability/DataAnalysis3. PlaneGeometry/CoordinateGeometry/Trigonometry
That’sit!Ofthesecategories,AlgebramakesupthemajorityoftheMathTest,accountingformorethanhalfofthequestions.PlaneGeometryandTrigonometrymakeupthesmallestpart—therewillonlybeamaximumof6questionsfromthatcategoryontheSAT.
TheMathquestionsonyourSATwillappearintwodifferentformats:
1. Regularmultiple-choicequestions2. Grid-Ins
TheGrid-InswillappearattheendofeachMathsection:5questionsintheNoCalculatorsectionand8questionsintheCalculatorsection.(SeeChapter17formoreontheGrid-Inquestions.)
THEINSTRUCTIONSBothoftheMathsectionsontheSATwillbeginwiththesamesetofinstructions.We’vereprintedtheseinstructions,justastheyappearontheSAT,intheMathsectionsofthepracticetestsinthisbook.Theseinstructionsincludeafewformulasandotherinformationthatyoumayneedtoknowinordertoanswersomeofthequestions.Youshouldlearntheseformulasaheadoftimesoyoudon’thavetowastevaluabletimeflippingbacktothemduringthetest.
Still, ifyoudosuddenlyblankoutononeof theformulaswhile taking the test,youcanalwaysrefreshyourmemorybyglancingbackat the instructions.Besure to familiarizeyourselfwith them thoroughlyaheadoftime,soyou’llknowwhichformulasarethere.
STANDARDSYMBOLSThefollowingstandardsymbolsareusedfrequentlyontheSAT:
SYMBOL MEANING= isequalto≠ isnotequalto< islessthan> isgreaterthan≤ islessthanorequalto≥ isgreaterthanorequalto
THEREAREONLYSIXOPERATIONSThereareonlysixarithmeticoperationsthatyouwilleverneedtoperformontheSAT:
1. Addition(3+3)2. Subtraction(3−3)3. Multiplication(3×3or3•3)4. Division(3÷3or3/3)
5. Raisingtoapower(33)6. Findingasquareroot( )
Ifyou’relikemoststudents,youprobablyhaven’tpaidmuchseriousattentiontothesetopicssincejuniorhighschool.You’llneedtolearnaboutthemagainifyouwanttodowellontheSAT.Bythetimeyoutakethetest,usingthemshouldbeautomatic.All thearithmeticconceptsarefairlybasic,butyou’llhavetoknow themcold.You’ll also have to knowwhen andhow to use your calculator,whichwill be quitehelpful.
WhatDoYouGet?Youshouldknowthefollowingarithmeticterms:
• Theresultofadditionisasumortotal.• Theresultofsubtractionisadifference.• Theresultofmultiplicationisaproduct.• Theresultofdivisionisaquotient.• Intheexpression52,the2iscalledanexponent.
TheSixOperationsMustBePerformedintheProperOrderVeryoften,solvinganequationontheSATwillrequireyoutoperformseveraldifferentoperations,oneafter another. These operations must be performed in the proper order. In general, the problems arewritteninsuchawaythatyouwon’thavetroubledecidingwhatcomesfirst.Incasesinwhichyouareuncertain,youneedtorememberonlythefollowingsentence:
PleaseExcuseMyDearAuntSally;shelimpsfromlefttoright.
That’sPEMDAS,forshort.ItstandsforParentheses,Exponents,Multiplication,Division,Addition,andSubtraction. First, do any calculations inside the parentheses; then take care of the exponents; thenperformallmultiplicationanddivision,fromlefttoright,followedbyadditionandsubtraction,fromlefttoright.
Thefollowingdrillwillhelpyoulearntheorderinwhichtoperformthesixoperations.First,setuptheequationsonpaper.Then,useyourcalculatorforthearithmetic.Makesureyouperformtheoperationsinthecorrectorder.
DoItYourselfSomecalculators
automaticallytakeorderofoperationsintoaccount,
andsomedon’t.Either
way,youcanveryeasilygowrongifyouareinthehabitofpunching
inlonglinesofarithmeticoperations.Thesafe,smartwayistoclearthecalculatorafter
everyindividualoperation,performing
PEMDASyourself.Whencalculatoruseisnot
allowed,makesuretowriteoutallthestepsonyourpapertoavoid
carelesserrors.
DRILL1Solve each of the following problems by performing the indicated operations in the proper order.Answerscanbefoundonthispage.
1. 107+(109−107)=
2. (7×5)+3=
3. 6−3(6−3)=
4. 2×[7−(6÷3)]=
5. 10−(9−8−6)=
WhicheverComesFirst
Foradditionandsubtraction,solvefromleftto
right.Thesameistrueofmultiplicationand
division.Andremember:Ifyoudon’tsolvein
orderfromlefttoright,youcouldendupwith
thewronganswer!Example:
24÷4×6=24÷24=1wrong
24÷4×6=6x6=36right
ParenthesesCanHelpYouSolveEquationsUsingparenthesestoregroupinformationinSATarithmeticproblemscanbeveryhelpful.Inordertodothis,youneed tounderstandabasic lawthatyouhaveprobablyforgottensince thedayswhenyou lasttookarithmetic—theDistributiveLaw.Youdon’tneedtorememberthenameofthelaw,butyoudoneed
toknowhowtouseittohelpyousolveproblems.
TheDistributiveLawIfyou’remultiplyingthesumoftwonumbersbyathirdnumber,youcanmultiplyeachnumberinyoursumindividually.Thiscomesinhandywhenyouhavetomultiplythesumoftwovariables.
If a problemgives you information in “factored form”—a(b +c)—then you should distribute the firstvariablebeforeyoudoanythingelse.Ifyouaregiveninformationthathasalreadybeendistributed—(ab+ac)—thenyoushouldfactoroutthecommonterm,puttingtheinformationbackinfactoredform.VeryoftenontheSAT,simplydoingthiswillenableyoutospottheanswer.
Herearesomeexamples:
Distributive:6(53)+6(47)=6(53+47)=6(100)=600
Multiplicationfirst:6(53)+6(47)=318+282=600
Yougetthesameanswereachway,sowhygetinvolvedwithuglyarithmetic?IfyouusetheDistributiveLawforthisproblem,youdon’tevenneedtouseyourcalculator.
ThedrillonthefollowingpageillustratestheDistributiveLaw.
Drill2Rewriteeachproblembyeitherdistributingorfactoring(Hint:Forquestions1,2,4,and5,tryfactoring)and then solve.Questions3,4, and5havenonumbers in them; therefore, theycan’tbe solvedwith acalculator.Answerscanbefoundonthispage.
1. (6×57)+(6×13)=
2. 51(48)+51(50)+51(52)=
3. a(b+c−d)=
4. xy−xz=
5. abc+xyc=
FRACTIONS
AFractionIsJustAnotherWayofExpressingDivision
Theexpression isexactlythesamethingasx÷y.Theexpression meansnothingmorethan1÷2.In
thefraction ,x isknownasthenumerator (hereafter referred toas“the top”),andy isknownas the
denominator(hereafterreferredtoas“thebottom”).
FractionsandYourCalculatorWhen calculator use is not allowed, be sure to write out all the steps on your paper to avoidcareless errors. When calculator use is allowed, you can use your calculator to solve fractionproblems.When you do, ALWAYS put each of your fractions in a set of parentheses. This willensurethatyourcalculatorknowsthattheyarefractions.Otherwise,theorderofoperationswillgetconfused.Onascientificcalculator,youcanwritethefractionintwodifferentways:
1. Youwillhaveafractionkey,whichlookssimilarto“a .”Ifyouwantedtowrite ,
you’dtype“5a 6.”
2. Youcanalsousethedivisionkey,becauseafractionbaristhesameas“dividedby.”Be
awarethatyouranswerwillbeadecimalforthissecondway,sowerecommendthefirst.
Onagraphingcalculator,you’llusethedivisionbartocreatefractions.Keepinmindthat,whatevercalculator you are using, you can always turn your fractions into decimals before you performcalculationswiththem.Justbeawarethattheanswerwon’talwaysbeexact.
AddingandSubtractingFractionswiththeSameBottomToaddtwoormorefractionsthatallhavethesamebottom,simplyaddthetopsandputthesumoverthecommonbottom.Considerthefollowingexample:
Subtractionworksexactlythesameway:
AddingandSubtractingFractionswithDifferentBottoms
Inschoolyouweretaughttoaddandsubtractfractionswithdifferentbottoms,ordenominators,byfindingthecommondenominator.Todothis,youhavetomultiplyeachfractionbyanumberthatmakesall thebottomsthesame.Moststudentsfindthisprocessannoying.
Fortunately, we have an approach to adding and subtracting fractions with different bottoms thatsimplifies theentireprocess.Use theexamplebelowasamodel.Justmultiply in thedirectionofeacharrow,andtheneitheraddorsubtractacrossthetop.Lastly,multiplyacrossthebottom.
WecallthisproceduretheBowtiebecausethearrowsmakeitlooklikeabowtie.UsetheBowtietoaddorsubtractanypairof fractionswithout thinkingabout thecommonbottom, justby following thestepsabove.
CalculatingFractions
Let’ssayyouwantedtofind + =usingyourcalculator.Forascientificcalculator,you’dtypein
“(1a 3)+(1a 2)=”Theanswerwillcomeuplookinglikesomethingsimilar to5|6,which
means 5/6. On a graphing calculator, you’d type in (1/3) + (1/2) [ENTER]. This gives you the
repeating decimal .833333. Now hit the [MATH] button and hit the [>FRAC] button and press
[ENTER].Thecalculatorwillnowshow“5/6.”Theshortcuttoturnadecimalintoafractionona
TI-80seriesgraphiccalculatoris[MATH][ENTER][ENTER].Rememberthoseparenthesesforall
fractioncalculations!
MultiplyingAllFractions
Multiplyingfractionsiseasy.Justmultiplyacrossthetop;thenmultiplyacrossthebottom.
Here’sanexample:
Whenyoumultiplyfractions,allyouarereallydoingisperformingonemultiplicationproblemontopofanother.
You shouldnevermultiply two fractionsbefore looking to see if youcan reduce eitherorboth. If youreducefirst,yourfinalanswerwillbeintheformthatthetestwritersarelookingfor.Here’sanotherwaytoexpressthisrule:Simplifybeforeyoumultiply.
DividingAllFractionsTodivideonefractionbyanother,flipover(orinvert)thesecondfractionandmultiply.
Here’sanexample:
JustFlipItDividingbyafractionis
thesamethingasmultiplyingbythereciprocalof
thatfraction.Sojustflipoverthefractionyouaredividingbyandmultiplyinstead.
Becarefulnottocancelorreduceuntilafteryouflipthesecondfraction.Youcanevendothesamethingwithfractionswhosetopsand/orbottomsarefractions.Theseproblemslookquitefrighteningbutthey’reactuallyeasyifyoukeepyourcool.
Here’sanexample:
ReducingFractionsWhenyouaddormultiplyfractions,youwillveryoftenendupwithabigfractionthatishardtoworkwith.Youcanalmostalwaysreducesuchafractionintoonethatiseasiertohandle.
StartSmallItisnoteasytoseethat
26and286haveacommonfactorof13,butit’s
prettyclearthatthey’re
bothdivisibleby2.Sostartfromthere.
Toreduceafraction,divideboththetopandthebottombythelargestnumberthatisafactorofboth.Forexample, to reduce ,divideboth the topand thebottomby12,which is the largestnumber that isa
factorofboth.Dividing12by12yields1;dividing60by12yields5.Thereducedfractionis .
Ifyoucan’timmediatelyfindthelargestnumberthatisafactorofboth,findanynumberthatisafactorofbothanddivideboth the topandbottomby thatnumber.Yourcalculationswill takea little longer,butyou’llendupinthesameplace.Inthepreviousexample,evenifyoudon’tseethat12isafactorofboth12and60,youcannodoubtseethat6isafactorofboth.Dividingtopandbottomby6yields .Now
divideby2.Doingsoyields .Onceagain,youhavearrivedattheanswer.
FastReductionWhencalculatoruseis
allowed,reducingfractionscanbeprettyeasy.To
reducefractionsinyourscientificcalculator,just
typeinthefractionandhittheequalskey.Ifyouare
usingagraphingcalculator,typeinthefraction,find
the[>FRAC]function,andhitENTER.
ConvertingMixedNumberstoFractionsAmixednumberisanumbersuchas2 .Itisthesumofanintegerandafraction.Whenyouseemixed
numbersontheSAT,youshouldusuallyconvertthemtoordinaryfractions.
Here’saquickandeasywaytoconvertmixednumbers.
• Multiplytheintegerbythebottomofthefraction.• Addthisproducttothetopofthefraction.• Placethissumoverthebottomofthefraction.
Forpractice, let’sconvert to2 afraction.Multiply2(theintegerpartof themixednumber)by4(the
bottomofthefraction).Thatgivesyou8.Addthattothe3(thetopofthefraction)toget11.Place11over
4toget .
Themixednumber2 isexactlythesameasthefraction .Weconvertedthemixednumbertoafraction
becausefractionsareeasiertoworkwiththanmixednumbers.
DRILL3Tryconvertingthefollowingmixednumbers.Answerscanbefoundonthispage.
1. 8
2. 2
3. 5
4. 2
5. 6
JustDon’tMix
Forsomereason,thetest
writersthinkit’sokayto
giveyoumixednumbers
asanswerchoices.On
Grid-Ins,however,ifyou
useamixednumber,you
won’tgetcredit.Youcan
seewhy.InyourGrid-In
box,3¼willbegridded
inas31/4,whichlooks
like .
FractionsBehaveinPeculiarWaysFractions don’t always behave theway youmightwant them to. For example, because 4 is obviously
greaterthan2,it’seasytoforgetthat is lessthan . It’sparticularlyconfusingwhenthenumerator is
somethingother than1.Forexample, is less than .Finally,youshouldkeep inmind thatwhenyou
multiplyonefractionbyanother,you’llgetafractionthatissmallerthaneitherofthefirsttwo.Studythe
followingexample:
AFinalWordAboutFractionsandCalculatorsThroughoutthissection,we’vegivenyousomehintsaboutyourcalculatorandfractions.Ofcourse,youstillneedtounderstandhowtoworkwithfractionstheold-fashionedwayfortheNoCalculatorsection.OntheCalculatorsection,yourcalculatorcanbeatremendoushelpifyouknowhowtouseitproperly.Make sure that youpracticewith your calculator so thatworkingwith fractions on it becomes secondnaturebeforethetest.
RememberYourResources!
CheckouttheonlinevideosinyourPremiumPortalforextrahelpwithtest-takingstrategiesfor
theMathTest.
DRILL4
Work these problems with the techniques you’ve read about in this chapter so far. Then check youranswers by solving them with your calculator. If you have any problems, go back and review theinformationjustoutlined.Answerscanbefoundonthispage.
1. Reduce .
2. Convert6 toafraction.
3. 2 −3 =
4. × =
5. ÷ =
6. =
7. =
DECIMALS
ADecimalIsJustAnotherWayofExpressingaFractionFractionscanbeexpressedasdecimals.Tofindafraction’sdecimalequivalent,simplydividethetopbythebottom.(Youcandothiseasilywithyourcalculator.)
=
3÷5=0.6
Adding,Subtracting,Multiplying,andDividingDecimalsManipulatingdecimalsiseasywithacalculator.Simplypunchinthenumbers—beingespeciallycarefulto get the decimal point in the right place every single time—and read the result from the display.Acalculatormakestheseoperationseasy.Infact,workingwithdecimalsisoneareaontheSATwhereyourcalculatorwill prevent you frommaking careless errors.Youwon’t have to lineupdecimal points orrememberwhathappenswhenyoudivide.Thecalculatorwillkeeptrackofeverythingforyou,aslongasyoupunchinthecorrectnumberstobeginwith.Justbesuretopracticecarefullybeforetestday.
WhatcanyoudowhenthemathdecimalsgetuglyontheNoCalculatorsection?Neverfear—youcanstillanswerthesequestions.Justroundtheawkwardnumberstoonesthatareeasiertoworkwith.Aslongasyouaren’troundingthingstoofar,likerounding33to50,theanswersarelikelytobespreadfarenoughapartthatonlyoneormaybetwowillbeclosetoyourestimatedanswer.
DRILL5Calculate each of the answers to the following questions on paper with your pencil, rounding anyawkward numbers tomake themath easier to handle. Then check your answers with your calculator.Answerscanbefoundonthispage.
1. 0.43×0.87=
2. =
3. 3.72÷0.02=
4. 0.71−3.6=
ComparingDecimalsSomeSATproblemswill askyou todeterminewhetheronedecimal is largeror smaller thananother.Many students have trouble doing this, but you will do fine as long as you remember to line up thedecimalpointsandfillinmissingzeros.
PlaceValueComparedecimals
placebyplace,goingfromlefttoright.
Here’sanexample:
Problem:Whichislarger,0.0099or0.01?
Solution:Simplyplaceonedecimalovertheotherwiththedecimalpointslinedup,likethis:
0.00990.01
Tomakethesolutionseemclearer,youcanaddtwozerostotherightof0.01.(Youcanalwaysaddzerostotherightofadecimalwithoutchangingitsvalue.)Nowyouhavethis:
0.00990.0100
Whichdecimalislarger?Clearly,0.0100is,justas100islargerthan99.Rememberthat0.0099= ,
while0.0100= .
AnalysisWatch out for problems like this with decimals in the answers. Any time you encounter a probleminvolvingthecomparisonofdecimals,besuretostopandaskyourselfwhetheryouareabouttomakeacarelessmistake.
EXPONENTSANDSQUAREROOTS
ExponentsAreaKindofShorthandManynumbersaretheproductofthesamefactormultipliedoverandoveragain.Forexample,32=2×2×2×2×2.Anotherwaytowritethiswouldbe32=25,or“thirty-twoequalstwotothefifthpower.”Thelittlenumber,orexponent,denotesthenumberoftimesthat2istobeusedasafactor.Inthesameway,103=10×10×10,or1,000,or“tentothethirdpower,”or“tencubed.”Inthisexample,the10iscalledthebaseandthe3iscalledtheexponent.(Youwon’tneedtoknowthesetermsontheSAT,butyouwillneedtoknowtheminordertounderstandourexplanations.)
ExponentsandYourCalculatorRaisinganumbertoapowerisshownintwodifferentwaysonyourcalculator,dependingonthetypeofcalculatoryouhave.Ascientificcalculatorwillusetheyxbutton.You’llhavetotypeinyourbasenumberfirst,thenhittheyxkey,andthentypetheexponent.So43willbetypedinas“4yx3=”andyou’llget64.IfyouhaveacalculatorfromtheTI-80series,yourbuttonwillbea ̂sign.You’llenterthesameproblemas“4^3[ENTER].”Thinkofthesetwokeysasthe“tothe”button,becauseyousay“4tothe3rdpower.”
MultiplyingNumberswithExponentsWhenyoumultiplytwonumberswiththesamebase,yousimplyaddtheexponents.Forexample,23×25
=23+5=28.
Warning#1Therulesformultiplyinganddividingexponentsdonotapplytoaddition
orsubtraction:22+23=12
(2×2)+(2×2×2)=12Itdoesnotequal25or32.
DividingNumberswithExponents
Whenyoudividetwonumberswiththesamebase,yousimplysubtracttheexponents.Forexample, =
25−3=22.
RaisingaPowertoaPowerWhenyouraiseapowertoapower,youmultiplytheexponents.Forexample,(23)4=23×4=212.
Warning#2Parenthesesarevery
importantwithexponents,becauseyoumust
remembertodistributepowerstoeverything
withinthem.Forexample,(3x)2=9x2,not3x2.
Similarly, ,not
.ButtheDistributive
Lawappliesonlywhenyoumultiplyordivide.
(x+y)2=x2+2xy+y2,notx2+y2.
MADSPMToremembertheexponentrules,allyouneedtodoisremembertheacronymMADSPM.Here’swhatitstandsfor:
• Multiply→Add• Divide→Subtract• Power→Multiply
Wheneveryouseeanexponentproblem,youshouldthinkMADSPM.ThethreeMADSPMrulesaretheonlyrulesthatapplytoexponents.
Here’satypicalSATexponentproblem:
14. Fortheequations =a10and(ay)3=ax,ifa>1,whatisthevalueofx?
A) 5B) 10C) 15D) 20
Here’sHowtoCrackItThis problem looks pretty intimidating with all those variables. In fact, you might be about to cry“POOD”andgoontothenextproblem.Thatmightnotbeabadideabutbeforeyouskipthequestion,pulloutthoseMADSPMrules.
For the firstequation,youcanuse theDivide-SubtractRule: =ax−y=a10. Inotherwords, the first
equationtellsyouthatx−y=10.
Forthesecondequation,youcanusethePower-MultiplyRule:(ay)3=a3y=ax.So,thatmeansthat3y=x.
Now,it’stimetosubstitute:x−y=3y−y=10.So,2y=10andy=5.Becareful,though!Don’tchoose(A).That’s thevalueofy,but thequestionwants toknowthevalueofx.Sincex=3y,x=3(5)=15,whichis(C).
Ifcalculatorusewasallowedonthisone,youcouldalsodothisquestionbyPluggingintheAnswers,orPITA,whichwillbediscussed inmoredetail later in thisbook.Ofcourse,youstillneed toknow theMADSPMrulestodothequestionthatway.
ThePeculiarBehaviorofExponentsRaisinganumbertoapowercanhavequitepeculiarandunexpectedresults,dependingonwhatsortofnumberyoustartoutwith.Herearesomeexamples.
• Ifyousquareorcubeanumbergreaterthan1,itbecomeslarger.Forexample,23=8.• Ifyousquareorcubeapositivefractionsmallerthanone,itbecomessmaller.
Forexample, .
• Anegativenumberraisedtoanevenpowerbecomespositive.Forexample,(−2)2=4.• Anegativenumberraisedtoanoddpowerremainsnegative.Forexample,(−2)3=−8.
SeetheTrapThetestwritersmayhope
youwon’tknowthesestrangefactsabout
exponentsandthrowtheminastrapanswers.Knowing
thepeculiarbehaviorofexponentswillhelpyouavoidthesetrickypitfalls
inaquestion.
You should also have a feel for relative sizes of exponential numbers without calculating them. Forexample,210 ismuchlargerthan102.(210=1,024;102=100)Totakeanotherexample,25 is twiceaslargeas24,eventhough5seemsonlyabitlargerthan4.
SquareRootsThe radical sign indicates the squareroot of a number. For example, = 5.Note that squarerootscannotbenegative.Ifthetestwriterswantyoutothinkaboutanegativesolution,they’llsayx2=25becausethenx=5orx=−5.
TheOnlyRulesYouNeedtoKnowHerearetheonlyrulesregardingsquarerootsthatyouneedtoknowfortheSAT:
1. .Forexample, =6.
2. .Forexample, .
3. =positiverootonly.Forexample, =4.
Notethatrule1worksinreverse: = × =5 .Thisisreallyakindoffactoring.Youareusing
rule1tofactoralarge,clumsyradicalintonumbersthatareeasiertoworkwith.Rule2worksinreverse
aswell. dividedby looksugly,but = =5.Andrememberthatradicalsarejustfractional
exponents,sothesamerulesofdistributionapply.
CarelessErrorsDon’tmakecarelessmistakes.Rememberthatthesquarerootofanumberbetween0and1islargerthan
theoriginalnumber.Forexample, = ,and > .
RootsandYourCalculator
Anotherimportantkeyistherootkey.Onascientificcalculatoritisoftenthesamebuttonasyx,but
you’llhave tohit shift first.Thesymbol is .So“the4th rootof81”wouldbe“81 4= .”
Sometimes thecalculatorwillhaveyxor asxyor .Theymean thesame thing.Justknow
whichnumberyou’resupposedtotypeinfirst.
The root key in the TI-80 graphing calculator series varies, but themost common symbol is the
squarerootsign,whichyoucangettobypressing“[SHIFT]x2.”Incaseyouwanttofindthe3rd,
4th,orotherrootofanumber,thereisabuttoninthe[MATH]directoryfor or .Inthecase
ofthe ,youhave to type in therootyouwant, thenhit [MATH]and ,andfinallyhityour
basenumber.Forexample,ifyouwantedtofindthe4throotof81,you’dtype“4[MATH],”then
select ,thentype81andpress[ENTER].Ifyoulookatitonthescreen,itwillappearas“4
81,”whichissimilartohowyou’dwriteit.Youcanalsousethe ̂symbolifyourememberthata
root is the same as the bottom part of a fractional exponent. So the fourth root of 81would be
writtenas“81 ̂(1/4)”onyourcalculator.
NegativeandFractionalExponentsSofarwe’vedealtwithonlypositiveintegersforexponents,buttheycanbenegativeintegersaswellasfractions. The same concepts and rules apply, but the numbers just look a little weirder. Keep theseconceptsinmind:
• Negativeexponentsareafancywayofwritingreciprocals:
• Fractionalexponentsareafancywayoftakingrootsandpowers:
Here’sanexample:
14. Ifx>0,whichofthefollowingisequivalentto ?
I.
II.
III.
A) NoneB) IandIIonlyC) IIandIIIonlyD) I,II,andIII
Here’sHowtoCrackIt
Thisproblemreallytestsyourknowledgeofexponents.First,convert intoanexponent,sinceallof
the Roman numerals contain expressions with exponents. (Plus, exponents are easier to work with
becausetheyhavethoseniceMADSPMrules.)So,usingthedefinitionofafractionalexponent, =
.YouwanttheitemsintheRomannumeralstoequal .
Now, it’s timetostartworkingwith theRomannumerals. In(I), the testwritersare tryingtobe tricky.
(There’s a surprise.) There’s no exponent rule for adding exponent expressions with like bases. So,
doesnotequal .(Ifyouwanttobesure,youcouldtryanumberforx:Ifx=4,then =8,
but4+4 =4+2=6.)So,crossoffanyanswerthatincludes(I):(B)and(D)aregone.
Now,sinceyouaredowntoeither(A)or(C),allyoureallyneedtodoistryeither(II)or(III).Ifeither
oneworks,theansweris(C).So,try(II).UsethePower-MultiplyRule: = = .Since(II)
works,(C)isthecorrectanswer.
Noticethatyoudidn’tevenneedtocheck(III).UsingPOEonaRomannumeralquestionoftenmeansthatyouwon’tneedtocheckalloftheRomannumerals.
HOWTOREADCHARTSANDGRAPHSAnotherbasicmath skillyouwillneed for theSAT is theability to interpretdata fromcharts,graphs,tables,andmore.Thissectionwillcover thebasicsofreadingthesefigures.HowtoanswerquestionsrelatedtochartsandotherfiguresindetailwillbediscussedinChapter14.
MoreMathBasicsYoucangetmoreguidanceinthefundamentalsofSATmathandmathstrategies
bywatchingthevideosinyourPremiumPortal.See“RegisterYourBook
Online!”(thispage)formoreinformation.
What’sUpwithAllofTheseFigures?TheSATnow includes charts, graphs, and tables throughout the test (not just in theMath sections) topresent data for students to analyze. ETS and the College Board believe this will better reflect whatstudents learn in school andwhat they need to understand in the real world. Questionswill typicallyincludereal-lifescenarios,suchasfinanceandbusinesssituations,socialscienceissues,andscientificmatters.
Sinceyou’llbeseeinggraphicsthroughoutthetest,let’slookatthetypesyoumayencounterandtheskillsyou’llneedtoworkwithandanalyzechartsandgraphs.
TypesofGraphics
TheScatterplotAscatterplot is a graphwith distinct data points, each representing one piece of information.On thescatterplotbelow,eachdotrepresentsthenumberoftelevisionssoldatacertainpricepoint.
Here’sHowtoReadItTofindthecostofatelevisionwhen225televisionsaresold,startat225ontheverticalaxisanddrawa
9. Acertainstoresellstelevisionsranginginpricefrom$500to$5,000inincrementsof$500.Thegraphaboveshowsthetotalnumberoftelevisionssoldateachpriceduringthelast12months.Approximatelyhowmuchmorerevenuedidthestorecollectfromthetelevisionsitsoldpricedat$3,500thanitdidfromthetelevisionsitsoldpricedat$1,000?
horizontallinetotherightuntilyouhitadatapoint.Usetheedgeofyouranswersheetasastraight-edgeifyouhavetroubledrawingyourownstraightlines.Onceyouhitapoint,drawastraightlinedownfromthepointtothehorizontalaxisandreadthenumberthelinehits,whichshouldbe$1,500.Todeterminethenumberoftelevisionssoldwhentheycostacertainamount,reversethesteps—startatthebottom,drawupuntilyouhitapoint,thenmoveleftuntilyouintersecttheverticalaxis.
Nowtryanexample.
A) $175,000B) $250,000C) $275,000D) $350,000
Here’sHowtoCrackItTherevenue is thecostof television×numberof televisions sold.Youneed the information from thegraph only for the television that costs $3,500 and for the television that costs $1,000 in order todetermine how much more revenue the $3,500 television produced. There were 150 of the $3,500televisionssold,forarevenueof$525,000.Therewere250ofthe$1,000televisionssold,forarevenueof$250,000.Thedifferencebetweenthetwois$525,000−$250,000=$275,000,whichis(C).
A questionmay ask you to draw a line of best fit on a scatterplot diagram.This is the line that bestrepresentsthedata.Youcanusetheedgeofyouranswersheetasarulertohelpyoudrawalinethatgoesthroughmostofthedata.
TheLineGraphAlinegraphissimilartoascatterplotinthatitshowsdifferentdatapointsthatrelatethetwovariables.Thedifferencewithalinegraph,though,isthatthepointshavebeenconnectedtocreateacontinuousline.
2. TheforecastedmonthlysalesofAlwaysSunnySunscreenarepresentedinthefigureabove.Forwhichperiodaretheforecastedmonthlysalesfiguresstrictlydecreasingthenstrictlyincreasing?
Here’sHowtoReadItReading a line graph is very similar to reading a scatterplot. Start at the axis that represents the datagiven,anddrawastraightlineuportotherightuntilyouintersectthegraphline.Thenmoveleftordownuntilyouhit theotheraxis.Forexample, inFebruary, indicatedbyanFonthehorizontalaxis,AlwaysSunnysunscreenhad2.5millioninsales.Besuretonoticetheunitsoneachaxis.IfFebruarysaleswereonly$2.50,ratherthan$2.5million,thenthiscompanywouldn’tbedoingverywell!
Let’slookataquestionaboutthislinegraph.
A) JanuarytoMarchB) FebruarytoAprilC) JunetoAugustD) SeptembertoNovember
14. Thepopulationsoffivecountriesareshowninthegraphabove.Ifpopulationdensityisdefinedas ,andtheareaofParaguayis400,000squarekilometers,whatisthe
populationdensityofParaguay,inpeoplepersquarekilometer?
Here’sHowtoCrackItLookupthevaluesforeachperiodinquestionanduseProcessofEliminationtogetridofthosethatdon’tfit.For(A),Januarysalesareforecastedtobe$2million,February$2.5million,andMarch$2million.This is an increase followedby a decrease, not the otherway around, so eliminate (A). For (B), youalreadyknowsalesdecreasedfromFebruarytoMarch,socheckforafollowingincreaseinApril.ThefigureforAprilis$3.5million,whichisanincreaseovertheMarchfigure,so(B)iscorrect.
TheBarGraph(orHistogram)Insteadofshowingavarietyofdifferentdatapoints,abargraphwillshowhowmanyitemsbelongtoaparticularcategory.Ifthevariableatthebottomisgiveninrangesinsteadofdistinctitems,thegraphiscalledahistogram,butyoureaditthesameway.
Here’sHowtoReadItTheheightofeachbarcorrespondstoavalueontheverticalaxis.Inthiscase,thebaraboveChilehitsthelinethatintersectswith15ontheverticalaxis,sothereare15millionpeopleinChile.Again,watchtheunitstomakesureyouknowwhatthenumbersontheaxesrepresent.Onthisgraph,horizontallinesaredrawnat5unitintervals,makingthegrapheasiertoread.Iftheselinesdonotappearonabargraph,useyouranswersheettodeterminetheheightofagivenbar.
Abargraphquestionmightlooklikethis:
A) 0.08
B) 0.8C) 1.25D) 12.5
Here’sHowtoCrackItStartbydeterminingthepopulationofParaguay.Thebarhitsrightatthehorizontallinefor5,whichisinmillions,sothereare5millionpeopleinParaguay.Nowusethedefinitionofpopulationdensityinthequestion.
Beverycarefulwiththenumberofzeroesyouputinthefraction—theanswerchoicesarepairsthatvarybyafactorof10,meaningthetestwritersexpectyoutomissazero.Theanswermustbegreaterthan1,sinceyournumeratorisbiggerthanyourdenominator,soeliminate(A)and(B).Choice(C)alsoseemstoo small, but check the math on your calculator (carefully). You should get 12.5 people per squarekilometer,so(D)iscorrect.
TheTwo-WayTableA two-way table is another way to represent data without actually graphing it. Instead of having thevariablesrepresentedontheverticalandhorizontalaxes,thedatawillbearrangedinrowsandcolumns.Thetoprowwillgivetheheadingsforeachcolumn,andtheleft-mostcolumnwillgivetheheadingsforeach row.The numbers in each box indicate the data for the category represented by the row and thecolumntheboxisin.
ComputerProduction MorningShift AfternoonShift
Monday 200 375Tuesday 245 330Wednesday 255 340Thursday 250 315Friday 225 360
Here’sHowtoReadItIfyouwanttofindthenumberofcomputersproducedonTuesdaymorning,youcanstartintheMorningShiftcolumnandlookdownuntilyoufindthenumberintherowthatsays“Tuesday,”oryoucanstartintherowforTuesdayandlooktotherightuntilyoufindtheMorningShiftcolumn.Eitherway,theresultis245.Sometableswillgiveyoutotalsinthebottomrowand/ortheright-mostcolumn,butsometimesyou
3. Computerproductionatafactoryoccursduringtwoshifts,asshowninthechartabove.Ifcomputersareproducedonlyduringthemorningandafternoonshifts,onwhichofthefollowingpairsofdaysisthegreatesttotalnumberofcomputersproduced?
willneedtofindthetotalsyourselfbyaddingupallthenumbersineachroworineachcolumn.Morecomplicated tables will havemore categories listed in rows and/or columns, or the tables may evencontainextraneousinformation.
Givethisoneatry.
A) MondayandThursdayB) TuesdayandThursdayC) WednesdayandFridayD) TuesdayandFriday
Here’sHowtoCrackItThisisaperfectcalculatorquestion.JustaddtheMorningShiftandtheAfternoonShiftforeachdayandseewhichtotal is thegreatest.Writeeachtotaldownnexttothedayonthechart,soyoudon’thavetokeeptrackofitallinyourhead.Mondayis200+375=575,Tuesdayis245+330=575,Wednesdayis255+340=595,Thursday is 250+315=565, andFriday is 225+360=585.According to thesecalculations,WednesdayandFridayhavethetwogreatesttotals,sothegreatestnumberofcomputersisproducedonthosetwodaystogether,making(C)therightanswer.
FigureFactsEverytimeyouencounterafigureorgraphicontheSAT,youshouldmakesureyouunderstandhowtoreaditbycheckingthefollowingthings:
• Whatarethevariablesforeachaxisortheheadingsforthetable?• Whatunitsareusedforeachvariable?• Arethereanykeypiecesofinformation(numbers,forexample)inthelegendofthechartthatyou
shouldnote?• Whattypeofrelationshipisshownbythedatainthechart?Forinstance,ifthechartincludes
curvesthatshowanupwardslope,thenthegraphshowsapositiveassociation,whilecurvesthatshowadownwardslopeshowanegativeassociation.
• Youcanusetheedgeofyouranswersheetasarulertohelpyoumakesureyouarelocatingthe
FundamentalsDrill1:NoCalculatorSectionWork these questions without your calculator, using the skills you’ve learned so far. Answers andexplanationscanbefoundonthispage.
1. Whichofthefollowingrepresentsthestatement“thesumofthesquaresofxandyisequaltothesquarerootofthedifferenceofxandy”?A) x2+y2=
B) x2−y2=
C) (x+y)2= −
D) =(x−y)2
4. Ifa=−2,thena+a2−a3+a4−a5=A) −22B) −18C) 32D) 58
6. If9−2= ,whatisthevalueofx?
A) 1B) 2C) 4D) 6
7.
In the equationabove, ifa andb are positive integers and is in its simplest reduced
form,whatisthevalueofa?A) 2B) 9
FundamentalsDrill2:Calculator-PermittedSectionThesequestionsaresimilartothosethatmightappearontheCalculatorsectionoftheMathTest.Besuretouseyourcalculatorwhennecessarytoavoidcarelesscalculationerrors.Don’tforget,though,thatusingitmayslowyoudownwhendoingthemathonpaperwouldbefaster.Answersandexplanationscanbefoundonthispage.
1. If7timesanumberis84,whatis4timesthenumber?A) 16B) 28C) 48D) 56
4. If3x=12,whatisthevalueof ?
A)
B)
C) 4
D) 6
6. Whichofthefollowinggraphsshowsastrongpositiveassociationbetweenxandy?
A)
B)
C)
D)
9. If +22=38,whatisthevalueofx?A) 4B) 16C) 32D) 256
14. Ifeachnumberinthefollowingsumwereincreasedbyt,thenewsumwouldbe4.22.Whatisthevalueoft?
A) 0.24B) 0.29C) 0.33D) 0.37
20. If4x·n2=4x+1·nandxandnarebothpositiveintegers,whatisthevalueofn?A) 2B) 4C) 6D) 8
CHAPTERDRILLANSWERSANDEXPLANATIONS
Drill11. 109
2. 38
3. −3
4. 10
5. 15
Drill21. 6(57+13)=6×70=420
2. 51(48+50+52)=51(150)=7,650
3. ab+ac−ad
4. x(y−z)
5. c(ab+xy)
Drill31.
2.
3.
4.
5.
Drill41. 3
2.
3. −1 or−
4.
5.
6.
7.
Drill5
EstimatedAnswer CalculatorAnswer
1. 0.4×0.9=0.36 0.3741
2. 44÷0.03=1,466 1,457.7
3. 3.7÷0.02=185 186
4. 0.7−3.6=−2.9 −2.89
FundamentalsDrill1:NoCalculatorSection1. A Takeitonephraseatatime.“Sum”meansyouwilladdtwothings.The“squaresofxandy”
meanstosquarexandsquarey,orx2andy2.Addthesetogetx2+y2.Crossoutanychoicethatdoesnothavex2+y2asthefirstpartoftheequation.You’releftwith(A),whichisthecorrectanswer.
4. D Pluginthenumbergivenforaintheexpressiontofindthevalue:−2+(−2)2−(−2)3+(−2)4−(−2)5.RememberPEMDAS,theorderofoperations:ThefirstthingtodohereisdealwiththeExponents,thenwecantakecareoftheAdditionandSubtraction:−2+4−(−8)+16−(−32),whichsimplifiesto−2+4+8+16+32=58,(D).
6. C Negative exponents mean to take the reciprocal and apply the positive exponent. So
.Nowfindwhatpowerof equals .Because34=81, = ,andxmust
be4.Thecorrectansweris(C).
7. B The lowest number that both 8 and 10 are factors of is 40. Convert the fractions to adenominatorof40: + = .There isnofactor that9and40have incommon,so the
fractioncannotbereduced.Thenumberinplaceofain is9,sotheansweris(B).Becareful
nottochoose(D),whichcontainsthevalueofb.
FundamentalsDrill2:Calculator-PermittedSection1. C Translatethewordsintomath:7×n=84,andyouneedtofindthevalueof4n.7n=84,son=
12,and4n=48,(C).
4. D First,solveforx.Dividebothsidesoftheequationby3,andyougetx=4.Thendivide24by4,whichgivesyou6,whichis(D).
6. D A“strongpositiveassociation”meansthatasonevariableincreases, theotheroneincreases.Thiswillbeshownasalinethatanglesthroughthegraphfromthelowerlefttotheupperright.Thesescatterplotsdon’thaveanylinesofbestfitdrawnonthem,soimaginethelinethatwouldgothroughmostofthepointsoneachgraph.In(A),thepointsareallovertheplace,sonolineofbestfitcanevenbedrawn.Eliminate(A).In(B),thelinethathitsmostofthepointswouldgofromtheupperlefttothelowerright.Thisisanegativeassociation,notapositiveone,soeliminate (B). In (C), the linewould go straight across, parallel to the x-axis. This is not apositiveassociation,soeliminate(C).Thecorrectansweris(D).
9. D Tosolvethisequation,get byitself. =16,sosquarebothsides:( )2=162, sox=256.Choice(D)iscorrect.
14. D To figure out how much you need to add to 2.74 to get to 4.22, take 4.22 • 2.74 on yourcalculator. The difference between the two numbers is 1.48. This increase reflects the samenumber,t,addedtoeachofthefournumbersonthelist.Divide1.48by4tofindthatt=0.37,whichis(D).
20. B First,simplifytheequation4x•n2=4x+1•nto4x•n=4x+1,andthentryaneasynumberforx.Ifx=2,then42•n=42+1.Since16n=43,then16n=64andn=4.Thecorrectansweris(B).
Summary◦ There are only six arithmetic operations tested on the SAT: addition, subtraction,multiplication,
division,exponents,andsquareroots.
◦ These operationsmust be performed in the proper order (PEMDAS), beginningwith operationsinsideparentheses.
◦ ApplytheDistributiveLawwheneverpossible.Thisisusuallyenoughtofindtheanswer.
◦ Afractionisjustanotherwayofexpressingdivision.
◦ Youmustknowhowtoadd,subtract,multiply,anddividefractions.Don’tforgetthatyoucanalsouseyourcalculatorinthesectionwhereitispermitted.
◦ If any problems involving large or confusing fractions appear, try to reduce the fractions first.Beforeyoumultiplytwofractions,forexample,seeifit’spossibletoreduceeitherorbothofthefractions.
◦ Ifyouknowhowtoworkoutfractionsonyourcalculator,useitwhenitisallowedtohelpyouwithquestions that involve fractions. If you intend to use your calculator for fractions, be sure topractice.Youshouldalsoknowhowtoworkwithfractionstheold-fashionedwaywithpaperandpencil.
◦ Adecimalisjustanotherwayofexpressingafraction.
◦ When a calculator is permitted, use it to add, subtract,multiply, and divide decimals.When thecalculator isnotallowed, tryroundingandestimatingbeforedoingthemathwithyourpencilandpaper.
◦ Exponentsareakindof shorthand forexpressingnumbers thatare theproductof the same factormultipliedoverandoveragain.
◦ Tomultiplytwoexponentialexpressionswiththesamebase,addtheexponents.
◦ Todividetwoexponentialexpressionswiththesamebase,subtracttheexponents.
◦ Toraiseoneexponentialexpressiontoanotherpower,multiplytheexponents.
◦ Toremembertheexponentrules,thinkMADSPM.
◦ Whenyouraiseapositivenumbergreaterthan1toapowergreaterthan1,theresultislarger.Whenyou raise a positive fraction less than 1 to an exponent greater than 1, the result is smaller. Anegativenumber raised toanevenpowerbecomespositive.Anegativenumber raised toanoddpowerremainsnegative.
◦ Whenyou’reaskedforthesquarerootofanynumber, ,you’rebeingaskedforthepositiverootonly.
◦ HerearetheonlyrulesregardingsquarerootsthatyouneedtoknowfortheSAT:
◦ Theruleforfractionalexponentsisthis:
◦ Therulefornegativeexponentsisthis:
◦ When you encounter questions with charts, carefully check the chart for important information.Rememberthatyoucanuseyouranswersheetasarulertohelpyoulocateinformationortodrawalineofbestfit.
Chapter12Algebra:CrackingtheSystemInthelastchapter,wereviewedsomefundamentalmathconceptsfeaturedontheSAT.ManyquestionsontheSATMathTestcombinesimplearithmeticconceptswithmorecomplexalgebraicconcepts.This isonewaythetestwritersraisethedifficultylevelofaquestion—theyreplacenumberswithvariables,orletters that stand for unknownquantities.This chapter coversmultipleways to answer these algebraicquestions.
SATALGEBRA:CRACKINGTHESYSTEMTheSATgenerallytestsalgebraconceptsthatyoumostlikelylearnedineighthorninthgrade.So,youareprobablyprettyfamiliarwiththelevelofalgebraonthetest.However,thetestwritersarefairlyadeptatwordingalgebraquestionsinawaythatisconfusingordistractinginordertomakethequestionsmoredifficultthanthemathematicalconceptsthatarebeingtested.
In thisway, theSATMathTest isnotonlya testofyourmathskills,butalso,andpossiblyevenmoreimportant to your score improvement, your reading skills. It is imperative that you read the questionscarefullyandtranslatethewordsintheproblemintomathematicalsymbols.
ENGLISH MATHEQUIVALENTSis,are,were,did,does,costs =what(oranyunknownvalue) anyvariable(x,y,k,b)more,sum +less,difference −of,times,product ×(multiply)ratio,quotient,outof,per ÷
FUNDAMENTALSOFSATALGEBRAManyproblemsontheSATrequireyoutoworkwithvariablesandequations.Inyourmathclasses,youprobablylearnedtosolveequationsby“solvingforx”or“solvingfory.”Todothis,youisolatexoryononesideoftheequalsignandputeverythingelseontheotherside.Thegoodthingaboutequationsisthatto isolate thevariableyoucandoanythingyouwant to them—add,subtract,multiply,divide,square—providedyouperformthesameoperationtoallthenumbersintheequation.
Thus,thegoldenruleofequations:
Whateveryoudotothetermsononesideoftheequalsign,youmustdotothetermsontheothersideofitaswell.
Let’slookatasimpleexampleofthisrule,withoutthedistractionofanswerchoices.
If2x−15=35,whatisthevalueofx?
Here’sHowtoCrackItYouwanttoisolatethevariable.First,add15toeachsideoftheequation.Nowyouhavethefollowing:
2x=50
Divideeachsideoftheequationby2.Thus,xequals25.
The skills for algebraic manipulation work just as well for more complex equations. The followingquestionisanotherexampleofthewaytheSATmayaskyoutomanipulateequations.Don’tpanicwhenyouseeaquestionlikethis;justusetheskillsyoualreadyhaveandworkcarefullysoyoudon’tmakeanavoidablemistakeinyouralgebra.
ALittleTerminologyHere are somewords that youwill need to know to understand the explanations in this chapter.Thesewordsmayevenshowupinthetextofaquestion,somakesureyouarefamiliarwiththem.
Term:Anequationislikeasentence,andatermistheequivalentofaword.Itcanbejustanumber,justavariable,oranumbermultipliedbyavariable.Forexample,18,−2x,and5yarethetermsintheequation18−2x=5y.
Expression: Ifanequation is likeasentence, thenanexpression is likeaphraseoraclause.Anexpressionisacombinationoftermsandmathematicaloperationswithnoequalorinequalitysign.Forexample,9×2+3xisanexpression.
Polynomial: A polynomial is any expression containing two or more terms. Binomials andtrinomialsarebothexamplesofpolynomials.
10. Supposetheevaporationrateofwaterinalakeisgivenbytheequation ,
whereEistheevaporationrateingallons/day,Taistheairtemperature,Tdisthedew
pointtemperature,Visthevolumeofwaterinthelake,Twisthewatertemperature,andh
isthenumberofhoursthewaterisexposedtosunlight.Whichofthefollowingexpresses
TwintermsofTa,Td,V,E,andh?
A)
B)
C)
D)
CuttheFatWordproblemsontheSAToftencontainunnecessaryinformation.Ifyoufindtheunnecessaryinformationdistracting,youcanlightly
strikethroughit.Inthisquestion,theexplanation
ofthevariablesisnotnec-essary,soyoucancrossouteverythingaftertheequationto“…thewaterisexposedtosunlight”withoutremovingany
informationnecessarytoansweringthequestion.
Here’sHowtoCrackItThegoalistogetTwbyitself.Anythingyoudotoonesideoftheequation,youmustalsodototheothersideoftheequation.Startbymultiplyingbothsidesbyh4togetridofthedenominatorontherightsideoftheequation.
Theequationbecomes
TogetthefractionwithTwaloneontherightside,subtracttheotherfractionfrombothsidestoget
MultiplybothsidesbyTwtogetthatvariableoutofthedenominator.
Nowdividethewholeexpressionbytheentirethinginsidetheparentheses.
This doesn’tmatch any of the answers exactly, but it looks a lot like (D). Tomake it match exactly,multiplythefractionalpartby ,whichwon’tchangethevalueofthefraction,toget
Then,justswapthepositionsofthetwopartsofthedenominatortoget(D).
SolvingRadicalEquationsRadicalequationsarejustwhatthenamesuggests:anequationwitharadical init.Nottoworry,justremembertogetridoftheradicalfirstbyraisingbothsidestothatpower.
Here’sanexample:
7. If7 −24=11,whatisthevalueofx?
A)
B)
C) 5
D) 25
Here’sHowtoCrackIt
Startbyadding24tobothsidestoget7 =35.Now,dividebothsidesby7tofindthat =5.Finally,squarebothsidestofindthatx=25,whichis(D).
SolvingRationalEquationsSince you are not always allowed to use your calculator on the SAT, therewill be some instances inwhichyouwillneedtosolveanequationalgebraically.Evenwhencalculatoruseispermitted,youmayfinditmoreefficienttouseyourmathematicalskillstoansweraquestion.Anotherwaythetestwritersmay make your calculator less effective is by asking you to solve for an expression. Algebraicmanipulationwilloftenbethemeansbywhichyoucansolvethatproblem.
Hereisanexample:
5. If ,whatisthevalueof ?
A)
B)
C) 2
D) 3
Here’sHowtoCrackIt
ThisquestionappearsintheNoCalculatorsection,soyoumustuseyourmathskillstosolveforr.You
cancross-multiplytoget18r=3(r+10)or18r=3r+30.Subtracting3rfrombothsidesgivesyou15r=
30,sor=2.Finally, = ,whichis(A).
ExtraneousSolutionsSometimes solving a rational or radical expressionmakes funny things happen. Look at the followingexample.
Giventheequationabove,whatisthevalueofz?
Here’sHowtoCrackItUsetheBowtiemethodtogetacommondenominatorforthefractionsontheleftsideoftheequation.Thenumeratorofthefractionontheleftbecomes(z−2)andthenumeratorofthefractionontherightbecomes(z+2).Thenumeratorsareaddedtogether,andthenewdenominatoristheproductoftheoldones.Theequationbecomes
Sincethedenominatorsareequal,thenumeratorsareequal.Thisgivesyou
(z−2)+(z+2)=4
Whenyousimplifytheleftside,youget2z=4,soz=2.Soundsgreat,right?However,youneedtoplugthissolutionbackintotheoriginalequationtomakesurethatitworks.Youget
Once simplified, twoof the threedenominators becomezero.That is not allowed, so the solutionyoufound isn’t reallya solutionat all. It is referred toas anextraneoussolution.That term refers to anyanswer you get to an algebraic equation that results in a false statementwhen plugged back in to theoriginalequation.
Here’sanotherexample.
29.
Intheequationabove,whatisthevalueoftheextraneoussolution,ifoneexists?A) 0B) 4C) 5D) Therearenoextraneoussolutions.
ExtraAnswersAnytimeyouaresolving
foravariable,makesureyoursolutionsactually
work.Iftheydonot,theyareextraneous,orextra.
Here’sHowtoCrackItStartbysquaringbothsidesoftheequationtogetridoftheradical.Theequationbecomes
t+4=(t−2)2
UseFOILtomultiplytherightsideoftheequationtogett2−2t−2t+4ort2−4t+4.Nowtheequationis
t+4=t2−4t+4
Subtracttand4frombothsidestoget
0=t2−5t
Therightsidefactorstot(t−5),sot=0or5.Eliminate(B),since4isnotasolutionatall,extraneousorotherwise.Nowplug0and5backintotheoriginalequationtoseeiftheywork.Ifbothdo,theansweris(D).Ifoneofthemdoesnot,thatoneistheextraneoussolution.
t=0 t=5
=0−2 =5−2
=−2 =3
2≠−2 3=3
Sincetheequationisfalsewhent=0,then0istheextraneoussolution.Thecorrectansweris(A).
SolvingforExpressionsSomealgebraproblemsontheSATaskyoutofindthevalueofanexpressionratherthanthevalueofavariable.Inmostcases,youcanfindthevalueoftheexpressionwithoutfindingthevalueofthevariable.
5. If4x+2=4,whatisthevalue4x−6?A) −6B) −4
C) 4D) 8
MathClassSolution:
Inmathclass,youwould
findthevalueofxand
thenplugthatvalueinto
theprovidedexpression.
So,subtract2fromboth
sidestofindthat4x=2.
Thendividebothsidesby
4tofindthatx= .Then,
4x−6=4 −6=−4.
So,theansweris(B).
Here’sHowtoCrackItSincethequestionasksforthevalueofanexpressioninsteadofthevalueofx,theremaybeashortcut.Theterm4xisinbothexpressions,soinsteadofsolvingforx,youcansolvefor4x.Subtract2frombothsidesof4x+2=4toget4x=2.Now,plug4x=2into4x−6toget(2)−6=−4,whichis(B).
Thisapproachwillsaveyoutime—providedthatyouseeitquickly.So,whileyoupractice,youshouldtrainyourselftolookforthesesortsofdirectsolutionswheneveryouareaskedtosolveforthevalueofanexpression.
However,don’tworrytoomuchifyoudon’talwaysseethefasterwaytosolveaproblemlikethisone.Themathclasswaywillcertainlygetyoutherightanswer.
Here’sanotherexample:
9. If =x−2,whatisthevalueof(x−2)2?
A)
B)
C) 5D) 25
LearnThem,LoveThem
Don’tgetboggeddownlookingforadirect
solution.Alwaysaskyourselfifthereisa
simplewaytofindtheanswer.Ifyoutrain
yourselftothinkintermsofshortcuts,youwon’t
wastealotoftime.However,ifyoudon’tseeaquicksolution,getto
work.Somethingmaycometoyouasyou
laboraway.
Here’sHowtoCrackItIf you were to attempt themath class way, you’d find that x = + 2 and then you would have tosubstitutethatintotheprovidedexpression.There’sgottobeaneasierway!
Theproblemismucheasierifyoulookforadirectsolution.Then,younoticethatalltheproblemwants
youtodoistosquaretheexpressionontherightoftheequalsign.Well,ifyousquaretheexpressionon
theright,thenyou’dbettersquaretheexpressionontheleft,too.So, =5=(x−2)2andtheanswer
is(C).Thatwasprettypainlessbycomparison.
SolvingSimultaneousEquationsSomeSATproblemswillgiveyoutwoormoreequationsinvolvingtwoormorevariablesandaskforthevalue of an expression or one of the variables. These problems are very similar to the problemscontainingonevariable.Thetestwriterswouldlikeyoutospendextratimetryingtosolveforthevalueofeachvariable,butthatisnotalwaysnecessary.
Here’sanexample:
10. If4x+y=14and3x+2y=13,thenx−y=?
Here’sHowtoCrackItYou’vebeengiventwoequationshere.Butinsteadofbeingaskedtosolveforavariable(xory),you’vebeenaskedtosolveforanexpression,(x−y).Why?Becausetheremustbeadirectsolution.
Inmathclass,you’reusuallytaughttosolveoneequationforonevariableintermsofasecondvariableandtosubstitutethatvalueintothesecondequationtosolveforthefirstvariable.
Forgetit.ThesemethodsarefartootimeconsumingtouseontheSAT,andtheyputyouatriskofmakingmistakes.There’s a betterway. Just stack themon top of each other, and then addor subtract the twoequations;eitheradditionorsubtractionwilloftenproduceaneasyanswer.Let’stryit.
Addingthetwoequationsgivesyouthis:
Unfortunately,thatdoesn’tgetyouanywhere.So,trysubtracting:
4x+y=143x+2y=13
Whenyousubtractequations,justchangethesignsofthesecondequationandadd.Sotheequationabovebecomes
Thevalueof(x−y)ispreciselywhatyouarelookingfor,sotheansweris1.
Youcanalsousethismethodtosolveproblemsinwhichyouareaskedtosolveforanexpressionandgives you fewer equations than variables. If you have dealtwith simultaneous equations in yourmathclasses,youmayknowthatthatputsyouinabindsinceitmaybeimpossibletosolveforeachindividualvariable.
Hereisanexample:
27.
3a−7b=4d−9−4c+10a=6b+7−2a+3c−4d=10
Giventhesystemofequationsabove,whatisthevalueof−10a−2b+2c?
Here’sHowtoCrackItNoticethatthetestwritershavemadethisproblemharderbymixingupthevariables.Yourfirststepistolineup thevariableson the left sideof the equationandarrange them in alphabeticalorder;move theconstantstotherightsideoftheequation.Combineliketermsineachequation,anduseaplaceholderforanyvariablesthataremissingineachequation.
Step1:
3a−7b+0c−4d=−910a−6b−4c+0d=7−2a+0b+3c−4d=10
“Nothing”isHelpfulIntheseequations,theplaceholdersare0c,
0d,and0brespectively.Because0timesany
numberis0,nothinghasbeenaddedtotheequation;
these0’saresimplyactingasplaceholders,so
thatallofthevariableslineupvertically.Youmayalsochoosetoleavethese
areasblank.
Onceyouhavethevariablesaligned,completethisproblemjustlikethepreviousproblembyaddingandsubtractingtheequationsuntilyougetsomethingthatlooksliketheexpressioninthequestion.
IFYOUADD:
IFYOUSUBTRACT:
Don’tForgettoSharetheLove
Don’tforgetthatwhenyousubtractanentireequation,youneedtosubtracteachcomponentoftheequation
—insimplerterms,changeeachsigntotheoppositeoperation,andthenaddtheequations.
Neitheroftheseanswersappearstobewhatthetestwritersareaskingfor,butoncloserinspection,theequationthatresultedfromsubtractioncanbemultipliedby2togettheexpressioninthequestion.
2(−5a−1b+1c)=2(−26)
−10a−2b+2c=−52
SolvingforVariablesinSimultaneousEquationsShortcutsareawesome,sotakethemwheneveryoucanontheSAT.Butoccasionally,youwon’thavetheoptionofusingashortcutwithsimultaneousequations,soknowinghowtosolveforavariableiscrucial.
Here’sanexample:
11. If3x+2y=17and5x−4y=21,whatisthevalueofy?
Here’sHowtoCrackItInthiscase,thestackandsolvemethoddoesn’tbringusanimmediateanswer:
Neitherof thesemethodsgivesyou thevalueofy.Thebestway to approach this question is to try toeliminateonevariable.Todothis,multiplyoneorbothoftheequationsbyanumberthatwillcausetheothervariabletohaveacoefficientof0whentheequationsareaddedorsubtracted.
Inthiscase,thequestionisaskingyoutosolvefory,sotrytomakethex termsdisappear.Youwanttomakethecoefficientofxzero,soyoucanquicklyfindthevalueofy.Here’show:
Usethecoefficientofxinthesecondequation,5,tomultiplythefirstequation:
5(3x+2y)=5(17)
15x+10y=85
Thenusetheoriginalcoefficientofxinthefirstequationtomultiplythesecondequation:
3(5x−4y)=3(21)15x−12y=63
Now stack your equations and subtract (or flip the signs and add, which is less likely to lead to amistake.)
Simplifyyourequationandyouhaveyouranswer.
22y=22y=1
SolvingInequalitiesIn an equation, one side equals the other. In an inequality, one side does not equal the other. Thefollowingsymbolsareusedininequalities:
≠ isnotequalto> isgreaterthan< islessthan≥ isgreaterthanorequalto;atleast≤ islessthanorequalto;nomorethan
HungryGatorThinkoftheinequalitysignasthemouthofahungryalligator.Thealligatoreats
thebiggernumber.
Solving inequalities is pretty similar to solving equations. You can collect like terms, and you cansimplifybyperformingthesameoperationtobothsides.Allyouhavetorememberisthatifyoumultiplyordividebothsidesofaninequalitybyanegativenumber,thedirectionoftheinequalitysymbolchanges.
Forexample,here’sasimpleinequality:
x>y
Now,justasyoucanwithanequation,youcanmultiplybothsidesofthisinequalitybythesamenumber.Butifthenumberyoumultiplybyisnegative,youhavetochangethedirectionofthesymbolintheresult.Forexample,ifyoumultiplybothsidesoftheinequalityaboveby−2,youendupwiththefollowing:
−2x<−2y
Remember:Whenyoumultiplyordivideaninequalitybyanegativenumber,youmustreversetheinequalitysign.
Here’sanexampleofhowaninequalityquestionmaybeframedonthetest.
8. If−3x+6≥18,whichofthefollowingmustbetrue?A) x≤−4B) x≤8C) x≥−4D) x≥−8
Here’sHowtoCrackItSimplifytheinequalitylikeanyotherequation:
−3x+6≥18
−3x≥12
Remembertochangethedirectionoftheinequalitysign!
x≤−4
Choice(A)isthecorrectanswer.
ARangeofValuesYoumayalsobeaskedtosolveinequalitiesforarangeofvalues.Intheseinstances,youcansimplifytheprocessbyinitiallytreatingtheinequalityastwoseparateproblems.
Here’sanexample:
If−8<– m+1≤− ,whatisonepossiblevalueofm?
Here’sHowtoCrackIt
First,workontheleftsideoftheequation:−8<− m+1.
−40<−3m+5
−40−5<−3m+5−5
−45<−3m
15>m
Then,workontherightsideoftheequation:− m+1≤−
− m+1−1≤− −1
− m≤−
−3m≤−21
m≥7
Onceyouhavebothpiecesoftheinequalitysimplified,youjustneedtoputthembacktogether.
If 15 >m andm ≥ 7, then 15 >m ≥ 7, but this inequality doesn’t make logical sense. Generally,inequalitiesarewrittenwiththesmallernumberontheleftandthelargernumberontheright,sowhenyousolvean inequality like this,youmayneedtorearrangetheequation.This isn’tdifficult; justmakesurethe“arrows”arestillpointingatthesamenumberswhenyouchangetheorder.
So,acorrectanswertothisquestionwouldbeanynumberbetween7and15,whichincludes7,butdoesNOTinclude15.
WritingYourOwnSystemofEquationsSometimesyou’llbeaskedtotakeawordproblemandcreateasystemofequationsorinequalitiesfromthatinformation.Ingeneral,youwillnotbeaskedtosolvethissystemofequations/inequalities,soifyouareabletolocateandtranslatetheinformationintheproblem,youhaveagoodshotatgettingthecorrectanswer.Alwaysstartwiththemoststraightforwardpieceofinformation.Whatisthemoststraightforwardpieceofinformation?Well,that’suptoyoutodecide.Considerthefollowingproblem.
9. Aubrie,Bera,andKeaarerunningalemonadeandsnackstandtoearnmoney.Theyaresellinglemonadefor$1.07acupandchocolatechipcookiesfor$0.78each.Theircustomersarriveonfootorbycar.Duringathree-hourperiod,theyhad47customerseachbuyingonlyoneitemandmade$45.94.Aubrie,Bera,andKeaneedtodetermineiftheyhaveenoughsuppliesfortomorrow.Solvingwhichofthefollowingsystemofequationswillletthemknowhowmanycupsoflemonade,x,andhowmanycookies,y,theysoldtoday?
A)
B)
C)
D)
Here’sHowtoCrackItFor some people, themost straightforward piece of information dealswith the number of items beingsold.Forothers,itmaybethepriceoftheitemsbeingsold.Whicheverpieceofinformationyouchoose,usethemathtoEnglishtranslationsinthischapter tohelpyouidentifythemathematicaloperationsyouwillneedtowriteyourequation.
Nowworkthroughtheproblem.
Youmay have noticed that the question provides background information that isn’t really necessary tosolvetheproblem.Lightlystrikingthroughtheunnecessaryinformationwillmaketheproblemlooklessintimidating.
9. Aubrie,Bera,andKeaarerunningalemonadeandsnackstandtoearnmoney.Theyaresellinglemonadefor$1.07acupandchocolatechipcookiesfor$0.78each.Theircustomersarriveonfootorbycar.Duringathree-hourperiodtheyhad47customerseachbuyingonlyoneitemandmade$45.94.Aubrie,Bera,andKeaneedtodetermineiftheyhaveenoughsuppliesfortomorrow.Solvingwhichofthefollowingsystemofequationswillletthemknowhowmanycupsoflemonade,x,andhowmanycookies,y,theysoldtoday?
The shortened problemmakes it a lot easier to recognize important information. Start by identifying astraightforwardpieceofinformation,soyoucanstartwritingyourownequations.
Theyaresellinglemonadefor$1.07acupandchocolatechipcookiesfor$0.78each.
This is a fairly straightforward piece of information. Once you identify which variable representslemonadeandwhichonerepresentscookies,youcanbegin towriteyourequation.In thisproblem, theverylastsentencegivesyoutheneededinformation.
…howmanyglassesoflemonade,x,andhowmanycookies,y…
Nowyouknowthatthenumberofcupsoflemonadetheysold,multipliedby$1.07percup,willgiveyouthe amount ofmoney theymade selling lemonade, and the number of cookies they sold,multiplied by$0.78,willgiveyoutheamountofmoneytheymadesellingcookies.Sincetheproblemalsogivesyouthetotalamountofmoneytheymade,$45.94,andstatesthatcustomerswere“eachbuyingonlyoneitem”youcanusetheinformationabovetowriteyourfirstequation.
Once you have your first equation, go to your answer choices to determine which answers you caneliminate.You’llquickly see that (A), (C), and (D)are allwrong, soyoucan select (B)without evenhavingtoconstructthesecondequation.
Nowtryoneonyourown.
7. Tosaveonheliumcosts,aballoonisinflatedwithbothheliumandnitrogengas.Betweenthetwogases,theballooncanbeinflatedupto8litersinvolume.Thedensityofheliumis0.20gramsperliter,andthedensityofnitrogenis1.30gramsperliter.Theballoonmustbefilledsothatthevolumetricaveragedensityoftheballoonislowerthanthatofair,whichhasadensityof1.20gramsperliter.Whichofthefollowingsystemofinequalitiesbestdescribeshowtheballoonwillbefilled,ifxrepresentsthenumberoflitersofheliumandyrepresentsthenumberoflitersofnitrogen?
A)
B)
C)
D)
Here’sHowtoCrackItStartwiththemoststraightforwardpieceofinformationandtranslateitintomath.Inthiscase,themoststraightforward information is about the total volume of the balloon. “Between the two gases”wouldindicateaddition,andthegasesarerepresentedasxandy,soyouneedx+yinthecorrectanswer.Theyallhavethat,sogotothenextpiece.Together,xandycanbe“upto8liters.”Thistranslatesto“lessthanorequalto8,”becausetheballoon’svolumecan’tbegreaterthan8,butitcouldbe8orless.Therefore,oneequationmustbex+y≤8.Youcaneliminate(A)and(B),asthoseanswershavedifferentequationsrelatedtox+y.Thenextpartmaybehardtotranslate,sopicksomenumbersandtrythemout.Makex=2andy=2.Thesecondequationin(D)iseasiertoworkwith,soseeifthesenumbersmakethatequationtrue.0.2(2)+1.30(2)=0.4+2.60=3.Thisisnotlessthan1.20,soeliminate(D)andchoose(C).
SimplifyingExpressionsIfaproblemcontainsanexpressionthatcanbefactored,itisverylikelythatyouwillneedtofactorittosolvetheproblem.So,youshouldalwaysbeonthelookoutforopportunitiestofactor.Forexample,ifaproblemcontainstheexpression2x+2y,youshouldseeiffactoringittoproducetheexpression2(x+y)willhelpyoutosolvetheproblem.
SomethingtoHideBecausefactoringor
expandingisusuallythekeytofindingtheanswer
onsuchproblems,learntorecognizeexpressionsthatcouldbeeitherfactoredorexpanded.Thiswillearn
youmorepoints.Thetestwriterswilltrytohidetheanswerbyfactoringorexpandingtheresult.
Ifaproblemcontainsanexpressionthat isalreadyfactored,youshouldconsiderusingtheDistributiveLawtoexpandit.Forexample,ifaproblemcontainstheexpression2(x+y),youshouldseeifexpandingitto2x+2ywillhelp.
Herearefiveexamplesthatwe’veworkedout:
1. 4x+24=4(x)+4(6)=4(x+6)
2.
3.
4. 2(x+y)+3(x+y)=(2+3)(x+y)=5(x+y)
5. p(r+s)+q(r+s)=(p+q)(r+s)
Here’showthismightbetestedontheSAT.
10. Whichofthefollowingisequivalentto ?
A)
B)
C)
D)
Here’sHowtoCrackIt
Dependingonwhatyouseewhenyouapproachthisproblem,youmaychoosetosolvebydistributionor
factoring.Youmaynoticethatthereisanfineachtermoftheexpression.Inthiscase,youmaychooseto
factortheexpressionto ,butthatdoesn’tgiveyouapossibleanswer;however,youcaneliminate
(B),since isnotequivalent toyourexpression.Nowyouare leftwithanexpressionyoumay
findhardtomanipulate.Gobackandlookatthemathematicsbehindtheinitialfactorizationsothenext
stepintheprocesswillmakemoresense.
Whenyoufactoranfoutoftheexpression,whatyouarereallydoingisthis:
Multiplytheexpressionby1sothatyoudonotchangetheexpression.
Thisleavesyouwiththesameexpressionas(A).
Ifyounoticethattheanswersareallexpressionsthemselves,youmaychoosetodistributethevariableinfrontoftheparenthesesinsteadoftryingtofactortheexpression.
Startwith(A):
Distributetoeachtermwithinthebinomial:
Cancelwhereyoucan:
Both methods give you the same answer; however, this type of algebra leaves you open to makingmistakes.Inthenextchapter,youwilldiscoverathirdwaytoapproachthisproblemthatyoumayfindeveneasierthanthepreviousmethods.
MultiplyingBinomialsMultiplyingbinomialsiseasy.JustbesuretouseFOIL(First,Outer,Inner,Last).
CombineSimilarTermsFirstWhen manipulating long, complicated algebraic expressions, combine all similar terms before doinganythingelse.Inotherwords,ifoneofthetermsis5xandanotheris−3x,simplycombinetheminto2x.Thenyouwon’thaveasmanytermstoworkwith.Here’sanexample:
(3x2+3x+4)+(2−x)−(6+2x)=3x2+3x+4+2−x−6−2x=3x2+(3x−x−2x)+(4+2−6)=3x2
TERMinologyRemember:Atermisanumber,variable,ora
numberandvariablethatarecombinedbymultipli-cationordivision.Soin
theexpression6x+10=y,6x,10,andyareallterms.
6x+10,however,isnotatermbecauseaterm
includesonlyvariablesandtheircoefficients.
EvaluatingExpressionsSometimesyouwillbegiventhevalueofoneof thevariables inanalgebraicexpressionandaskedtofind thevalueof theentireexpression.Allyouhave todo isplug in thegivenvalueandseewhatyoucomeupwith.
Hereisanexample:
Problem:If2x=−1,then(2x−3)2=?
Solution:Don’tsolveforx;simplyplugin−1for2x,likethis:
(2x−3)2=(−1−3)2
=(−4)2=16
SolvingQuadraticEquationsTosolvequadraticequations,remembereverythingyou’velearnedsofar:Lookfordirectsolutionsandeitherfactororexpandwhenpossible.
Here’sanexample:
9. If(x+3)2=(x−2)2,whatisthevalueofx?
Here’sHowtoCrackItExpandbothsidesoftheequationusingFOIL:
(x+3)(x+3)=x2+6x+9
(x−2)(x−2)=x2−4x+4
x2+6x+9=x2−4x+4
Nowyoucansimplify.Eliminatethex2terms,becausetheyareonbothsidesoftheequalsign.Nowyouhave6x+9=−4x+4,whichsimplifiesto
10x=−5
x=−
FactoringQuadratics
Tosolveaquadratic,youmightalsohavetofactortheequation.FactoringaquadraticbasicallyinvolvesdoingareverseformofFOIL.
Forexample,supposeyouneededtoknowthefactorsofx2+7x+12.Here’swhatyouwoulddo:
1. Writedown2setsofparenthesesandputanxineachonebecausetheproductofthefirsttermsisx2.
x2+7x+12=(x)(x)
2. Lookatthenumberattheendoftheexpressionyouaretryingtofactor.Writedownitsfactors.Inthiscase,thefactorsof12are1and12,2and6,and3and4.
FactoringWhenfactoringanequation
likex2+bx+c,think“A.M.”FindtwonumbersthatAdduptothemiddleterm(b)andMultiplytogivethelastterm(c).
3. Todeterminewhichsetoffactorstoputintheparentheses,lookatthecoefficientofthemiddletermofthequadraticexpression.Inthiscase,thecoefficientis7.So,thecorrectfactorswillalsoeitheraddorsubtracttoget7.Writethecorrectfactorsintheparentheses.
x2+7x+12=(x__3)(x__4)
4. Finally,determinethesignsforthefactors.Togetapositive12,the3andthe4areeitherbothpositiveorbothnegative.But,since7isalsopositive,thesignsmustbothbepositive.
x2+7x+12=(x+3)(x+4)
YoucanalwayscheckthatyouhavefactoredcorrectlybyFOILingthefactorstoseeifyougettheoriginalquadraticexpression.
Tryanexample:
16. Intheexpressionx2+kx+12,kisanegativeinteger.Whichofthefollowingisapossiblevalueofk?A) −13B) −12C) −6D) 7
Here’sHowtoCrackItSincethequestiontoldyouthatkisanegativeinteger,youcanimmediatelyeliminate(D)becauseitisapositive integer.Tosolve thequestion,youneed to factor.Thisquestion is justa twiston theexampleusedabove.Don’tworrythatyoudon’tknowthevalueofk.Thequestionsaidthatkwasaninteger,soyouneedtoconsideronlytheintegerfactorsof12.Thepossiblefactorsof12are1and12,2and6,and3
and4.Since12ispositiveandkisnegative,thenyou’llneedsubtractionsignsinbothfactors.
Thepossibilitiesareasfollows:
x2+kx+12=(x−1)(x−12)
x2+kx+12=(x−2)(x−6)
x2+kx+12=(x−3)(x−4)
IfyouFOILeachofthesesetsoffactors,you’llgetthefollowingexpressions:
(x−1)(x−12)=x2−13x+12
(x−2)(x−6)=x2−8x+12
(x−3)(x−4)=x2−7x+12
Thecorrectansweris(A),as−13istheonlyvaluefromaboveincludedintheanswers.Ofcourse,youdidn’tneedtowritethemalloutifyoustartedwith1and12asyourfactors.
SATFavoritesThetestwritersplayfavoriteswhenitcomestoquadraticequations.Therearethreeequationsthattheyuseallthetime.Youshouldmemorizetheseandbeonthelookoutforthem.Wheneveryouseeaquadraticthatcontainstwovariables,itisalmostcertaintobeoneofthesethree.
(x+y)(x−y)=x2−y2
(x+y)2=x2+2xy+y2
(x−y)2=x2−2xy+y2
Here’sanexampleofhowtheseequationswilllikelybetestedontheSAT.
11. If2x−3y=5,whatisthevalueof4x2−12xy+9y2?A)
B) 12C) 25D) 100
Here’sHowtoCrackItHereyouhaveaquadraticequationthatcontainstwovariables.
Inthiscase,workwith2x−3y=5.Ifyousquaretheleftsideoftheequations,youget
(2x−3y)2=4x2−12xy+9y2
That’spreciselytheexpressionforwhichyouneedtofindthevalue.It’salsothethirdoftheequationsfromthebox.Now,sinceyousquaredtheleftside,allyouneedtodoissquarethe5ontherightsideoftheequationtodiscoverthattheexpressionequals25,(C).
Did you notice that this questionwas just another version of being asked to solve for the value of anexpressionratherthanforavariable?Quadraticsareoneofthetestwriters’favoritewaystodothat.
SolvingQuadraticsSettoZeroBeforefactoringmostquadratics,youneedtosettheequationequaltozero.Why?Well,ifab=0,whatdoyouknowaboutaandb?Atleastoneofthemmustequal0,right?That’sthekeyfactyouneedtosolvemostquadratics.
Here’sanexample:
9. If3− x+7,andx≠0,whichofthefollowingisapossiblevalueforx?
A) −7B) −1C) 1D) 3
Here’sHowtoCrackItThetestwritershavetriedtohidethattheequationisactuallyaquadratic.Startbymultiplyingbothsidesoftheequationbyxtogetridofthefraction.
3x−3=x2+7x
Rearrangethetermstosetthequadraticequalto0.You’llgetx2+4x+3=0.Nowit’stimetofactor:
x2+4x+3=(x+1)(x+3)=0
So,atleastoneofthefactorsmustequal0.Ifx+1=0,thenx=−1.Ifx+3=0,thenx=−3.Since−1is(B),that’stheoneyouwant.
Inadditiontosolvingeasilyfactorablequadratics,thetestwriterswouldalsoliketoseeyoudemonstrateyourunderstandingofthequadraticformula.Weknowwhatyou’rethinking:“Notthatthingagain!Can’tIjustsolveitwiththatniftyprogramIhaveonmygraphingcalculator?”Whyyes,yesyoucan,butonlyiftheproblemappearsinthecalculator-permittedsectionofthetest.Trustusonthisone;thetestwritersarenotalwaysgoingtoputthesetypesofproblemsinthecalculatorsection.Knowingthequadraticformulaisaneasywaytogainpointsonaquestionthetestwritersintendtobe“hard.”
Foraquadraticequationintheformy=ax2+bx+c,thequadraticformulais:
Tofindtherootsofaquadratic,orthepointswherey=0,simplyplugyourvaluesfora,b,andcintothequadraticformula.
TheSignsTheyAreaChangin’
Thequadraticformulaworksforquadraticsin
theformy=ax2+bx+c.Thereisonlyadditioninthatform,sobecareful
whenyourquadratichasnegativesignsinit.
Here’sanexample:
7x2−5x−17=0
Soa=7,b=−5,andc=−17.Pluggingtheconstantsintothequadraticequationyouget
Let’sputyourquadraticskillstoworkwithaproblemyoumayseeontheSAT.
12. Whatistheproductofallthesolutionstotheequation3z2−12z+6=0?A)
B) 2C) 4D) 4
Here’sHowtoCrackIt
Usingthequadraticformulax= youwoulddothefollowing:
Sox=2+ or2− .“Product”meanstomultiply,souseFOILtomultiply(2+ )×(2− )toget4−2 +2 −( )2=4−2=2,whichis(B).
Wow, thatwasa lotofwork!Wouldn’t itbegreat if therewereashortcut?Actually, there is!Whenaquadraticisintheformy=ax2+bx+c,theproductoftherootsisequaltothevalueofcdividedbythevalueofa.Inthiscase,that’s6÷3=2!It’sthesameanswerforalotlesswork.(Seetheinset“TheRootoftheProblems”forthisandanotherhandytrick—they’reworthmemorizing.)
TheRootoftheProblemsSometimesyou’llbeaskedtosolveforthesumortheproductoftherootsofaquadraticequation.You can use the quadratic formula and then add or multiply the results, but it’s quicker to justmemorizethesetwoexpressions.
sumoftheroots:−
productoftheroots:
IMAGINARYANDCOMPLEXNUMBERSSofaryouhavebeenworkingwithrealnumbers,whichareanynumbersthatyoucanplaceonanumberline.TheSATwillalsoaskyoutodomathematicaloperationswithimaginaryorcomplexnumbers.
ImaginaryNumbersAnimaginarynumber,verysimply,isthesquarerootofanegativenumber.Sincethereisnowaytohavearealnumberthatisthesquarerootofanegativenumber,mathematiciansneededtocomeupwithawaytorepresentthisconceptwhenwritingequations.Theyuseanitalicizedlowercase“I”todothat:i=,andtheSATwilllikelytellyouthatinanyprobleminvolvingimaginarynumbers.
Anothercommonpieceofinformationyouwillneedtoknowaboutiishowitbehaveswhenitisraisedtoapower.Hereisiraisedtothepowers1through8.Canyoucompletethenextfourvaluesofiintheseries?
Did you notice anything about the answer? If you said that there is a repeating pattern, then you arecorrect.Thispatternwillbehelpfulinansweringquestionscontainingimaginaryandcomplexnumbers.
ComplexNumbersComplex numbers are another way in which the SAT may test the concept of imaginary numbers. Acomplexnumberisonethathasarealcomponentandanimaginarycomponentconnectedbyadditionorsubtraction.8+7iand3−4iaretwoexamplesofcomplexnumbers.
Complexnumbersmightbetestedinavarietyofways.Youmaybeaskedtoaddorsubtractthecomplexnumbers.Whenyouarecompletingtheseoperations,youcantreatiasavariable.Justcombinetheliketermsintheseexpressionsandthensimplify.(Don’tforgettodistributethesubtractionsign.)
Here’sanexample:
2. Fori= ,whatistheresultofsubtracting(2+4i)from(−5+6i)?
A) −7+2iB) −3−10i
C) 3+2iD) 7−10i
Here’sHowtoCrackItSetupthesubtraction:
(−5+6i)−(2+4i)
Distributethenegativesigntobothtermsinthesecondsetofparenthesestoget
−5+6i−2−4i
Combineliketermstoget−7+2i,whichis(A).
Sinceyouneverendedupwithani2term,youneverevenneededtoworryaboutthefactthati= Youjusttreatiasaregularvariable.
TheSATmayalsotestyourabilitytomultiplycomplexnumbers.Againyoucantreatiasavariableasyouworkthroughthemultiplicationasifyouweremultiplyingbinominals.Inotherwords,useFOILtoworkthroughtheproblem.Theonlydifferenceisthatyousubstitute−1fori2.
Finally,youmaybeaskedaboutfractionswithcomplexnumbersinthedenominator.Don’tworry—youwon’tneedpolynomialorsyntheticdivisionforthis.Youjustneedtorationalizethedenominator,whichismucheasierthanitmaysound.
To rationalize the denominator of a fraction containing complex numbers, you need to multiply thenumeratoranddenominatorby theconjugate.Tocreate theconjugateofacomplexnumber,yousimplyneedtoswitchtheadditionorsubtractionsignconnectingtherealandimaginarypartsofthenumberforitsopposite.
Forexample,theconjugateof8+7iis8–7i,andtheconjugateof3–4iis3+4i.
Justlikewhenyouexpandtheexpression(x+y)(x−y)togetx2–y2,youcandothesamewithacomplexnumberanditsconjugate.TheOuterandInnertermswillcancelout,givingyou(x+yi)(x−yi)=(x2–i2y2)=(x2+y2).
(8+7i)×(8–7i)=82–72i2,andsubstitutingi2=–1givesyou82+72=113.
Here’sanexampleofhowtheSATwillusecomplexnumbersinafraction.
3. i= ,whichofthefollowingisequivalentto ?
A) 2+ i
B) 2–
C)
D) 28–14 i
MultiplyingbyOne(inDisguise)
Inordertokeepafraction
thesame,youmustmulti-
plyby1.Ifyoumultiplythe
numeratorofafractionby
theconjugate,youmustdo
thatsameoperationtothe
denominatororyouhave
changedthefraction:
isthesamethingas
multiplying ×1.
Here’sHowtoCrackItNoneoftheanswerchoiceshaveiinthedenominator,iftheyhaveadenominatoratall,soyouneedtogetridofthati.Rootsindenominatorsaregenerallynotaccepted,either.Togetridofboththings,youneedtomultiplythewholefractionbytheconjugateofthedenominator.Thismeansyoukeepthesametermsbut switch the sign between them. Be very careful to not make a sign error as you work through theproblem.Theexpressionbecomes
Multiplythetwofractions,usingFOILonthedenominatorstoget
Combineliketermsinthedenominator,andtheexpressionbecomes
Thereisstillaniinthedenominator,butyoucangetridofit.Sincei= ,i2=–1,sosubstitutethatintothefractiontoget
Reducingthefractiongivesyou2+ ,whichis(A).
WhenValuesAreAbsoluteAbsolutevalue is just ameasureof thedistancebetweenanumberand0.Sincedistancesarealwayspositive, the absolute value of a number is also always positive. The absolute value of a number iswrittenas|x|.
Whensolvingforthevalueofavariableinsidetheabsolutevaluebars,itisimportanttorememberthatthevariablecouldbeeitherpositiveornegative.Forexample,if|x|=2,thenx=2orx=−2,asboth2and−2areadistanceof2from0.
SATSmokeandMirrorsWhenyou’reaskedto
solveanequationinvolvinganabsolutevalue,itis
verylikelythatthecorrectanswerwillbethenegative
result.Why?Becausethetestwritersknowthatyouarelesslikelytothinkaboutthenegativeresult!
Anotherwaytoavoidmistakesistodoallthemath
insidetheabsolutevaluesymbolsfirst,andthen
maketheresultpositive.
Here’sanexample:
9.
|x+3|=6|y−2|=7
Fortheequationsshownabove,whichofthefollowingisapossiblevalueofx−y?A) −14B) −4C) −2D) 14
Here’sHowtoCrackItTosolvethefirstequation,setx+3=6andsetx+3=−6.Ifx+3=−6,thentheabsolutevaluewouldstillbe6.So,xcanbeeither3or−9.Now,dothesamethingtosolvefory.Eithery=9ory=−5.
Tofindthecorrectanswer,youneedtotrythedifferentcombinations.Onecombinationisx=−9andy=−5.So,x−y=−9−(−5)=−4,whichis(B).
AlgebraDrill1:NoCalculatorSectionWork these questions without your calculator using the skills you’ve learned so far. Answers andexplanationscanbefoundonthispage.
5.
y=3x−1
y+x=1
Inthesystemofequationsabove,if(x,y)isthesolutiontothesystem,whatisthevalueof?
A)
B)
C)
D)
8. Fortheequation =x+3,thevalueofmis−3.Whatisthesolutionsetfortheequation?A) {−3,3}B) {−2}C) {−2,−7}D) {3,6}
11. Ifi= ,whatistheproductof(4+7i)and ?
A) 16− i
B) 14+ i
C) 2−8i−142
D) i
14.
rx2= x+3
Aquadraticequationisprovidedabove,whererandsareconstants.Whatarethesolutionsforx?
A) x=
B) x=
C) x=
D) x=
AlgebraDrill2:Calculator-PermittedSectionWork these questions using your calculator as needed and applying the skills you’ve learned so far.Answersandexplanationscanbefoundonthispage.
4. Ifx+6>0and1−2x>−1,thenxcouldequaleachofthefollowingEXCEPT
A) −6
B) −4
C) 0
D)
7. If ,whatisthevalueofx?
A) −
B)
C) 0
D) 2
10. Iftheproductofxandyis76,andxistwicethesquareofy,whichofthefollowingpairsofequationscouldbeusedtodeterminethevaluesofxandy?
A) xy=76x=2y2
B) xy=76x=(2y)2
C) x+y=76x=4y2
D) xy=76x=2y
12. If–6<–4r+10≤2,whatistheleastpossiblevalueof4r+3?A) 2B) 5C) 8D) 11
16. Howmanysolutionsexisttotheequation|x|=|2x–1|?A) 0B) 1C) 2D) 3
25. Thesumofthreenumbers,a,b,andc,is400.Oneofthenumbers,a,is40percentlessthanthesumofbandc.Whatisthevalueofb+c?A) 40B) 60C) 150D) 250
CHAPTERDRILLANSWERSANDEXPLANATIONS
AlgebraDrill1:NoCalculatorSection
5. C Startbymultiplyingthesecondequationby2toclearthefractions.Theequationbecomesy
+2x=2.Togetitintothesameformastheotherequations,subtract2xfrombothsidesto
gety=–2x+2.Setthetwoxexpressionsequaltoget3x–1=–2x+2.Add2xand1to
bothsides,sotheequationbecomes5x=3,thendivideby5tofindthatx= .Plug this
valueintothey=3x–1togety= .Finally,findthevalueof
: = ,whichis(C).
8. B Sincethequestiongivesthevalueofm,thefirststepistoplugthatvalueintotheoriginal
equation to get = x+3. Now square both sides of the equation to remove the
squareroot =(x+3)2or–3x–5=x2+6x+9.Nowcombineliketerms.Ifyou
combinethetermsontherightsideoftheequation,youcanavoidhavinganegativex2term.
Theequationbecomes0=x2+9x+14.Factortheequationtofindtheroots:0=(x+2)(x
+ 7). The possible solutions to the quadratic are –2 and –7. Don’t forget to plug these
numbers back into the original equation to check for extraneous solutions. Begin by
checkingx=–2.Whenyoudothis,youget =(–2)+3,or =1,or =
1, which is true. Now, check x = –7. Set it up as = (–7) + 3, and start
simplifying toget =–4.Youcan technicallystopsimplifyinghere,as there isa
negativenumberontheright-handsideoftheequalsign.Remember,whentakingasquare
rootwitharadicalprovided,itwillyieldthepositiverootonly.So–7cannotbepartofthe
solutionset.Beverycarefulof(C),whichisatrapanswer,andchoose(B).
11. A UseFOILtomultiplythetwobinomials together.Theexpressionbecomes4 –8i+7i
–14i2.Simplify theresultbymultiplying throughwhereyoucan toget2–8i+ i–
14i2.Tocombinetheiterms,multiply8by toget .Nowtheexpressionis2– i+ i
–14i2,whichcanbefurthersimplifiedto2– i–14i2.Substitute–1for i2andcombine
liketerms:2– i–14=16– i,whichis(A).
14. A Thefirststepistogettheequationintothestandardformofaquadraticequationbymoving
all terms to the left or right side of the equation and setting it equal to zero, like this:
.Nowthatyouhavetheequationinstandardform,youcanbegintosolve
for the roots. Since you are given variables instead of numbers, factoring this quadratic
would require higher-level math, if it were even possible. You may have noticed the
familiarformoftheanswerchoices.Theyareinaformsimilartothequadraticequation.
Rememberthataquadraticinstandardformisrepresentedbytheequationax2+bx+c=
0,andthequadraticformulais .Inthisequation,a=r,b=− ,andc=–3.
Therefore, x = = . This exact format is not present in the
answerchoices,buttherootpartonlymatchestheonein(A),sothatislikelytheanswer.
Youwillhave todoa littlemoremanipulationbeforeyoucanget theequations tomatch
exactly.Thefractionsneedtobesplitup,sorewritetheequationasx= orx=
.
AlgebraDrill2:Calculator-PermittedSection
4. A Solvethefirstinequalitybysubtracting6fromeachsidesothatx>–6.Youarelookingforvalues thatwon’tworkforx,andx cannotequal–6.Therefore, theanswermustbe (A).Just tobesure,solvethenextinequalitybysubtracting1fromeachsidetoget–2x>–2.Divide by –2, remembering to switch the sign because you are dividing by a negativenumber,togetx<1.Thevaluesin(B),(C),and(D)fitthisrequirementaswell,sotheyarevaluesforxandnotthecorrectanswer.
7. B Tosolvethisequation,usecrossmultiplicationtoget(2x)(x+2)=(x2+1)(2).Expandthe
equationtoget2x2+4x=2x2+2.Onceyoucombineliketerms,theresultis2x2–2x2+4x
=2or4x=2.Solveforxbydividingbothsidesby4togetx= ,whichis(B).
10. A Translateeachstatement,piecebypiece.Thefirstparttellsusthat“theproductofxandyis76.”Sinceproductmeansmultiplication,thefirstequationmustbexy=76,soyoucaneliminate(C).Thesecondpartsaysthat“xistwicethesquareofy,”whichtranslatestox=2y2,soeliminate(B)and(D),and(A)istheonlychoiceleft.Noticethatonlytheyneedstobesquared,whichiswhy(B)iswrong.Thesecondequationfor(B)wouldbewrittenas“thesquareoftwicey,”whichisnotwhattheproblemstates.
12. D Noticethatthisquestionisaskingforanexpressioninsteadofavariable,somanipulatetheinequality to so that you get 4r + 3 in the inequality. Treat each side of the inequalityseparatelytoavoidconfusion.Startingwiththe–6<–4r+10part,multiplybothsidesofthe inequalityby–1, remembering toswitch thesign, toget6>4r–10.Add13 toeachside toget19>4r+3.Then solve the right sideof the inequality.Again,multiplybothsidesoftheinequalityby–1,switchingthesigntoget4r–10≥–2.Nowadd13toeachsideoftheequation:4r+3≥11.Finally,combinetheequationstogettherangefor4r+3.Sincethequestionasksfortheleastpossiblevalueoftheexpression,11,(D),isthecorrectanswertothequestion.Ifyouseetheanswerbeforethelaststepabove,youdon’tneedtocombinetheequations.
16. C If|x|=|2x–1|,eitherx=2x–1or–x=2x–1.Thesolutionstotheseequationsare1and
,respectively.However, theonlythingyouneedtorecognizeis that theequationhastwodifferentsolutionstoestablishthatthecorrectansweris(C).
25. D This isa systemofequationsquestion indisguise.First, locateapieceof information inthisquestionthatyoucanworkwith.“Thesumofthreenumbers,a,b,andc,is400,”seemsverystraightforward.Writetheequationa+b+c=400.Nowthequestiontellsyouthat“oneofthenumbers,a,is40percentlessthanthesumofbandc.”Translatethispiecebypiecetogeta=(1–0.4)(b+c),ora=0.6(b+c).Distributethe0.6togeta=0.6b+0.6c.Arrangethesevariablessotheylineupwiththoseinthefirstequationasa–0.6b–0.6c=0.Tosolveforb+c,stacktheequationsandmultiplythesecondequationby–1:
a+b+c=400–1(a–0.6b–0.6c)=0(–1)
Nowsolve:
Simplifybydividingbothsidesby1.6togetb+c=250.Thecorrectansweris(D).
Summary◦ Don’t“solveforx”or“solvefory”unlessyouabsolutelyhaveto.(Don’tworry;yourmathteacher
won’t find out.) Instead, look for direct solutions to SAT problems.Math Test questions rarelyrequiretime-consumingcomputationsorendlessfiddlingwithbignumbers.There’salmostalwaysatrick—ifyoucanspotit.
◦ Ifaproblemcontainsanexpressionthatcanbefactored,factorit.Ifitcontainsanexpressionthatalreadyhasbeenfactored,unfactorit.
◦ Tosolvesimultaneousequations,simplyaddorsubtracttheequations.Ifyoudon’thavetheanswer,look for multiples of your solutions.When the simultaneous equation question asks for a singlevariable and addition and subtraction don’twork, try tomake something disappear.Multiply theequationstomakethecoefficient(s)ofthevariable(s)youdon’twantgotozerowhentheequationsareaddedorsubtracted.
◦ SomeSATproblems requirealgebraicmanipulation.Use trickswhenyoucan,but ifyouhave tomanipulate the equation, take your time and work carefully to avoid unnecessary mistakes. Youdon’tgetpartialcreditforgettingtheproblemmostlycorrect.
◦ When working with inequalities don’t forget to flip the sign when you multiply and divide bynegativenumbers.
◦ When working with inequalities over a range of values, treat each side of the inequality as aseparate problem. Then combine the problems in a logical order,making sure the “arrows” arepointingtothecorrectnumbers.
◦ Whenwritingasystemofequations,startwiththemoststraightforwardpieceofinformation.Youcanalsousetheequationsintheanswerchoicestohelpyounarrowdownthepossibilitiesforyourequations.Eliminateanyanswersinwhichanequationdoesn’tmatchyourequation.
◦ Whenaquestionasksforanextraneoussolution,firstsolvetheequation,andthenplugtheanswersbackintotheequation.Iftheequationisnottruewhensolvedwiththesolution,thenthatsolutionisextraneous.
◦ When solving quadratic equations, you may need to FOIL or factor to get the equation into theeasiestformforthequestiontask.Don’tforgetaboutthecommonequationsthatthetestwritersusewhenwritingquestionsaboutquadratics.
◦ Tosolvefortherootsofaquadraticequation,setitequaltozerobymovingallthetermstotheleftsideoftheequation,orusethequadraticformula:
Whensolvingforthesumorproductoftheroots,youcanalsousetheseformulas:
sumoftheroots:−
productoftheroots:
◦ Theimaginarynumberi= ,andthereisarepeatingpatternwhenyouraiseitoapower:i,–1,–i,1.Whendoingalgebrawith i, treat itasavariable,unlessyouareable tosubstitute–1for i2whenappropriate.
◦ A complex number is a number with a real and an imaginary component joined by addition orsubtraction.Inordertorationalizeacomplexnumber,youneedtomultiplyitbyitsconjugate,orthesamecomplexnumberwiththeadditionorsubtractionsignswitchedtotheoppositesign.
◦ The absolute value of a number is its distance from zero; distances are always positive.Whenworking inside the | |, remember to consider both the positive and the negative values of theexpression.Alsorememberthat||worklike();youneedtocompletealltheoperationsinsidethe||beforeyoucanmakethevaluepositive.
Chapter13OtherAlgebraStrategiesNowthatyou’refamiliarwiththebasicsofalgebra,it’stimetolearnhowtoavoidusingalgebraontheSAT.Yes,youreadthatcorrectly.AlgebraproblemsontheSATarefilledwithtrapscarefullylaidbythetestwriters, soyouneed toknowhow toworkaround them.Thischaptergivesyou the strategiesyouneedtoturntrickyalgebraproblemsintosimplearithmetic.
PRINCETONREVIEWALGEBRA,ORHOWTOAVOIDALGEBRAONTHESATNow that you’ve reviewed some basic algebra, it’s time for some PrincetonReview algebra.At ThePrincetonReview,we like to avoid algebrawhenever possible, andwe’re going to showyouhow toavoiddoingalgebraontheSAT.Now,beforeyoustartcryingandcomplainingthatyoulovealgebraandcouldn’tpossiblygiveitup,justtakeasecondtohearusout.Wehavenothingagainstalgebra—it’sveryhelpfulwhensolvingproblems,anditimpressesyourfriends.ButontheSAT,usingalgebracanactuallyhurtyourscore,andwedon’twantthat.
Weknowit’sdifficulttocometotermswiththis.ButifyouusealgebraontheSAT,you’redoingexactlywhatthetestwriterswantyoutodo.Yousee,whenthetestwritersdesigntheproblemsontheSAT,theyexpect thestudents tousealgebra tosolve them.ManySATproblemshavebuilt-in trapsmeant to takeadvantage of common mistakes that students make when using algebra. But if you don’t use algebra,there’snowayyoucanfallintothosetraps.
Plus,whenyouavoidalgebra,youaddoneotherpowerfultooltoyourtoolbelt:IfyouareonSection4,youcanuseyourcalculator!Evenifyouhaveasuperfancycalculatorthatplaysgamesanddoublesasaglobalpositioningsystem,chancesare itdoesn’tdoalgebra.Arithmetic,on theotherhand, iseasy foryourcalculator.It’swhycalculatorswereinvented.Ourgoal,then,istoturnallthealgebraontheSATintoarithmetic.WedothatusingsomethingwecallPluggingIn.
YourBestFriendPluggingInallowsyoutouseyourcalculator
onmanyofthealgebraproblemsthatshowupon
theCalculatorsectionoftheMathTest.
PLUGGINGINTHEANSWERS(PITA)Algebrausesletterstostandfornumbers.Youdon’tgotothegrocerystoretobuyxeggsorygallonsofmilk.Mostpeoplethinkaboutmathintermsofnumbers,notlettersthatstandfornumbers.
YoushouldthinkintermsofnumbersontheSATasmuchaspossible.OnmanySATalgebraproblems,evenverydifficultones,youwillbeabletofindETS’sanswerwithoutusinganyalgebraatall.Youwilldothisbyworkingbackwardfromtheanswerchoicesinsteadoftryingtosolvetheproblemusingyourstandardmath-classmethods.
PluggingIntheAnswersisa techniqueforsolvingwordproblemsinwhichtheanswerchoicesareallnumbers.UsingthispowerfultechniquecansolvemanyalgebraproblemsontheSATsimplyandquickly.
Inalgebraclassatschool,yousolvewordproblemsbyusingequations.Then,youcheckyoursolutionbyplugginginyouranswertoseeifitworks.Whynotskiptheequationsentirelybysimplycheckingthefourpossiblesolutionsonthemultiple-choicequestions?Oneoftheseisthecorrectanswer.Youdon’thaveto
doanyalgebra,youwillseldomhave to trymore than twochoices,andyouwillneverhave to tryallfour.Notethatyoucanusethistechniqueonlyforquestionsthataskforaspecificamount.
Here’sanexample:
9. Zoëwontheraffleatafair.Shewillreceivetheprizemoneyin5monthlypayments.Ifeachpaymentishalfasmuchasthepreviousmonth’spaymentandthetotalofthepaymentsis$496,whatistheamountofthefirstpayment?A) $256B) $96C) $84D) $16
Here’sHowtoCrackItThetestwriterswouldlikeyoutogothroughalloftheeffortofsettingupthisequation:
Then,ofcourse,theywantyoutosolvetheequation.But,lookatallthosefractions!Thereareplentyofopportunitiestomakeamistakeandyoucanbetthatthetestwritershavefiguredmostofthemoutsotheycanhaveatrapanswerwaiting.So,let’sworkwiththeanswersinstead.
RepresentationMakesureyouknowwhatthenumbersintheanswerchoicesrepresent.Besure
tolabelthem!
Toworkwiththeanswerchoices,firstyouneedtoknowwhattheyrepresentsothatyoucanlabelthem.In this case, the question asks for the first payment, so write something like “first payment” over theanswers.
Now,it’stimetostartworkingthestepsoftheproblem.Butfirst,noticethattheanswerchoicesareinnumericallydescendingorder.ETS likes tokeep theirproblemsorganized so theywill alwaysput theanswersinorder.Youcanusethattoyouradvantagebystartingwithoneofthemiddleanswerchoices.Firsttry(C).
Grab(C)andaskyourself,“Ifthefirstpaymentis$84,what’sthenextthingIcanfigureout?”Inthiscase,youcouldfigureoutthesecondpayment.
So,makeachartandwritedown42(halfof84)nexttothe84.Keepdoingthattofindthevaluesofthethird,fourth,andfifthpayments.Whenyouhaveworkedallthesteps,yourproblemshouldlooklikethis:
9. Zoëwontheraffleatafair.Shewillreceivetheprizemoneyin5monthlypayments.Ifeachpaymentishalfasmuchasthepreviousmonth’spaymentandthetotalofthepaymentsis$496,whatistheamountofthefirstpayment?
Youneedtodetermineifthatwasthecorrectanswer.Theproblemsaysthatthetotalissupposedtobe$496,soaddupthepayments:84+42+21+10.50+5.25=162.75,whichismuchsmallerthan496.So,crossoff(C)and(D).
Now,allyouneedtodoistry(B).If(B)works,thenyou’redone.And,if(B)doesn’twork,you’restilldonebecausetheanswermustbe(A).That’sputtingyourPOEtogooduse!Ifthefirstpaymentis$96,thenthepaymentsare96+48+24+12+6=186,whichisstilltoosmall.Thatmeanstheanswermustbe(A),andyoudon’treallyneedtocheckit.
HerearethestepsforsolvingaproblemusingthePITAapproach:
TosolveaproblembyPluggingIntheAnswers:
1. Labeltheanswerchoices.2. Startingwithoneofthemiddleanswerchoices,workthestepsoftheproblem.Besureto
writedownalabelforeachnewstep.3. Lookforsomethingintheproblemthattellsyouwhatmusthappenfortheanswertobe
correct.4. Whenyoufindthecorrectanswer,STOP.
6.
2x+y=6
7x+2y=27
Thesystemofequationsaboveissatisfiedbywhichofthefollowingorderedpairs(x,y)?A) (−5,4)B) (4,−2)C) (5,4)D) (5,−4)
WhichWay?Sometimesit’shardtotellifyouneedalarger
numberorasmallernumberifthefirstansweryoutrieddidn’twork.Don’t
fret.Justpickadirectionandgo!Spendyourtime
tryinganswersratherthanworryingaboutgoingin
thewrongdirection.
Here’sHowtoCrackItWhen you feel the urge to do awhole lot of algebra, it is a good time to checkwhether itwould bepossible to justPlug In theAnswers instead. In this case, tryingyour answerchoiceswillbenotonlyeffectivebutalsoincrediblyfast.
Itdoesn’tseemlikeyouwillbeabletotellwhethertomoveupordownthistime,astheorderedpairsdon’treallyhaveanascendingordescendingorder,butstart inthemiddleanyway.Evenifyouenduptryingallfour,youwillbesavingtimebyPluggingIntheAnswersinsteadofsolving.
Startingwith(B)givesyou4forxand−2fory.Trythatoutinthefirstequation:2(4)+(−2)=6.Thatmatchesthefirstequation,sothisisapossibility.Tryitout inthesecondequation:7(4)+2(−2)=24.Thatdoesnotmatchthesecondequation,soyoucaneliminate(B).
Tryout(C)next.Ifx=5andy=4,then2(5)+4=14,andyouwantedittobe6,soyoucaneliminatethisanswerchoiceaswell.
Moveonto(D).Thatwouldgiveyou2(5)+(−4)=6.Sofarsogood!Trythesecondequationtoseeifthischoicesatisfiesboth:7(5)+2(−4)=27.Since(D)satisfiesbothequations,thisisyouranswer!
Youmayrecallthatwecoveredquestionslikethisinthelastchapter.Itisimportanttoknowhowtosolve
12. Abakerysoldexactly85%ofthecupcakesitbakedonTuesday.WhichofthefollowingcouldbethetotalnumberofcupcakesbakedonTuesday?
these, in case a question like this comes up in one of the Grid-In sections.When you have answersavailabletoyou,though,don’tbeafraidtousethem!
One last thing about PITA:Here’s how to determinewhether you should use this approach to solve aproblem.
Threewaystoknowthatit’stimeforPITA:
1. Therearenumbersintheanswerchoices.2. Thequestionasksforaspecificamountsuchas“whatwasthefirstpayment.”3. Youhavetheurgetowriteanalgebraicequationtosolvetheproblem.
PluggingIntheAnswers:AdvancedPrinciplesPluggingIntheAnswersworksthesamewayondifficultproblemsasitdoesoneasyandmediumones.Youjusthavetowatchyourstepandmakecertainyoudon’tmakeanycarelessmistakes.
Here’soneexample:
A) 150B) 145C) 140D) 130
Here’sHowtoCrackItIsyourfirstreactionthatthereisn’tnearlyenoughinformationheretostartonthisproblem?ThatmakesitagreatopportunitytoPlugIntheAnswers!Startwithoneofthemiddleanswerchoicesandtest itout.Sometimes,evenifyoucan’tseehowaproblemworksaheadoftime,itstartstomakealotmoresenseonceyouplugrealnumbersintoit.
Choice(B)is145,but145what?Readthequestionverycarefully.ThequestionasksforthetotalnumberofcupcakesbakedonTuesday,solabelthecolumnofanswerchoices“Total.”
Next,workyourwaythroughtheproblem.If145isthetotalnumberofcupcakesbakedonTuesday,the
numberthebakerysoldonTuesdayis85%of145,or123.25.Haveyoueverbought0.25cupcakesatabakery?Itwouldbereallyweirdforabakerytosellfractionsofcupcakes,sothisanswercouldnotbethetotalnumberbakedonTuesday.
Inthisparticularquestion,itishardtotellwhetheryoushouldtrybiggerorsmallernumbersnext,butyouhavelearnedtwothingsfromyourfirstattempt:Youcangetridof(B),andthecorrectanswerwillbetheonethatgivesyouawholenumberofcupcakes.Insteadofspendingtimetryingtopredictwhichdirectiontogofortheanswer,justgettoworkontheotheranswerchoices.
Try (C) next. If the bakery baked 140 cupcakes on Tuesday, they sold 85% of 140, or 119. Is thereanything wrongwith selling 119 cupcakes? No! Since the bakery sold only whole cupcakes, you canselect(C).
Here’sanotherexample:
7. Forwhatvalueofxis|2x+3|+5=0?A) −4B) 0C) 4D) Thereisnosuchvalueofx.
Here’sHowtoCrackItAlthoughwecovered it in the last chapter, solvingalgebraicallyonanabsolutevaluequestioncanbetreacherous:Therearesomanywaystogowrongwiththosesigns!Luckily,thisabsolutevaluequestioncomescompletewithanswerchoices,sowecansimplyPlugIntheAnswerstogetasolution.
Startwith(C).Whenyouput4inforx,youget|2(4)+3|+5=0,or16=0.Thisisclearlynottrue,socrossoff(C)andmoveonto(B).Ifxis0,thentheoriginalequationsays|2(0)+3|+5=0or8=0,soyoucaneliminate(B)aswell.Next,try(A):|2(−4)+3|+5=0couldberewrittenas|−8+3|+5=0,or|−5|+5=0.Aslongasyourememberthattheabsolutevalueofanumberisalwayspositive,itisclearthatthisgivesyou5+5=0.Sincethisisalsoclearlyuntrue,eliminate(A)andchoose(D).Apparently,thereisnosuchvalueofx!
Hey,Smarty!Ifyouthinkyoucan
improveyourSATMathscorewithoutlearningtoplugin,you’reinfor
anunpleasantsurprise.Seriously,thistechniqueworks.Justbearinmind
thatthisisamultiple-
choicetest;thecorrectanswersarealreadyright
thereonthepage.
SolvingRationalEquationsA rational equation is basically an equation in which one (ormore) of the terms is a fractional one.Rationalequationslookscary,butthereareverysimplewaysofsolvingthem.Onewayistofactoroutliketermsandthencancel.Allinall,thetestwriterscan’tgettoomessyhere,sotheywillkeepthemathniceandtidy.
Trythisone.
18. If ,thenwhichofthefollowingcouldbeavalueofx?
A) −7B) −5C) 0D) 6
QuickandPainlessUsePITA!Justbecareful
withyourcalculations,sinceyoucan’tuseyour
calculator.
Here’sHowtoCrackItHate factoring? PITA! Start with (C) and plug in 0 for x. Does everything work out? In this case, itdoesn’t.Keeptryingotheranswerchoicesuntilyoufindonethatworks.Choice(A)does,sothat’s thecorrectanswer.See?Theseareallbarkandnobite.
SolvingRadicalEquationsWecovered this topic in thepreviouschapter,buthere’sanotherexampleof solving radical equationsusingthePITAapproach.
11.
Ifk=3,whatisthesolutionsetoftheequationabove?A) {−2}B) {2}C) {2,6}D) {6}
Here’sHowtoCrackItInthelastchapter,weshowedyouhowtosolvethese—anecessaryskilliftherearenoanswerchoicestoplugin.Here,PITAisdefinitelythewaytogo.Startbyplugginginthevaluegivenfork,whichis3.Theequationbecomes .
Nowpickavalueforxfromtheanswerchoicesandplugitintotheequationtoseeifitworks.Ratherthan starting with a specific answer choice, start with a number that appears more than once in theanswers,suchasx=2.Theequationbecomes ,then ,and1=1.That’strue,soeliminate(A)and(D),whichdon’tinclude2.
Try it again with x = 6 to see if the correct answer is (B) or (C). You get or.Thisdoesn’twork,soeliminate(C)andchoose(B).
PLUGGINGINYOUROWNNUMBERSPlugging In the Answers enables you to find the answer to problems whose answer choices are allnumbers.Whataboutproblems thathaveanswerchoicescontainingvariables?On theseproblems,youwillusuallybeabletofindtheanswerbyplugginginyourownnumbers.
PluggingIniseasy.Ithasthreesteps:
1. Picknumbersforthevariablesintheproblem.2. Useyournumberstofindananswertotheproblem.Circleyouranswer.
3. PlugyournumbersfromStep1intotheanswerchoicestoseewhichchoiceequalstheansweryoufoundinStep2.
TheBasicsofPluggingInYourOwnNumbersThissortofPluggingInissimpletounderstand.Here’sanexample:
13. Whichofthefollowingisequivalenttotheexpression
A) 7−
B) 7−
C) 7−
D)
Here’sHowtoCrackIt
First,pickanumberforx.Picksomethingeasytoworkwith,like2.Inyourtestbooklet,writex=2,so
youwon’tforget.Ifx=2,then7x−4=10,andx+9=11.So,whenx=2,theexpressionintheproblem
equals .Circleit!Thatisyourtargetanswer.Whenyoufindtheanswerchoicethatalsogivesyou
whenyoupluginx=2,youwillknowyouhavefoundanequivalentexpression.
Startwiththeeasieranswerchoices:(C)and(D).For(C),does ?No!Eliminateitandmove
onto(D): alsodoesnotequalyourtargetanswer,soitcannotbeanequivalentexpression.
Nowtry(B):Whenyouputin2forx,youget .Thisisthenumberthat
youarelookingfor.UnlikePITA,whenyoupluginyourownnumbers,youmustcheckallfouranswer
choices,justincasemorethanoneworks.Goaheadandtrythelastanswerjusttomakesurethatyou’re
right.Choice(A)doesnotgiveyouyourtargetanswer,soyouknowthat(B)istheone!
GetRealTryingtoimaginehownumbersbehaveintheabstractisawasteof
time.So,iftheproblemsaysthatTinaisxyearsold,whynotpluginyour
ownage?That’srealenough.Youdon’thaveto
19. Duringaspecialsaleatafurniturestore,Ericaboughtafloorlampata10%discount.Shepaidatotaloftdollars,whichincludedthediscountedpriceofthefloorlampanda6%salestaxonthediscountedprice.Intermsoft,whatwastheoriginalpriceofthefloorlamp?
changeyournametoTina.
Here’sanotherexample:
A)
B) (0.9)(1.06)t
C)
D) 0.96t
Here’sHowtoCrackItThis could be a pretty tricky algebra question, but if you read the question carefully and plug in easynumbers,itwillbeabreeze.
Startatthebeginning.WhenEricaboughtthatfloorlamponsale,whatdidyoureallywishyouknew?Itwouldbeveryhelpfultostartthisproblemknowingtheoriginalpriceofthefloorlamp.So,startplugginginthere.Pluginanumberthatyouknowhowtotakeapercentageof,like100.Writedown“original=100”onyourscratchpaperandmoveonthenextstepoftheproblem.Ericagota10%discount,sotake10%oftheoriginalprice.Thatmeansshegota$10discount,andthediscountedpriceofherfloorlampwas$90.Writethatdownandmoveontothesalestax.Ifyoureadcarefully,itisclearthatthesalestaxis6%of thediscountedprice.So,youneedto take6%of the$90discountedprice,or$5.40.Togethertotal,addthe$5.40oftaxtothe$90forthediscountedfloorlamp,andyouget$95.40.Thisiswherethecarefulreadingcomesin.Thevariabletinthisproblemissupposedtobethetotalamountshepaid,somakesurethatyoulabelthisonyourscratchpaper“t=$95.40.”
Next,readthelastsentenceofthequestionagaintobesureyouknowwhichoftheanswersisyourtargetanswer.Thequestionasksfortheoriginalpriceofthefloorlamp,socirclethenumberyoupluggedinfortheoriginalprice.Yourtargetansweris100.
Ontotheanswerchoices!Whenyouput$95.40infor t in (A),youget99.375.This isnotyour targetanswer,soyoucaneliminate(A).Choice(B)givesyou91.0116,sothatwillnotworkeither.Pluggingin$95.40into(C)yieldsthetargetof100,sohangontoitwhileyoucheck(D)justincase.Whenyoupluginfor(D),youget91.584.Sincethatdoesnotmatchyourtarget,youcaneliminate(D)andchoose(C)!
14. If60equallypriceddownloadscostxdollars,thenhowmuchdo9downloadscost?
WhichNumbers?Althoughyoucanpluginanynumber,youcanmakeyourlifemucheasierbypluggingin“good”numbers—numbersthataresimpletoworkwithorthatmaketheproblemeasiertomanipulate.Pickingasmallnumber,suchas2,willusuallymakefindingtheanswereasier.Iftheproblemasksforapercentage,plugin100.Iftheproblemhastodowithminutes,try30or120.
Except inspecialcases,youshouldavoidpluggingin0and1; thesenumbershaveweirdproperties.Usingthemmayallowyoutoeliminateonlyoneortwochoicesatatime.Youshouldalsoavoidplugginginanynumber thatappears in thequestionor inanyof theanswerchoices.Using thosenumberscouldmakemorethanoneanswermatchyourtarget.Ifmorethanoneanswerchoicematchesyourtarget,pluginanewnumberandcheckthoseanswerchoices.YoumayhavetoPlugInmorethanoncetoeliminateallthreeincorrectanswers.
BeGood“Good”numbersmakea
problemlessconfusingbysimplifyingthearithmetic.
ThisisyourchancetomaketheSATeasier
foryou.
Manytimesyou’llfindthatthereisanadvantagetopickingaparticularnumber,evenaverylargeone,becauseitmakessolvingtheproblemmorestraightforward.
Here’sanexample.
A)
B)
C) 60x+9
20. Awatchlosesxminuteseveryyhours.Atthisrate,howmanyhourswillthewatchloseinoneweek?
D)
Here’sHowtoCrackItShouldyouplugin2forx?Youcould,butpluggingin120wouldmaketheproblemeasier.Afterall,if60downloadscostatotalof$120,theneachdownloadcosts$2.Writex=120inyourtestbooklet.
Ifeachdownloadcosts$2,then9downloadscost$18.Writean18inyourtestbookletandcircleit.Youarelookingfortheanswerchoicethatworksoutto18whenyouplugin$120forx.Tryeachchoice:
A)
B)
C) 60(120)+9≠18
D) =18Here’syouranswer.
Let’stryanotherexample.
A) 7xy
B)
C)
D)
Here’sHowtoCrackItThisisanextremelydifficultproblemforstudentswhotrytosolveitusingmath-classalgebra.You’llbeabletofindtheanswereasily,though,ifyouPlugIncarefully.
Whatnumbersshouldyouplugin?Asalways,youcanpluginanything.However,ifyouthinkjustalittlebitbeforechoosingthenumbers,youcanmaketheproblemeasiertounderstand.Therearethreeunitsoftime—minutes,hours,andweeks—andthat’sabigpartofthereasonthisproblemishardtounderstand.Ifyouchooseunitsoftimethatareeasytothinkabout,you’llmaketheproblemeasiertohandle.
Startbychoosingavalueforx,whichrepresentsthenumberofminutesthatthewatchloses.Youmightbetemptedtochoosex=60andthatwouldmakethemathprettyeasy.However,it’susuallynotagoodideatochooseaconversionfactorsuchas60,theconversionfactorbetweenminutesandhours,whenpluggingin.Whendealingwithtime,30isusuallyasaferchoice.So,writedownx=30.
Next,youneedanumberfory,whichrepresentsthenumberofhours.Again,youmightbetemptedtousey=24,butthat’stheconversionfactorbetweenhoursanddays.Therefore,y=12isasaferchoice.Writedowny=12.
Now, it’s time to solve the problem to comeupwith a target. If thewatch loses 30minutes every 12hours,thenitloses60minutesevery24hours.Putanotherway,thewatchlosesanhoureachday.Inoneweek,thewatchwilllose7hours.That’syourtargetsobesuretocircleit.
Now,youjustneedtochecktheanswerchoicestoseewhichonegivesyou7whenx=30andy=12.
A) 7xy=7(30)(12)=Somethingtoobig!Crossitoff.
B) .Alsowrong.
C) Crossitoff.
D) Chooseit!
InequalitiesPluggingInworksonproblemscontaininginequalities,butyouwillhavetofollowsomedifferentrules.Plugginginonenumberisoftennotenough;let’slookatanexamplewherethisisthecase.
6. MammothPrintingCompanychargesafeeof$28toprintanoversizedposter,and$7foreachcolorofinkusedintheposter.ColossalPrintingchargesafeeof$34toprintanoversizedposterand$5.50foreachcolorofinkused.Ifxrepresentsthenumberofcolorsofinkusedtoprintaposter,whatareallthevaluesofxforwhichMammothPrintingCompanywouldchargemoretoprinttheposterthanColossalPrinting?A) x<4B) 2≤x≤4
C) 4≤x≤7D) x>4
Here’sHowtoCrackItSinceyou are looking for an amount thatwouldmake theMammothPrintingCompany’s pricegreaterthanColossalPrinting’sprice,youhaveaninequality.
PluggingInonan inequalityquestionmeansselectingavalue forx that answers thequestion, and thencomparing it to the inequalities in the answer choices.Remember, youmay have to trymore than onenumberwith inequalityquestions,since thenumberyou try firstmaysatisfy the inequality inmore thanoneanswerchoice!
Start out by trying a small number, likex = 2.Sincex is the number of colors of ink used,MammothPrintingCompanywouldcharge$28toprinttheposter,plus$7foreachofthe2colors,foratotalof$42.ColossalPrintingwouldcharge$34toprinttheposter,plus$5.50foreachofthe2colors,or$45total.Thatmeansthatwhenx=2,MammothPrintingCompanywouldchargelessthanColossalPrinting,and2isnotanumberthatworksasasolutiontothisproblem.
Tryabiggernumber,suchasx=5.Iftheposterhad5colors,MammothPrintingCompanywouldcharge$28toprinttheposter,plus$7foreachofthe5colors,foratotalof$63.ColossalPrintingwouldcharge$34toprinttheposter,plus$5.50foreachofthe5colors,or$61.50total.Thatmeansthatwhenx=5,thepriceMammothchargeswouldbemorethanColossal’sprice,sothisisapossiblevalueforx.
Once you have a value for x that satisfies the question, it’s time tomove to the answer choices.Youshouldeliminate(A)and(B),becausex=5doesnotsatisfyeitherofthoseinequalities.Choices(C)and(D)aresatisfiedwhenx=5,sotheyarestillpossible.
Next,youneedtofindanumberthatwillsatisfytheinequalityinoneoftheremaininganswerchoicesbutnot the other, so you can determine whether (C) or (D) is your final answer. Looking at the answerchoices,youcanseethatwewillhavetothinkaboutplugginginanumberthatwilleliminateoneanswerchoicebutnottheother.Tryoutx=4,becauseitsatisfies(C)butnot(D).MammothPrintingCompanywouldcharge$56fora4-colorposter.
$28+$7(4)=$56
ColossalPrintingwouldalsocharge$56fora4-colorposter.
$34+$5.50(4)=$56
SinceMammoth would not charge more to print the poster than Colossal, you can eliminate (C) andchoose(D).
Using different integers got you down to one answer choice on that question. Sometimes, to find the
answer,youmayhavetopluginseveralnumbers,includingweirdnumberslike−1,0,1, ,and .
WeirdNumbersAsyoumayhavenoticed,
somenumbershaveuncommonproperties.Becauseofthis,youshouldplugtheminonlyundercertain
circumstances,likesolvinginequalities,forexample.
Thefivenumbersjustmentionedallhavespecialproperties.Negatives,fractions,0,and1allbehaveinpeculiarwayswhen,forexample,theyaresquared.Don’tforgetaboutthem!
PluggingIn:AdvancedPrinciplesIf there are variables in the answer choices, you should definitely consider Plugging In. However,sometimesaquestionwillbeaPlugInquestionthatdoesn’thavevariablesintheanswerchoices.Itis,instead,aHiddenPlugInquestion.Itwillrefertosomeunknownamount,butneveractuallygiveyouanumber.So,you’regoingtohavetomakeupyourownnumber.
Here’sanexample.
15.
Vikisdecidingwhichbrandofgranolatobuy.Heprefersgranolawithalotofcashews,sohehasmadeachart(above)showingthecashewcontent,asapercentageofthetotalweightofthegranola,ofeachofthe4leadingbrandsofbulkgranola.IfHealthyGranolacosts$4apound,CrunchyGranolacosts$5.40apound,We’reNuts!Granolacosts$7.00apound,andHolaGranolacosts$5apound,whichbrandofgranolawouldofferVikthegreatestamountofcashewsperdollar?A) HealthyGranolaB) CrunchyGranolaC) We’reNuts!D) HolaGranola
Here’sHowtoCrackItThisisoneofthosequestionsthathassomuchinformationinit,itisalmostimpossibletoknowwheretostart. Itdoesn’thelp thatall theamountsarepercentages,andyoudon’tevenknowthe totalamountofgranolaVikisgoingtobuy.ThatfeelingthatyouwishyouhadsomerealamounttostartwithtellsyouthatthisisagreatopportunitytoPlugIn,eventhoughtherearenovariablesintheanswerchoices.ThisisaHiddenPlugIn.
YouhavealreadyrealizedthatthemosthelpfulthingtoknowherewouldbehowmuchgranolaVikwillbuy, so start by plugging in for that amount. The easiest number to plug in when you will be usingpercentagesis100,soeventhoughitisaprettyridiculousamountofgranolaforoneguy,findoutwhathappens ifVikbuys100poundsofgranola.Writedown“total=100pounds” inyour testbooklet,and
starttoworktheproblemonepieceatatime.
Onceyouhavea100poundtotal,itisrelativelysimpletocomeupwiththeamountofcashewsineachgranola.Keeptrackoftheminyourtestbooklet:
100lbsHealthyGranola=25lbsofcashews
100lbsCrunchyGranola=30lbsofcashews
100lbsWe’reNuts!=35lbsofcashews
100lbsHolaGranola=20lbsofcashews
Thenextpieceisprice.Addthepriceof100poundsofeachgranolatoyourscratchpaper:
100lbsHealthyGranola=25lbsofcashews=$400total
100lbsCrunchyGranola=30lbsofcashews=$540total
100lbsWe’reNuts!=35lbsofcashews=$700total
100lbsHolaGranola=20lbsofcashews=$500total
Withthisinformation,youcanstarttofigureouthowmuchVikispayingperpoundofcashews.
HealthyGranolacontains25lbsofcashewsfor$400.Ifyoudothemath,thatis$400÷25lbscashewsor$16perpoundofcashews.CrunchyGranolacosts$540for30lbsofcashewsor$540÷30lbscashews=$18/lbcashews.Sincethisismoreexpensive,youcaneliminate(B).ThisisnothowVikisgoingtogetthegreatestamountofcashewsperdollar.We’reNuts!,besideshavingagreatname,alsohasa reallyhighpercentageofcashews.YoumightthinkthatwouldbeVik’sbestbuy,butwhenyoudothemath,$700for35lbsofcashewsis$700÷35lbscashewsor$20/lbcashews.Thisislesscashewperdollarthan(A), soeliminate (C).HolaGranolacosts$500 for20 lbsofcashews,and$500÷20 lbscashews isgoing to come out to awhopping $25/lb cashews. That is definitely not the best deal on cashews, soeliminate(D).
Apparently,nothingisgoingtobeatHealthyGranolaintermsofthecashewcontentperdollar!Youcanchoose(A),andleaveViktofigureoutwhatheisgoingtodowithallthatgranola.
MeaninginContextSomequestions,insteadofaskingyoutocomeupwithanequation,justwantyoutorecognizewhatapartof theequationstands for. It sounds likea simpleenough task,butwhenyou lookat theequation, theyhavemadeitreallyhardtoseewhatisgoingon.Forthisreason,meaning-in-contextquestionsareagreatopportunitytopluginrealnumbersandstarttoseehowtheequationreallyworks!
First things first, though, youwant to think about your POOD:Does this question fit into your pacinggoals?Itmighttakeabitoflegworktogetananswer,andyoumayneedthattimetogocollectpointsoneasier,quickerquestions.
Ifthisquestiondoesfitintoyourpacingplan,youshouldreadcarefully,labeleverythingyoucanintheequation,andPOEtogetridofanyanswerchoicesthatareclearlyonthewrongtrack.Then,it’stimetoplugsomeofyourownnumbersintoseewhatisgoingoninthere.
Here’sanexample.
7.
n=1,273−4p
Theequationabovewasusedbythecafeteriainalargepublichighschooltomodeltherelationshipbetweenthenumberofslicesofpizza,n,solddailyandthepriceofasliceofpizza,p,indollars.Whatdoesthenumber4representinthisequation?A) Forevery$4thepriceofpizzadecreases,thecafeteriasells1moresliceofpizza.B) Foreverydollarthepriceofpizzadecreases,thecafeteriasells4moreslicesof
pizza.C) Forevery$4thepriceofpizzaincreases,thecafeteriasells1moresliceofpizza.D) Foreverydollarthepriceofpizzaincreases,thecafeteriasells4moreslicesof
pizza.
Here’sHowtoCrackItFirst,readthequestionverycarefully,anduseyourpenciltolabelthevariables.Youknowthatpisthepriceofpizza,andnisthenumberofslices,soyoucanaddthatinformationtotheequation.Ifyoucan,eliminate answer choices that don’tmake sense. Butwhat if you can’t eliminate anything, or you caneliminateonlyananswerchoiceortwo?
Evenwitheverythinglabeled,thisequationisdifficulttodecode,soit’stimetoPlugIn!Tryafewofyourownnumbersintheequation,andyouwillgetamuchbetterunderstandingofwhatishappening.
Tryitoutwithp=2.Whenyouput2inforp,n=1,273−4(2)or1,265.
So,whenp=2,n=1,265.Inotherwords,at$2aslice,thecafeteriasells1,265slices.
Whenp=3,n=1,261,soat$3aslice,thecafeteriasells1,261slices.
Whenp=4,n=1,257,soat$4aslice,thecafeteriasells1,257slices.
Now,usePOE.Firstofall,isthecafeteriasellingmorepizzaasthepricegoesup?No,asthepriceofpizzagoesup,thecafeteriasellsfewerslicesofpizza.Thatmeansyoucaneliminate(C)and(D).
Choice (A)says that forevery$4 thepricegoesdown, thecafeteriasells1moresliceofpizza.Doesyourplugginginbackthatup?No.Thecafeteriasells8moreslicesofpizzawhenthepricedropsfrom$4to$2,so(A)isnogood.
Nowtakealookat(B).Doesthecafeteriasell4moreslicesofpizzaforeverydollarthepricedrops?Yes!Choice(B)isthecorrectanswer.
HerearethestepsforusingPluggingIntosolvemeaning-in-contextquestions:
MeaninginContext
1. Readthequestioncarefully.Makesureyouknowwhichpartoftheequationyouarebeingaskedtoidentify.
2. Useyourpenciltolabelthepartsoftheequationyoucanidentify.3. Eliminateanyanswerchoicesthatclearlydescribethewrongpartoftheequation,orgo
againstwhatyouhavelabeled.4. PlugIn!Useyourownnumberstostartseeingwhatishappeningintheequation.5. UsePOEagain,usingtheinformationyoulearnedfromplugginginrealnumbers,untilyou
cangetitdowntooneanswerchoice.Orgetitdowntoasfewchoicesasyoucan,andguess.
Let’slookataslightlydifferentonenow.
10.
7x+y=133
JeffreyhassetamonthlybudgetforpurchasingfrozenblendedmochadrinksfromhislocalSpendBuckscoffeeshop.Theequationabovecanbeusedtomodeltheamountofhisbudget,y,indollarsthatremainsafterbuyingcoffeeforxdaysinamonth.Whatdoesitmeanthat(19,0)isasolutiontothisequation?A) Jeffreystartsthemonthwithabudgetof$19.B) Jeffreyspends$19oncoffeeeveryday.C) Ittakes19daysforJeffreytodrink133cupsofcoffee.
D) Ittakes19daysforJeffreytorunoutofmoneyinhisbudgetforpurchasingcoffee.
Here’sHowtoCrackItStartbylabelingthexandthey intheequationtokeeptrackofwhattheystandfor.Useyourpenciltowrite“days”above thex and“budget”above they.So7×days+budget=133.Hmm, still notveryclear,isit?Onewaytoapproachthisistopluginthepoint.Ifx=days=19wheny=budget=0,thenJeffreywillhavenobudgetleftafter19days.Thismatches(D).
Ifyouhave trouble seeing this, youcanuse the answer choices tohelpyouPlug In. If (A) is true, thebudgetatthestartofthemonth,whendays=0,is$19.Plugthesevaluesintotheequationtoseeifitistrue.Is7×0+19=133?Notatall,soeliminate(A).If(B)istrue,Jeffreydrinksalotofcoffee!Trysomenumbersandseeifitworks.Forx=1,theequationbecomes7(1)+y=133ory=126,andforx=2,itis7(2)+y=133ory=119.Thedifferenceiny,thebudgetremaining,is126−119=7,sothat’snot$19perday.Eliminate(B)soonly(C)and(D)remain.Thesebothhave19forthenumberofdays,andthepoint(19,0)wouldindicatethat19isthex-value,ordays.Ifyousawthatrightaway—great!Thatwouldallowyoutoskiprighttotesting(C)and(D).
For(C),youcanplugin19fordaysintheequationtoget7×19+budget=133,orbudget=0.DoesthattellyouhowmanycupsofcoffeeJeffreydrank?Youhavenoinformationaboutthecostofasinglecupofcoffee,sotheanswercan’tbe(C).Itdoestellyou,however,thatafter19days,Jeffreyhasnobudgetleft,so(D)isnotonlytheoneremaininganswer,butitisalsothecorrectone!
AlgebraStrategiesDrill1:NoCalculatorSectionWork these algebra questions without your calculator, using Plugging In or PITA. Answers andexplanationscanbefoundonthispage.
5. Thelengthofacertainrectangleistwicethewidth.Iftheareaoftherectangleis128,whatisthelengthoftherectangle?A) 4B) 8C) 16
D)
10. Ifxy<0,whichofthefollowingmustbetrue? I.x+y=0 II.2y−2x<0 III.x2+y2>0A) IonlyB) IIIonlyC) IandIIID) IIandIII
13. If ,whatisthevalueofx?
A) 4B) 16C)
D) 32
15. Ify=3xandxandyarebothintegers,whichofthefollowingisequivalentto9x+3x+1?A) y3
B) 3y+3C) y(y+3)D) y2+3
AlgebraStrategiesDrill2:Calculator-PermittedSectionFeelfreetouseyourcalculatorasneededtoapplythePluggingInskillsyou’velearnedsofar.Answersandexplanationscanbefoundonthispage.
8. IfAlexcanfold12napkinsinxminutes,howmanynapkinscanhefoldinyhours?
A)
B)
C)
D)
12. Nailsaresoldin8-ounceand20-ounceboxes.If50boxesofnailsweresoldandthetotalweightofthenailssoldwaslessthan600ounces,whatisthegreatestpossiblenumberof20-ounceboxesthatcouldhavebeensold?A) 33B) 25C) 17D) 16
18. Ifais63%ofxandcis ofx,whichofthefollowingistheclosestequivalentofthe
ratioofatoc?A) 0.236B) 0.381C) 0.595D) 1.680
21. If andx>y>0,thenwhichofthefollowingisequalto ?
A) x+y
B) x−y
C)
D)
24. Agasstationsellsregulargasolinefor$2.39pergallonandpremiumgasolinefor$2.79pergallon.Ifthegasstationsoldatotalof550gallonsofbothtypesofgasolineinonedayforatotalof$1,344.50,howmanygallonsofpremiumgasolineweresold?A) 25B) 75C) 175D) 475
25. Therearekgallonsofgasolineavailabletofillatank.Afterdgallonshavebeenpumped,intermsofkandd,whatpercentofthegasolinehasbeenpumped?
A)
B)
C)
D)
CHAPTERDRILLANSWERSANDEXPLANATIONS
AlgebraStrategiesDrill1:NoCalculatorSection5. C PlugIntheAnswers.Ifyoustartwith(B),thelengthis8,andthewidthishalfthat,or4.Areais
length×width.Theareaofthisrectangleis8×4,whichisnowherenear128.Eliminate(A)and(B),asbotharetoosmall.Try(C):Ifthelengthis16,thewidthis8.So,does128=16×8?Youcouldwriteitallout,sinceyoucan’tuseyourcalculator,butyoucanalsoestimate.16×10=160, so16×8wouldbeabout130.Thenumber in (D) is too largeandwillgiveaweirdfraction,so(C)iscorrect.Alternatively,writeanequation.Theequationisarea=w×2w.So,128=2w2.Divideby2toget64=w2.Takethesquarerootofbothsidestofindw=8.Thelengthistwicethiswidth,solength=2×8=16,andtheansweris(C).
10. B AquestionwithunknownvariablesindicatesagoodplacetoPlugIn.Youneednumbersforxandy thatwillgiveyouanegativeproduct.Tryx=1andy=−2. Ifyouplug these into thestatementsintheRomannumerals,youfindthat(I)isfalse,but(II)and(III)aretrue.Youcaneliminate any answer choice that contains (I). This leaves (B) and (D). Now try differentnumberstoseeifyoucaneliminateanotherchoice.Ifyoutryx=−1andy=2,youfindthat(II)isfalseand(III)isstilltrue.Thisleavesyouwith(B),whichiscorrect.
13. D PlugIntheAnswers,startingwith(B).Ifx=16,theleftsideoftheequationis .
Doesthatequal ?No—it’stoosmall.Choice(C)isuglytoworkwith,sotry(D)next.Ifit
is too big, (C) is your answer. For (D), x = 32, and the left side of the equation becomes
. It’s a match, so (D) is correct. You could also solve this
algebraically.Multiplybothsidesby2toget .Squarebothsidestogetx=16×2=
32.Choice(D)iscorrect.
15. C Therearevariablesintheanswerchoices,whichmeansthisisaperfectPlugInproblem.Sinceyoucan’tuseacalculator,makeupaneasyvalueforx,suchas2.9x+3x+1thenbecomes92+32+1=81+27=108.Usethenumberyoupluggedinforxtotrytofindy:y=3x,soy=32=9.Nowpluginy=9toeachanswerchoicetoseewhichonegivesyou108.Choice(C)isy(y+3),whichis9(12)=108,thecorrectanswer.
AlgebraStrategiesDrill2:Calculator-PermittedSection8. C TwovariablestellsyouthisisagreatplacetoPlugIn.Picknumbersthatmakethematheasy.
Youcantryx=30andy=2.Soin2hoursthereare4periodsof30minuteseach:12×4=48.Alexcanfold48napkinsin2hours.48isyourtarget.Pluggingintoyouranswerchoicesgivesyou(C).
12. D ThisisaperfectquestionforPITA.Thequestionasksforthegreatestpossiblenumberof20-ounceboxes.Startwith(B).Iftherearetwenty-five20-ounceboxes,thentherearetwenty-five8-ounce boxes because a total of 50 boxeswas purchased. In this case, the twenty-five 20-ounceboxesweigh500ounces,andthetwenty-five8-ounceboxesweigh200ounces;thetotalis700ounces.Thisistoobigbecausethequestionsaysthetotalweightwaslessthan600.If(B)istoobig,(A)mustalsobetoobig;eliminatebothanswers.Ifyoutry(C),thetotalweightis604ounces,whichisstilltoobig.Thus,theansweris(D).
18. D Sinceyouarenevertoldwhatxis,andthereisnowaytofindit,pluginforx.Saythatx=100.
63%of100is63,and of100is37.5.Theratioofatocis .So, =1.68.Tosavetime,
youcanBallparktheanswer,sincea>cand(D)istheonlychoicegreaterthan1.
21. D Here’s yet another chance to Plug In because of the variables in the answer choices. In this
case,youhaveseveralvariables.Youshouldstartbyplugginginvaluesforxandy,and then
workoutc.Becausex>y>0,sayx=6andy=3.Therefore, .The
questionasksforthevalueof ,whichisthereciprocalof ,or2.Thisisyourtargetanswer.If
youplugx=6andy=3intoalloftheanswerchoices,you’llfindthatonly(D)equals2.
24. B Whenaskedforaspecificvalue,tryPluggingIntheAnswers.Labelthemasgallonsofpremiumand startwith thevalue in (B). If 75gallonsof premiumwere sold, the stationwouldmake75($2.79)=$209.25forthosesales.Atotalof550gallonswassold,sothestationwouldhavesold550−75=475gallonsofregulargasoline.Thesalesfortheregulargasolinewouldbe475($2.39) = $1,135.25. The total sales for both types of gasoline would be $209.25 +$1,135.25=$1,344.50.Thatmatchestheinformationinthequestion,so(B)iscorrect.
25. A Variablesintheanswerchoices?PlugIn!Thisisapercentquestion,somakek=100andd=40. If 40 out of the 100gallons have beenpumped, that equals 40%.So40% is your targetanswer.Whenyouplugk=100andd=40intotheanswers,only(A)givesyou40.Remember,PluggingIncanturnadifficultquestionintoamuchmorestraightforwardone.
Summary◦ Whenanalgebraquestionhasnumbersintheanswerchoices,plugeachoftheanswerchoicesinto
theproblemuntilyoufindonethatworks.
◦ Ifyoustartwithoneofthemiddlenumbers,youmaybeabletocutyourwork.Theanswerchoiceswillbeinorder,soifyournumberistoohighortoolow,you’llknowwhattoeliminate.
◦ Whenthequestionhasvariablesintheanswerchoices,youcanoftenpluginyourownamountsfortheunknownsanddoarithmeticinsteadofalgebra.
◦ When you Plug In, use “good” numbers—ones that are simple to work with and that make theproblemeasiertomanipulate:2,5,10,or100aregenerallyeasynumberstouse.
◦ PluggingInworksonproblemscontaininginequalities,butyouwillhavetobecarefulandfollowsomedifferentrules.Plugginginonenumberisoftennotenough;tofindtheanswer,youmayhavetopluginseveralnumbers.
◦ NoteveryPlugInquestionhasvariablesintheanswerchoices.Forsomeproblems,therewillbesomeunknownamount.Inthatcase,trymakingupanumber.
◦ PluggingIncanalsobeusedonmeaning-in-contextquestions. Ifaquestionasksyou to identifyapartofanequation,plugyourownamountsintotheequationsoyoucanstarttoseewhatisgoingon.
Chapter14AdvancedArithmeticNowthatwehavereviewedsomemathematicalfundamentalsandsomealgebra, it is timetojumpintoour reviewof themoreadvancedarithmeticconceptsyouwill findon theSAT.Manyquestionson theMathsections testconceptsyou learned in juniorhighschool, suchasaveragesandproportions.Somedifficultquestionsbuildon thesebasicconceptsby requiringyou tousechartsanddata toobtainyournumbersorcombinemultiple techniques. In thischapter,wewill reviewthearithmeticconceptsyou’llneedtoknowfortheSATandshowyouhowtoapplytheseconceptswhenworkingwithchartsanddata.All of the questions in this chapter represent the kinds of questions that appear in the calculator-permittedsectionofthetest.
RATIOSANDPROPORTIONS
ARatioIsaComparisonManystudentsgetextremelynervouswhentheyareaskedtoworkwithratios.Butthere’snoneedtobenervous.Aratioisacomparisonbetweenthequantitiesofingredientsyouhaveinamixture,beitaclassfull of people or a bowl of cake batter. Ratios can be written to look like fractions—don’t get themconfused.
Theratioofxtoycanbeexpressedinthefollowingthreeways:
1.
2. theratioofxtoy
3. x:y
Part,Part,WholeRatios are a lot like fractions. In fact, anything you can do to a fraction (convert it to a decimal orpercentage,reduceit,andsoon),youcandotoaratio.Thedifferenceisthatafractiongivesyouapart(thetopnumber)overawhole(thebottomnumber),whilearatiotypicallygivesyoutwoparts(boystogirls,CDstocassettes,sugartoflour),anditisyourjobtocomeupwiththewhole.Forexample,ifthereisonecupofsugarforeverytwocupsofflourinarecipe,that’sthreecupsofstuff.Theratioofsugartoflouris1:2.Addthepartstogetthewhole.
Ratiosvs.FractionsKeepinmindthataratio
comparespartofsomethingtoanotherpart.
Afractioncomparespartofsomethingtothe
wholething.
Ratio:
Fraction:
RatiotoRealIfaclasscontains3studentsandtheratioofboystogirlsinthatclassis2:1,howmanyboysandhowmanygirlsarethereintheclass?Ofcourse:Thereare2boysand1girl.
Now,supposeaclasscontains24studentsandtheratioofboystogirlsisstill2:1.Howmanyboysandhowmanygirlsarethereintheclass?Thisisalittleharder,buttheansweriseasytofindifyouthinkaboutit.Thereare16boysand8girls.
Howdidweget theanswer?Weaddedup thenumberof“parts” in theratio (2partsboysplus1partgirls,or3partsalltogether)anddivideditintothetotalnumberofstudents.Inotherwords,wedivided24by3.Thistoldusthattheclasscontained3equalpartsof8studentseach.Fromthegivenratio(2:1),weknewthattwoofthesepartsconsistedofboysandoneofthemconsistedofgirls.
AneasywaytokeeptrackofallthisistouseatoolwecalltheRatioBox.
Here’showitworks.
Let’sgobacktoourclasscontaining24students,inwhichtheratioofboystogirlsis2:1.Quicklysketchatablethathascolumnsandrows,likethis:
Thisistheinformationyouhavebeengiven.Theratiois2:1,soyouhave2partsboysand1partgirls,foratotalof3parts.Youalsoknowthattheactualnumberofstudentsinthewholeclassis24.Youstartbywritingthesenumbersintheproperspacesinyourbox.
Yourgoalistofillinthetwoemptyspacesinthebottomrow.Todothat,youwillmultiplyeachnumberinthepartsrowbythesamenumber.Tofindthatnumber,lookinthelastcolumn.Whatnumberwouldyoumultiplyby3toget24?Youshouldseeeasilythatyouwouldmultiplyby8.Therefore,writean8inall threeblanksintheMultiplyBy row. (Thespaces in this rowwillalwayscontain thesamenumber,althoughofcourseitwon’talwaysbean8.)Here’swhatyourRatioBoxshouldlooklikenow:
Thenextstepistofillintheemptyspacesinthebottomrow.Youdothatthesamewayyoudidinthelastcolumn,bymultiplying.First,multiplythenumbersintheboyscolumn(2×8=16).Then,multiplythenumbersinthegirlscolumn(1×8=8).
Here’swhatyourboxshouldlooklikenow:
12. Anacidicsolutionismixedsothatthemassratioofnitricacidtowateris2:7.Ifatotalof270gramsofacidsolutionismixed,howmanymoregramsofwateraretherethanthenitricacid?
Nowyouhaveenoughinformationtoansweranyquestionyoumightbeasked.Herearesomeexamples:
• Whatistheratioofboystogirls?Youcanseeeasilyfromtheratio(parts)rowoftheboxthattheratiois2:1.
• Whatistheratioofgirlstoboys?Youcanseeeasilyfromtheratio(parts)rowoftheboxthattheratiois1:2.
• Whatisthetotalnumberofboysintheclass?Youcanseeeasilyfromthebottomrowoftheboxthatitis16.
• Whatisthetotalnumberofgirlsintheclass?Youcanseeeasilyfromthebottomrowoftheboxthatitis8.
• Whatfractionalpartoftheclassisboys?Thereare16boysinaclassof24,sothefractionrepresentingtheboysis ,whichcanbereducedto .
Asyoucansee, theRatioBox isaneasyway to find,organize,andkeep trackof informationonratioproblems.And itworks thesamenomatterwhat informationyouaregiven. Just remember thatall theboxesintheMultiplyByrowwillalwayscontainthesamenumber.
Here’sanotherexample:
A) 60B) 110C) 150D) 210
Here’sHowtoCrackItForthisquestion,yourRatioBoxshouldlooklikethis:
Nowfindthemultiplier.Whatdoyoumultiply9bytoget270?Thatnumberis30,sowrite30ineachboxintheMultiplyByrow.
Thequestionaskshowmanymoregramsofwaterareinthesolutionthantherearegramsofnitricacid,somultiplybothcolumnstofindtheactualnumbers.
Tofindthedifferencebetweenthenumberofgramsofnitricacidandwater,subtract:210−60=150.Thecorrectansweris(C).
Don’t forget thatyoucanusemore thanone technique to solveaproblem.There’sno reasonwhyyoucan’tcombinetheRatioBoxwithsomeformofPluggingIn.Infact,ifonetechniquemakestheproblemeasy,twotechniquesmightmakeitdownrightsimple!
17. InMissHoover’sclass,theratioofboystogirlsisxtoy.Ifthetotalnumberofchildrenintheclassisfivetimesthenumberofboysintheclass,andxandyareintegers,whichofthefollowingcouldbethesumofxandy?
Here’saproblemforwhichcombiningtechniquesisjusttheticket.
A) 9B) 10C) 11D) 12
Here’sHowtoCrackItSincetheproblemusesthewordratio,youcanusetheRatioBox.However,theRatioBoxworksbestwithnumbersrather thanvariables.What todo?PlugIn,ofcourse!It’sdifficult topluginforxandy,becausetheratiowilldependonthenumberofboysintheclass.Startwiththatnumberandsaythereare4boysintheclass.Thetotalnumberofstudentsistherefore20,orfivetimes4.Now,it’stimetodrawtheRatioBoxandfillinwhatyouknow:
Nowusetheboxtofindtheratio,whichwillgiveyouyourxandyvalues.Ifthereare4boys,thereare16girls.Pluginasimplemultiplier,like2.Workbackwardstofindthepartsoftheratio.Ifthereare4actualboysandthemultiplieris2,theboyspartoftheratiois2.Thegirlspartoftheratiois8.Here’swhatyourfilled-inboxshouldlooklike:
5. If2packagescontainatotalof12doughnuts,howmanydoughnutsaretherein5packages?
Inthisexample,x=2andy=8,sothesumis10,whichhappenstobeoneoftheanswerchoices:(B).Wegotluckywiththenumberswepickedandgotexactlywhatwewanted.Sometimes,youmayneedtopluginafewtimestoseeifthereisapattern.Regardlessofwhereyoustart,thesumoftheratiopartsinthisclasswillalwaysbeamultipleof5.
ProportionsAreEqualRatiosSome SAT math problems will contain two proportional, or equal, ratios from which one piece ofinformationismissing.
Here’sanexample.
A) 24B) 30C) 36D) 60
Here’sHowtoCrackItThisproblemsimplydescribestwoequalratios,oneofwhichismissingasinglepieceofinformation.Here’sthegiveninformationrepresentedastwoequalratios:
21. Garyisusinga3Dprintertocreateaminiatureversionofhimself.Thescaleoftheminiatureis0.4inchesto1footofGary’sactualheight.IfGaryis5feetand9inchestall,whatwillbetheheightofhis3D-printedminiature?(12inches=1foot)
Becauseratioscanbewrittensotheylooklikefractions,youcantreatthemexactlylikefractions.Tofind
theanswer,allyouhavetodoisfigureoutwhatyoucouldpluginforxthatwouldmake .Now
cross-multiply:
Theansweris(B).
Manyproportionquestionswillalso involveunitconversion.Besure topayattentions to theunitsandhavethesameunitsinbothnumeratorsandthesameunitsinbothdenominators.
Let’slookatanexample.
A) 2.0inchesB) 2.3inchesC) 2.6inchesD) 2.9inches
Here’sHowtoCrackItThescaleofthe3Dprinterisininchesandfeet—0.4inchesontheminiatureforevery1footinreallife.Startbyconvertingeverymeasurementtoinches.Thereare12inchesineachfoot,sothescalewillbe0.4 inches = 12 inches in real life. Now convert Gary’s height into inches. Begin by setting up aproportiontofindouthowmanyinchesarein5feet.
15. Theamountoftimeittakestoconsumeabuffalocarcassisinverselyproportionaltothenumberofvultures.Ifittakes12vultures3daystoconsumeabuffalo,howmanyfewerhourswillittakeifthereare4morevultures?
Cross-multiplytofindthat5feetequals60inches.Garyis5feetand9inchestall,soheis60+9=69inchestall.NowsetupaproportionwiththescaleoftheminiatureandGary’sheightininches.
Cross-multiplytoget12x=27.6,andthendividebothsidesby12tofindthatx=2.3inches.Theansweris(B).
DirectandInverseVariationProblemsdealingwithdirectvariation(afancytermforproportion)areexactlywhatyou’vejustseen:Ifonequantitygrowsordecreasesbyacertainamount(afactor),theotherquantitygrowsordecreasesbythesameamount.Inversevariations(alsoknownasinverseproportions)arejusttheoppositeofthat.Asonequantitygrowsordecreases,theotherquantitydecreasesorgrowsbythesamefactor.
What’sinaName?Whenyouseevariation,
thinkproportion.
Themainformulayouwanttorememberforinverseproportionsis
x1y1=x2y2
Tryone:
A)
B)
C) 18
D) 54
Translate!Directmeansdivide.
Sinceinverseistheopposite,inverse
meansmultiply.
Here’sHowtoCrackItForinverseproportions,followtheformula.First,convertthedays:3daysisequalto72hours.Nowsetuptheequation:(12vultures)(72hours)=(16vultures)(x).Solvetogetx=54,whichis18fewerhours.Theansweris(C).
Since ratiosandproportionsare relatedconcepts,youmightbewonderinghowyoucan tellwhenyoushould set the problem up as a proportion and when you should use a Ratio Box. Here are someguidelinestohelpyoudecide.
• Ifthequestiongivesyouaratioandanactualnumber,useaRatioBox.• Ifthequestioncomparesitemsthathavedifferentunits(likefeetandseconds),setupa
proportion.• Ifyoudon’tneedthetotalcolumnintheRatioBox,thenyoucanalsodothequestionbysetting
upaproportion.
PERCENTAGES
PercentagesAreFractionsThereshouldbenothingfrighteningaboutapercentage.It’sjustaconvenientwayofexpressingafractionwhosebottomis100.
Percentmeans“per100”or“outof100.”Ifthereare100questionsonyourmathtestandyouanswer50ofthem,youwillhaveanswered50outof100,or ,or50percent.Tothinkofitanotherway:
MemorizeThesePercentage-Decimal-FractionEquivalentsTheseshowupallthetime,sogoaheadandmemorizethem.
0.01= =1percent
0.1= =10percent
0.2= =20percent
0.25= =25percent
0.5= =50percent
0.75= =75percent
ConvertingPercentagestoFractionsToconvertapercentagetoafraction,simplyputthepercentageover100andreduce:
80percent=
AnotherWayYoucanalsoconvert
fractionstopercentagesbycross-multiplying:
4x=3(100)
x=
x=75
ConvertingFractionstoPercentagesBecauseapercentage is just anotherway toexpressa fraction,you shouldn’tbe surprised to seehow
easyitistoconvertafractiontoapercentage.Todoso,simplyuseyourcalculatortodividethetopofthefractionbythebottomofthefraction,andthenmultiplytheresultby100.Here’sanexample:
Problem:Express asapercentage.
Solution: =0.75×100=75percent.
Convertingfractionstopercentagesiseasywithyourcalculator.
ConvertingPercentagestoDecimalsToconvertapercentagetoadecimal,simplymovethedecimalpointtwoplacestotheleft.Forexample,25percentcanbeexpressedasthedecimal0.25;50percentisthesameas0.50or0.5;100percentisthesameas1.00or1.
ConvertingDecimalstoPercentagesToconvertadecimaltoapercentage,justdotheoppositeofwhatyoudidintheprecedingsection.Allyouhavetodoismovethedecimalpointtwoplacestotheright.Thus,0.5=50percent;0.375=37.5percent;2=200percent.
Thefollowingdrillwillgiveyoupracticeworkingwithfractions,decimals,andpercentages.
FRACTIONS,DECIMALS,ANDPERCENTSDRILLFindthemissinginformationinthefollowingtable.Answerscanbefoundonthispage.
Translation,Please!Wordproblemscanbetranslatedintoarithmeticsymbols.LearninghowtotranslatefromEnglishtomathwillhelpyouimmenselyontheSATMathTest.Herearesomeofthemostcommontermsyouwillseeinwordproblemsandtheirmathsymbolequivalents:
Word Symbolis,are,costs =greaterthan,morethan +fewerthan,lessthan −of ×(multiply)percent ÷100what n(variable)
DoYouSpeakMath?Problem:Whatnumberis5morethan10percentof20?
15. Abusinesspaid$300torentapieceofofficeequipmentforoneyear.Therentwasthenincreasedby10%eachyearthereafter.Howmuchwillthecompanypayforthefirstthreeyearsitrentstheequipment?
Studentsoftenmakecarelesserrorsonquestions like thisbecause theyaren’t surehowto translate the
wordstheyarereadingintomath.Youwon’tmakemistakesifyoutakethewordsslowly,oneatatime,
andtranslateeachoneintoamathematicalsymbol.Let’susethechartonthepreviouspagetowritethis
question inmath.Whatnumbermeans “variable,” sowe canwrite that asn (or x orwhatever letter
worksforyou).Ismeans“equals,”sonowwehaven=5.Morethantranslatesto+,and10percentis
.Thatgivesusn=5+ .Finally,of20meansmultiplyby20,sonowwehavetheequation:
Youwillseethewordsof,is,product,sum,andwhatpopupalotinmathquestionsontheSAT.Don’tletthesewordsfoolyoubecausetheyall translateintosimplemathfunctions.Memorizeallofthesetermsandtheirmathequivalents.ItwillsaveyoutimeonthetestandmakeyourlifewiththeSATmuchlessunpleasant.
WhatPercentofWhatPercentofWhat?OnmorechallengingSATquestions,youmaybeaskedtodeterminetheeffectofaseriesofpercentageincreasesordecreases.Thekeypointtorememberonsuchproblemsisthateachsuccessiveincreaseordecreaseisperformedontheresultofthepreviousone.
Here’sanexample:
A) $920B) $960
C) $990D) $993
Bite-SizePiecesAlwayshandle
percentageproblemsinbite-sizepieces:
onepieceatatime.
Here’sHowtoCrackIt
ThisproblemisagreatplacetouseBite-SizedPieces.Youknowthatthebusinesspaid$300torentthe
pieceofofficeequipmentforthefirstyear.Then,youweretoldthattherentincreasesby10percentfor
eachyearthereafter.That’sasuresignthatyou’regoingtoneedtherentforthesecondyear,sogoahead
andcalculateit.Forthesecondyear,therentis300+ =330.
Now,theproblemtellsyouthatthebusinessrentstheequipmentforthreeyears.So,youneedtodothecalculation one more time. At this point, you might want to set up a chart to help keep track of theinformation.
Year1:$300
Year2:$330=300+
Year3:$363=330+
Tofindtheanswer,allyouneedtodoisaddupthecostsforeachofthethreeyears.
Thecorrectansweris(D),$993.
WhatPercentofWhatPercentof…Yikes!Sometimes youmay find successive percentage problems inwhich you aren’t given actual numbers toworkwith.Insuchcases,youneedtopluginsomenumbers.
Here’sanexample.
17. Anumberisincreasedby25percentandthendecreasedby20percent.Theresultiswhatpercentoftheoriginalnumber?
A) 80B) 100C) 105D) 120
Careful!Number17isatrickyquestion.Bewareofpercentagechangeproblemsinthelater
questions.Theanswerstotheseproblemsalmost
alwaysdefycommonsense.Unlessyouarecareful,youmayfallfor
atrapanswer.
Here’sHowtoCrackItYouaren’tgivenaparticularnumbertoworkwithinthisproblem—just“anumber.”Ratherthantryingtodeal with the problem in the abstract, you should immediately plug in a number to work with.Whatnumberwouldbeeasiesttoworkwithinapercentageproblem?Why,100,ofcourse.
1. 25percentof100is25,so100increasedby25percentis125.2. Nowyouhavetodecrease125by20percent;20percentof125is25,so125decreasedby20
percentis100.3. 100(theresult)is100percentof100(thenumberyoupluggedin),sotheansweris(B).
Remember,never try tosolveapercentageproblembywritinganequation ifyoucanplug innumbersinstead.PluggingInonpercentageproblemsisfaster,easier,andmoreaccurate.Whyworkthroughlong,arduousequationsifyoudon’thaveto?
PercentChangeThere’sonemorefundamentalconceptthatyoushouldknowaboutpercents.Someproblemswillaskforapercentincreaseorpercentdecrease.Fortheseproblems,usethefollowingformula.
Mostof the time thatyouuse the formula, itwillbeprettyclearwhichnumberyou shoulduse for theoriginal.However,ifyou’renotsure,rememberthatyoushouldusethesmallernumberfortheoriginalifyouarefindingapercentincrease.Youshouldusethelargernumberfortheoriginalifyouarefindingapercentdecrease.
Here’sanexampleofhowtousetheformula:
8.
Thechartshownaboveshowsthenumberofvisits,inthousands,atArchesNationalParkfortheyears2003to2006.Whichofthefollowingistheclosestapproximationofthepercentincreaseinthenumberofvisitsfrom2004to2006?A) 5%B) 15%C) 20%D) 115%
23. Beccadeposits$100intoabankaccountthatearnsanannualinterestrateof4%.Ifshedoesnotmakeanyadditionaldepositsandmakesnowithdrawals,howlongwillittakeher,inyears,toincreasethevalueofheraccountbyatleast60%?
Here’sHowtoCrackItFirst, you need to get the data from the chart. In 2004, the chart shows that therewere approximately730,000visitorstoArches.In2006,thechartshowsthattherewereabout830,000visitorstothepark.Now,it’stimetousethepercentchangeformula.Thedifferenceisabout100,000andtheoriginalisthe730,000visitorsin2004:
Thecorrectansweris(B).
Percentages:AdvancedPrinciplesAnotheraspectofpercentquestionsmay relate to things that increaseordecreasebyacertainpercentover time. This is known as growth and decay. Real-world examples include population growth,radioactivedecay, andcreditpayments, tonamea few.WhilePlugging Incanhelpon these, it is alsousefultoknowthegrowthanddecayformula.
Whenthegrowthordecayrateisapercentofthetotalpopulation:
finalamount=originalamount(1±rate)numberofchanges
Let’sseehowthisformulacanmakequickworkofanotherwisetediousquestion.
A) 12B) 15C) 25D) 30
Here’sHowtoCrackItYoucouldadd4%totheaccountoverandoveragainuntilyougettothedesiredamount,butthatwould
29. Asummerbeachvolleyballleaguehas750playersinit.Atthestartoftheseason,150oftheplayersarerandomlychosenandpolledonwhethergameswillbeplayedwhileitisraining,orifthegamesshouldbecanceled.Theresultsofthepollshowthat42ofthepolledplayerswouldprefertoplayintherain.Themarginoferroronthepollis±4%.Whatistherangeofplayersintheentireleaguethatwouldbeexpectedtoprefertoplayvolleyballintherainratherthancancelthegame?
takealongtime.Knowingtheformulawillmakeitaloteasier.First,setuptheequationwiththethingsyouknow.100istheoriginalamount,andtherateis4%,or0.04.Theaccountisincreasing,soyouaddtherate,andyoucanputin“years”forthenumberofchanges.Theformulabecomes
finalamount=100(1+0.04)years
Nowyouneedtofigureoutwhatyouwantthefinalamounttobe.TranslatetheEnglishtomath:thevalueofheraccount(100)willincrease(+)by60percent(0.6)ofthecurrentvalue(×100).Thisbecomes100+(0.6)(100)=100+60=160.Nowtheformulais
160=100(1.04)years
TheanswerchoicesrepresentthenumberofyearsBeccakeepshermoneyintheaccount.NowyouareallsettoeasilyPlugIntheAnswers.Startwith(B),soyears=15.Is100(1.04)15=160?Useyourcalculatorto check,making sure to followPEMDAS rules anddo the exponent beforeyoumultiplyby100.Theresultis$180.09.Thatisabittoomuchmoney,sotheanswerwilllikelybe(A),butlet’sjustcheckit.100(1.04)12=$160.10,whichisatleast$160.
Afinalnoteongrowthanddecay:Sometimesthepopulationistriplingorhalvinginsteadofchangingbyacertainpercent.Inthatcase,theformulachangesto
finalamount=originalamount(multiplier)numberofchanges
Twomoretopicsrelatedtopercentagesmaybetested.Youmaybegivenasampleofapopulationthatfitsacertainrequirementandaskedtodeterminehowmanymembersofthegeneralpopulationwillalsobeexpectedtofitthatrequirement.Youmayalsobegiventheresultsofastudyorpollandtoldthatthereisamarginoferrorofacertainpercentage.
Let’slookatanexamplethattestsbothoftheseadvancedideas.
A) 24−32
B) 39−48C) 150−195D) 180−240
Here’sHowtoCrackItThefirststepistodeterminethepercentofpolledplayersthatwantedtoplayintherain.
=0.28or28%
Nowapplythispercenttotheentirepopulationoftheleague.Since28%ofthepolledplayerswantedtoplayintherain,28%ofallplayersshouldwanttoplayintherain.
×750=210
The only range that contains this value is (D), so that is the correct answer. To actually calculate themarginoferror,addandsubtract4%totheactualpercentof28%togetarangeof24−32%ofthetotal.
24%of750=180
32%of750=240
Therefore,theentirerangeis180to240.
AVERAGES
WhatIsanAverage?Theaverage,alsocalledthearithmeticmean,ofasetofnnumbersissimplythesumofallthenumbersdividedbyn.Inotherwords,ifyouwanttofindtheaverageofthreenumbers,addthemupanddivideby
3.Forexample,theaverageof3,7,and8is ,whichequals ,or6.
Thatwasaneasyexample,butaveragequestionsontheSATwon’talwayshaveclearsolutions.Thatis,youwon’t always be given the information for averages in away that is easy toworkwith. For thatreason,wehaveavisual aid, like theRatioBox for ratios, thathelpsyouorganize the informationonaveragequestionsandfindtheanswer.
WecallittheAveragePie.Here’swhatitlookslike:
The total is the sum of all the numbers you’re averaging, and thenumber of things is the number ofelementsyou’reaveraging.Here’swhattheAveragePielookslikeusingthesimpleaverageexamplewejustgaveyou.
Here’showtheAveragePieworksmathematically.Thehorizontallineinthemiddlemeansdivide.Ifyouknowthetotalandthenumberofthings,justdividetogettheaverage(18÷3=6).Ifyouknowthetotaland theaverage, justdivide toget thenumberof things (18÷6=3). Ifyouknow theaverageand thenumber of things, simplymultiply to get the total (6 × 3 = 18). The key tomost average questions isfindingthetotal.
Here’sanothersimpleexample:
Problem:Iftheaverageofthreetestscoresis70,whatisthetotalofallthreetestscores?
Solution:Justputthenumberofthings(3tests)andtheaverage(70)inthepie.Thenmultiplytofindthetotal,whichis210.
10. Mariahastakenfourchemistrytestsandhasanaverage(arithmeticmean)scoreof80.Ifshescoresa90onherfifthchemistrytest,whatisheraverageforthesefivetests?
TotalWhencalculating
averagesandmeans,alwaysfindthetotal.It’stheonepieceof
informationthatETSlovestowithhold.
Averages:AdvancedPrinciplesTosolvemostdifficultaverageproblems,allyouhavetodoisfilloutoneormoreAveragePies.Mostofthetimeyouwillusethemtofindthetotalofthenumberbeingaveraged.Here’sanexample:
A) 80B) 81C) 82D) 84
MarkIt!Makesureyou’redrawinganewAveragePieeachtimeyouseethewordaverageinaquestion.
Here’sHowtoCrackItStartbydrawinganAveragePieandfillinginwhatyouknow.Youcanput4inforthenumberofthingsand80 for theaverage.Youcancalculate thatMariahasgotten320 totalpointsonher first four tests.
Yourpieshouldlooklikethis:
Now,drawanotherAveragePieandfillinwhatyouknow.Thistime,therearefivetests.Thequestionwantstoknowtheaverage,soyoualsoneedtofillthetotal.Thetotalforallfivetestsisthetotalfromthefirstfourtestsplusthescorefromthefifthtest:320+90=410.Putthatonthepieanddividetofindtheaverage:
Theansweris(C),82.
Averages,andmanyotherarithmetictopics,maybetestedusingchartsanddata.Tofindthenumberstoaverage,lookthemuponthegraphicprovidedandwatchoutformismatchedunits.
24.
ChargeNo. BatteryLife1 1:112 1:053 0:59
16. Theaverage(arithmeticmean)ofalistof5numbersisn.Whenanadditionalnumberisaddedtothelist,theaverageofall6numbersisn+3.Whichofthefollowingisthevalue,intermsofn,ofthenumberaddedtothelist?
4 0:555 0:556 0:547 0:54
Atoydroneisopenedandchargedtofullbatterylife.Thetableaboveshowsthedurationofthebatterylifeinhoursandminutesbetweencharges.Whatistheaveragebatterylifeforthefirstfivecharges?A) 55minutesB) 58minutesC) 1hourand1minuteD) 1hourand5minutes
Here’sHowtoCrackIt
Tofindtheaverage,addupthebatterylifevaluesforthefirst5chargesanddivideby5.Makesurethat
youconvertthebatterychargetimeforCharge1and2intominutesbeforecalculating:1:11=60+11=
71minutes,and1:05=60+5=65minutes.Theaverageisequalto
minutes,whichisequalto1hourand1minute.Therefore,(C)isthecorrectanswer.
Don’tforgetthatyoucanalsoPlugInwhenusingtheAveragePie.
A) 6n+18B) 5nC) n+18D) n+6
Here’sHowtoCrackIt
PlugInforthevalueofn.Ifn=20,thenyoucanusetheAveragePietofindthetotalofthefivenumbersonthelist.
AsshownontheAveragePieabove,thetotalofthe5numbersis100.Now,it’stimeforanotherAveragePie.Forthispie,youknowthatthereare6numbersandthattheiraverageis20+3=23.
UsingtheAveragePieasshownabove,thetotalofthesixnumbersis138.Sincethedifferenceinthetwototalswascausedbytheadditionofthesixthnumber,thesixthnumbermustbe138−100=38.That’sthetarget,sobesuretocircleit.Only(C)is38whenn=20.
OntheSAT,you’llalsoneedtoknowthreeotherstatisticaltopicsrelatedtoaverages:median,mode,andrange.Thesetopicshaveprettystraightforwarddefinitions.OnewaytheSATwillcomplicatetheissueisbypresentingthedatainachartorgraph,makingithardertoseethenumbersyouareworkingwith.
WhatIsaMedian?Themedian of a listofnumbers is thenumber that is exactly in themiddleof the listwhen the list isarrangedfromsmallesttolargest,asonanumberline.Forexample,inthegroup3,6,6,6,6,7,8,9,10,10,11,themedianis7.Fivenumberscomebefore7inthelist,and5comeafter.Rememberitthisway:Mediansoundslikemiddle.
Let’sseehowthisideamightbetested.
MissingtheMiddle?Tofindthemedianofasetcontaininganeven
numberofitems,taketheaverageofthetwomiddle
numbers.
23.
FivesamplesofeachofthreedifferentrocktypeswerecollectedonahikingtripinColorado.Eachsamplewasanalyzedforitsgoldcontent.Themilligramsofgoldfoundineachsamplearepresentedinthetableabove.Howmuchlargeristhemedianoftheamountofgoldinthegranitesamplesthanthatofthelimestonesamples?A) 0.00B) 0.37C) 0.45D) 0.55
Here’sHowtoCrackItStartbyputtingthegoldweightsforlimestoneinordertoget:
0.41,0.42,0.45,0.55,0.58
Themedianforlimestoneisthemiddlenumber:0.45mg.
Next,placethegoldweightsforgraniteinordertoget:
0.55,0.73,0.82,0.87,0.94
Themedianforgraniteis0.82.
Therefore,thedifferencebetweenthemedianamountofgoldinthegraniteandlimestonesamplesis0.82−0.45=0.37,andthecorrectansweris(B).
WhatIsaMode?Themodeofagroupofnumbersisthenumberinthelistthatappearsmostoften.Inthelist3,4,4,5,7,7,8,8,8,9,10,themodeis8,becauseitappearsthreetimeswhilenoothernumberinthegroupappearsmorethantwice.Rememberitthisway:Modesoundslike“most.”
Modeisoftentestedwithbargraphsorpointsonascatterplot.Lookforthetallestbaronthebargraphortheroworcolumnwiththemostpointsinascatterplottofindthemode.
6.
ThepHofthewaterinLakeMichiganwastestedat13locationsalongtheIllinoisshoreline.Thedataispresentedinthescatterplotabove.WhichanswerchoicebestrepresentsthemodeofthepHinthecollecteddata?A) 7.2
B) 7.3C) 7.4D) 7.5
Here’sHowtoCrackItThemodeisthedatapointthatoccursmostfrequently.Eachdiamondisadatapoint,solookforthelinewiththemostdiamondsonit.Thatlineis7.2,whichmeansthatwhenthelakewastested,thepHlevelmostoftenread7.2.Thecorrectansweris(A).
WhatIsaRange?Therange of a list of numbers is the difference between the greatest number on the list and the leastnumberonthelist.Forthelist4,5,5,6,7,8,9,10,20,thegreatestnumberis20andtheleastis4,sotherangeis20−4=16.
3.
TheforecastedmonthlysalesofAlwaysSunnySunscreenarepresentedinthefigureabove.Whichofthefollowingbestdescribestherangeofmonthlysales,inmillionsofdollars,throughouttheyearshown?A) 2.5B) 3.5C) 4.0D) 4.5
Here’sHowtoCrackItTherangeofasetofvaluesisthedifferencebetweenthegreatestandthesmallestvalue.Lookingatthechart,thelowestmonthlysalesnumberforAlwaysSunnycanbefoundwherethelinedipsclosesttothebottomof thegraph.Thishappens inbothJanuaryandMarch,whentheforecastedsalesare2million.Makesure to read theunitscarefully.Thehighestpoint iswhere the linegoesclosest to the topof thegraph.ThishappensinJulyandAugust,whentheforecastedmonthlysalesare6.5million.Therefore,therangeis6.5million−2million=4.5million.Thecorrectansweris(D).
Bytheway,youmayrecognizethisgraphfromChapter11.OntheSAT,thesamechartorfiguremaybeusedfortwodifferentquestions.We’lltalkmoreaboutsetsofquestionslaterinthischapter.
TheSATmightevenhaveaquestionthattestsmorethanoneofthesestatisticalconceptsatthesametime.TakeitonestepatatimeanduseProcessofEliminationwhenyoucan.
23.
Thegramsofpreciousmetalsinrecycledcatalyticconvertersweremeasuredforavarietyofautomobiles.Thedataispresentedinthetableabove.Ifthelowestdatapoint,1gram,andhighestdatapoint,17grams,areremovedfromtheset,whichofthefollowingquantitieswouldchangethemost?A) ModeB) MeanC) RangeD) Median
Here’sHowtoCrackItStartbyevaluatingtheeasieranswerchoicesandsavemeanforlast.Themodeofthecurrentlistis6,andremoving1and17fromthelistwon’tchangethat.Eliminate(A).Therangeisthedifferencebetweenthesmallestnumberandthelargestnumberonthelist.Rightnow,therangeis17−1=16.Ifthoseextremes
areremovedfromthelist,thenewrangeis15−2=13,andtherangechangedby3units.Keep(C)fornow.Themedianisthemiddlenumberinthelist,ortheaverageofthemiddletwonumbers.Currently,bothmiddlenumbersare9,sothemedianis9.Thiswon’tchangeif1and17areremoved,soeliminate(D). The mean of a list is not likely to change dramatically with the removal of the numbers at theextremes,so(C)islikelycorrect.Toactuallyevaluatethemean,youneedtoaddupallthenumbersonthelistanddividebythenumberofitemsinthelist.Forthecurrentlist,thetotalis152forthe18items,so the average is 8.44. To find the new total if 1 and 17 are removed, don’t re-add everything; justsubtract18fromtheprevioustotal.Thenewlistwillhaveonly16items,sothenewaverageis8.375.Thisisonlyslightlydifferentthanthepreviousmean,soeliminate(B)andchoose(C).
RATESRateisaconceptrelatedtoaverages.Carstravelatanaveragespeed.Workgetsdoneatanaveragerate.Becausetheideasaresimilar,youcanalsouseapietoorganizeyourinformationonratequestions.
Here’sasimpleexample:
Problem:Ifafishermancantie9fliesforflyfishinginanhourandahalf,howlongdoesittakehimtotieonefly,inminutes?
Solution:First,convertthehourandahalfto90minutes,soyourunitsareconsistent.Then,fillinthetop
ofthepiewiththeamount(9flies)andthelowerrightpartwiththetime(90minutes).Divide9by90to
gettherate, ,oroneflyevery10minutes.
25. Brianplanstocompletea100-milebikeraceforcharity.Accordingtohisregistrationmaterials,hewillneedtorideatanaveragespeedof12.5milesperhourifhewantstocompletethecoursebeforeitcloses.Onapracticeridetheweekbeforetherace,Brianrides60milesandtrackshisspeed.Forthefirst30miles,hisaveragespeedis16milesperhour,andforthenext30miles,hisaveragespeedis15milesperhour.IfBriancanmatchthesespeedsforthefirst60milesofthecharityrace,thenherestsforatotalof1hourafterthat,whatapproximatespeedmusthemaintainforthelast40milesinordertocompletetherideontime?
Rates:AdvancedPrinciplesJustaswithcomplicatedaveragequestions,morechallengingratequestionswillalsorequiremorethanonepietosolve.Here’sanexample.
A) 8milesperhourB) 10milesperhourC) 13milesperhourD) 14milesperhour
Here’sHowtoCrackItDrawaRatePie,fillinginthenumbersfortheentireride.Youcanputin100inforthetotalmilesand12.5infortherate.Dividing100by12.5tellsyouthatBrianhas8hourstocompletetheride.Yourpiewilllooklikethis:
NowdrawtwomorepiestodeterminehowmuchtimeBrianwoulduseforthefirst60miles.Heridesat16milesanhourforthefirst30milesand15milesperhourformiles31–60.Again,dividethenumberofmilesbytheratetogetthetimeforeachportion,whichis1.875hoursforthefirstpartand2hoursforthesecondpart.
Therefore,thefirst60milestookBrian1.875+2=3.875hourstocomplete.Afterrestingforanhour,he’susedup4.875ofhis8hours,sohehas3.125hoursleft.Heneedstogo40milesinthattime,sodrawonemorepiewith40atthetopand3.125inthelowerrightfortime.Divide40by3.125toget12.8or13milesperhour(itisokaytoround,sinceyouarelookingfortheapproximatespeed).
Thecorrectansweris(C).
PROBABILITYProbabilityisamathematicalexpressionofthelikelihoodofanevent.Thebasisofprobabilityissimple.The likelihood of any event is discussed in terms of all of the possible outcomes. To express theprobabilityofagivenevent,x,youwouldcount thenumberofpossibleoutcomes,count thenumberofoutcomesthatgiveyouwhatyouwant,andarrangetheminafraction,likethis:
Everyprobability isa fraction.The largestaprobabilitycanbe is1;aprobabilityof1 indicates total
certainty. The smallest a probability can be is 0, meaning that it’s something that cannot happen.
Furthermore,youcanfindtheprobabilitythatsomethingWILLNOThappenbysubtractingtheprobability
thatitWILLhappenfrom1.Forexample,iftheweathermantellsyouthatthereisa0.3probabilityofrain
today, then theremust be a 0.7 probability that itwon’t rain, because 1 − 0.3 = 0.7. Figuring out the
probability of any single event is usually simple.When you flip a coin, there are only two possible
2. Abagcontains7bluemarblesand14marblesthatarenotblue.Ifonemarbleisdrawnatrandomfromthebag,whatistheprobabilitythatthemarbleisblue?
17. Ajarcontainsonlyredmarblesandwhitemarbles.Iftheprobabilityofselectingared
outcomes,headsandtails;theprobabilityofgettingheadsistherefore1outof2,or .Whenyourolla
die, there are six possible outcomes, 1 through 6; the odds of getting a 6 is therefore . The odds of
gettinganevenresultwhenrollingadieare becausethereare3evenresultsin6possibleoutcomes.
Here’sanexampleofaprobabilityquestion:
A)
B)
C)
D)
Here’sHowtoCrackIt
Here, there are 21marbles in the bag, 7 of which are blue. The probability that a marble chosen at
randomwouldbeblueistherefore ,or .Thecorrectansweris(A).
Someprobabilityquestionsmightincludevariables.Nottoworry.PluggingInwillsavetheday!
Here’sanexample:
marbleis ,whichofthefollowingexpressionsgivestheprobabilityofselectingawhite
marble,intermsofrandy?
A)
B)
C)
D)
Here’sHowtoCrackIt
PlugIn!Youcouldmaketheprobabilityofchoosingaredmarblebe .Then = ,whichmeansthatr
=2andy=3.
Now,togetthenumericalanswer,youneedtorememberthattheprobabilitiesofall thethingsthatcan
happenalwaysaddupto1.Sincethereareonlyredmarblesandwhitemarblesinthejar,choosingared
marbleorchoosingawhitemarblearetheonlythingsthatcanhappen.So,theprobabilityofselectinga
whitemarblecanbefoundbysubtractingtheprobabilityofgettingaredmarblefrom1:Probabilityof
white=1− = .That’syourtarget,socircleit.
Now,gofindtheanswerthatgivesyou whenr=2andy=3.Choice(B)is .Sinceno
otheranswerworksoutto ,(B)istheanswer.
Finally,let’slookataprobabilityquestionbasedonachart.Again,gettingtothecorrectanswerinvolvesreadingthechartcarefullytofindtorightnumberstouse.
26.
Attwohighschools,thoseplanningtoattendcollegeaftergraduationwerepolled.Thesizesofthecollegestheyplannedtoattendbasedonstudentbodysizesweretabulatedinthetableabove.The255polledstudentsfromManhattanHighEasthadanaverageSATscoreabove1100,andthe249polledstudentsfromManhattanHighWesthadanaverageSATscorebelow1100.Ifapollrespondentwerechosenatrandomfromthoseplanningtoattendacollegewithatleast5,000students,whatistheprobabilitythattherespondentwouldbeenrolledatManhattanHighWest?
A)
B)
C)
D)
Here’sHowtoCrackItProbability is defined as the number of things that fit the requirements divided by the total number ofpossibleoutcomes.Read thegraph carefully to figureout howmany respondents fit into eachof thesecategories.Therespondent ischosenfromamongthoseplanningtoattendcollegeswith“at least5,000students.”Thatmeansthatthetotalnumberofpossibleoutcomesincludesthe267respondentswhoplanto attend medium schools and the 173 who plan to attend large schools, for 440 total. That is thedenominatoroftheprobabilityfraction,andtheanswerchoicesaren’treduced,sotheanswermustbe(B)or(C).Tofindthenumberfromamongthese440respondentswhoareenrolledatManhattanHighWest,lookinthatrowandaddthe112fromthemediumcolumntothe98fromthelargecolumntoget210forthenumerator.Thecorrectansweris(B).
DidtheaverageSATscoresofthestudentsatthesetwoschoolsaffecttheansweratall?No!WatchoutforextraneousinformationontheSAT.Thetestwritersmayincludeittodistractyou.
4. Howmanycarsdidthe9thgradeclasswashduringthecarwash?
SETSOFQUESTIONSSometimes, two questions will refer to the same information. These will usually be found in thecalculator-permittedsection,where therewillbeoneset in theGrid-Inpartandabout threesets in themultiple-choice part of that section.Often, these sets are about arithmetic concepts, but they can alsocoverthingslikefunctionsorexponentialgrowth.
Trythefollowingarithmeticset.
Questions4and5refertothefollowinginformation.
A) 5B) 51C) 122D) 180
Here’sHowtoCrackIt
Lookupthenumbersyouneedonthechart,ignoringalltheextraneousinformation.Tofindouthowmany
5. Howmanymorecookiesweresoldbythe10thgradethanweresoldbythe12thgrade?
carsthe9thgraderswashed,taketheFundsRaisedanddividebythePriceperitemintherowforthe9th
graders. =51,whichis(B).
A) 60B) 90C) 120D) 150
Here’sHowtoCrackIt
First,findthenumberofcookiessoldby10thgraders,againdividingFundsRaisedbyPriceperitem:
=180.Nowfindthenumberofcookiessoldby12thgraders: =120.Nowsubtractto
findouthowmanymorecookiesthe10thgraderssold:180−120=60,whichis(A).
ANALYSISINSCIENCEIfsomeofthesequestionsareremindingyouofscienceclass,you’renotcrazy.Oneofthe“Cross-Testscores” theSATaims tomeasure is calledAnalysis inScience.Thismeans thatquestionson science-basedideaswillshowupinReadingandWritingpassagesandalsoinMathquestions.That’spartofthereason for all these charts and graphs.Many times, youwill be asked if a conclusion can be reachedbasedonthechart.Inthosecases,justdoasyouhavebeenthroughoutthischapter—carefullylookupthenumbersinquestion,dotherequiredcalculations,andeliminateanswersthataren’ttrue.
Youmayalsobeaskedtographthedatapresentedinatable.YourknowledgeofpositiveandnegativerelationshipsfromChapter11willhelp—youcaneliminatethingswiththewrongrelationship.
Takealookatthisnextexample.
7.
Temperaturein°F NumberofCustomers10 420 930 3740 6650 100
Acoffeeshopnoticedthattheoutsidetemperatureaffectedthenumberofcustomerswhocametotheshopthatday,asshowninthetableabove.Whichofthefollowinggraphsbestrepresentstherelationshipbetweentheoutsidetemperatureandthenumberofcustomers,asindicatedbythetable?A)
B)
C)
D)
Here’sHowtoCrackItNoticethatthenumberofcustomersincreasesasthetemperatureincreases.Thelineofbestfitwillgoupasyoufollowthegraphfromlefttoright,soeliminate(B)and(D).Todetermineifthecorrectgraphis(A)or (C), try roughlyplotting thedatapoints, and then lookatyourgraph.Notice that thenumberofcustomers does not increase by the same number for each 10-degree temperature increase. This is an
14. Whentreesbecomeirondeficient,theirleaveswillturnyellowprematurely.Abotanististestingiron-dopedfertilizersonmapletreeswithirondeficiencies.Thebotanisthasselected200mapletreesinthestateofWisconsinthathavebeenidentifiedashavinganirondeficiency.Halfofthetreesarerandomlychosentoreceivetheiron-dopedfertilizer,whiletheotherhalfaregivenafertilizerwithoutiron.Theresultsfromthetestshowthattreesadministeredtheiron-dopedfertilizerhadfewerprematureyellowleaves,indicatinganincreaseintheirironlevels.Whichofthefollowingstatementsbestdescribestheresultsofthetest?
exponentialincrease,notalinearincrease.Therefore,thegraphwillbecurved.Eliminate(C).Only(A)fitsthedatainthechart.
Sometimesyouwillbeaskedtodrawconclusionswithoutmuchdataatall.Thefollowingquestionfromthecalculatorsectionhasonlyonenumberinit,makingthecalculatorprettyuseless.Juststicktothefactsofthestudyandbesurenottotakeaconclusiontoofar.
A) Theiron-dopedfertilizerwillimproveironlevelsinanytree.B) Theiron-dopedfertilizerreducesprematureyellowleavesbetterthananyother
fertilizer.C) Theiron-dopedfertilizerwillcauseasignificantincreaseinironlevels.D) Theiron-dopedfertilizerwillresultinfewerprematureyellowleavesinmaple
treesinWisconsin.
Here’sHowtoCrackItFor this typeofquestion, underlinekeywords abouthow the studywas conducted andwhat the studyfound. In this case, the study was on 200 maples trees with iron deficiencies inWisconsin, and theconclusionisTheresultsfromthetestshowthattreesadministeredtheiron-dopedfertilizerhadfewerprematureyellowleaves,indicatinganincreaseintheirironlevels.Eliminateanswersthatdon’thitthismark or go too far. In (A), it says that this treatmentwill helpany tree. You are told only about200maplestreesinthestateofWisconsin,soyoucan’tdrawconclusionsaboutothertrees.Eliminate(A).In(B), the fertilizer used is compared to other fertilizers,which you also don’t know about.Choice (C)soundsgood,butitishardtosaywhatqualifiesasasignificantincreaseinironlevels.Thestatementin(D)matchesthekeywordsyouunderlinedperfectlywithouttakinganyaspecttoofar.Therefore,(D)iscorrect.
AdvancedArithmeticDrill:Calculator-PermittedSectionWorktheseproblemsusingtheadvancedarithmetic techniquescoveredin thischapter.ThesequestionsaresimilartothoseyouwillseeontheCalculatorsectionofthetest.Answersandexplanationscanbefoundonthispage.
5.20−2x20−x20
20+x20−x
Whatistheaverage(arithmeticmean)ofthelistofnumbersabove?
A) 20
B) 100
C) 20+
D)
8.
Alappingslurrycontainsmicrobeadssuspendedinasolutionandisusedtopolishasiliconwaferbyabrasionofthesurface.Thedistributionoftheparticlesize,inmicrometers,isshownabove.Iftheparticlesizedistributionrangeswerechangedto0-20
micrometersand21-40micrometers,whichofthefollowingistheclosesttotheratioofthenumberof0-20micrometermicrobeadstothenumberof21-40micrometermicrobeads?A) 3:1B) 4:1C) 5:2D) 9:1
11. Steverana12-mileraceatanaveragespeedof8milesperhour.IfAdamranthesameraceatanaveragespeedof6milesperhour,howmanyminuteslongerdidAdamtaketocompletetheracethandidSteve?A) 12B) 16C) 24D) 30
15.
Thepopulationsandareasoffivecountriesareshowninthegraphsabove.Ifpopulation
densityisdefinedas ,whichofthefivecountrieshasthehighestpopulation
density?
A) EcuadorB) Uruguay
C) VenezuelaD) Chile
19. TheamountoftimethatAmywalksisdirectlyproportionaltothedistancethatshewalks.Ifshewalksadistanceof2.5milesin50minutes,howmanymileswillshewalkin2hours?A) 4.5B) 5C) 6D) 6.5
20. Atotalof140,000voteswerecastfortwocandidates,SkinnerandWhitehouse.IfSkinnerwonbyaratioof4to3,howmanyvoteswerecastforWhitehouse?A) 30,000B) 40,000C) 60,000D) 80,000
23.SPICEPRICESOFDISTRIBUTORD
Spice PricePerPoundCinnamon $8.00Nutmeg $9.00Ginger $7.00Cloves $10.00
Theownerofaspicestorebuys3poundseachofcinnamon,nutmeg,ginger,andclovesfromdistributorD.Shethensellsallofthespicesat$2.00perounce.Whatishertotalprofit,indollars?
(1pound=16ounces)A) $192B) $282C) $384D) $486
25.
FivesamplesofeachofthreedifferentrocktypeswerecollectedonahikingtripinColorado.Eachsamplewasanalyzedforitsgoldcontent.Themilligramsofgoldfoundineachsamplearepresentedinthetableabove.Whatisthepercentdifferenceoftheaveragegoldcontentinthegranitesampleswhencomparedtotheaveragegoldcontentofthegneisssamples?A) Thegoldcontentinthegneisssamplesis62%higherthanthegoldcontentinthe
granitesamples.B) Thegoldcontentinthegranitesamplesis62%higherthanthegoldcontentinthe
gneisssamples.C) Thegoldcontentinthegneisssamplesis87%higherthanthegoldcontentinthe
granitesamples.D) Thegoldcontentinthegranitesamplesis87%higherthanthegoldcontentinthe
gneisssamples.
26. Ofallthehousesinacertainneighborhood,80%havegarages.Ofthosehouseswithgarages,60%havetwo-cargarages.Ifthereare56houseswithgaragesthatarenottwo-cargarages,howmanyhousesarethereintheneighborhood?A) 93B) 117C) 156D) 175
28. OnTuesday,awatchmakermade4morewatchesthanhemadeduringthepreviousday.Ifhemade16%morewatchesonTuesdaythanonMonday,howmanywatchesdidhemakeonTuesday?A) 20B) 21C) 25D) 29
CHAPTERDRILLANSWERSANDEXPLANATIONS
Fractions,Decimals,andPercentsDrill1. ,0.5,50
2. ,3.0,300
3. ,0.005,0.5
4. ,0.3333,33
AdvancedArithmeticDrill:Calculator-PermittedSection
5. A Variables in the answers? Plug In!Make up a value for x. Say that x is 3. The list ofnumbersthenbecomes20−2(3),20−3,20,20+3,20+2(3),sothelistis14,17,20,23,and26.Tofindtheaverage,makeanAveragePie:Youknowthenumberofthings(5)andthetotal(14+17+20+23+26=100),sotheaverageis100÷5=20,whichis(A).
8. B In thenewgroupings,79%of theparticlesare in the0–20micrometergrouping (33%+46%=79%)and21%oftheparticlesareinthe21–40micrometergrouping(16%+5%)=21%.Thatisaratioof79:21.Becausethequestionisaskingfortheclosestratio,roundthenumberstogetaratioof80:20,or4:1.Thecorrectansweris(B).
11. D UseaRatePietocalculatethetimeforeachrunner.Steveruns12milesat8milesperhour,sohispielookslikethis:
Tofindhistime,dividehisdistancebyhisrate,whichmeansthatherunsforhours(or1.5ifyou’reusingyourcalculator).Adamrunsthesame12milesat6milesperhour,sothisishisRatePie:
Thismeans thatAdam runs for 2 hours.Adam takes half an hour longer to complete therace,andhalfanhouris30minutes:(D).
15. A The top graph is of the countries’ populations, and the bottomgraph is of the countries’
areas.Findthepopulationdensity, ,foreachcountrybytakingitsnumberfrom
thetopgraphanddividingthatbyitsnumberfromthebottomgraph:
Ecuador= ,whichequals33.33
Uruguay= ,whichequals12.5
Venezuela= ,whichequals20
Chile= ,whichequals18.75
ThehighestvalueamongthecountriesisthatofEcuador,whichis(A).
19. C Since you know the time that Amy walked and the distance she walked are directly
proportional,youcansetupaproportiontoshowherdistance÷time.Youwanttoknow
howmanymilesshe’llwalkintwohours,soput120(60×2)minutesinthesecondhalfof
theratio: = .Tosolve,cross-multiply,andyou’llget50x=2.5×120;50x=300;x
=6miles,whichis(C).
20. C Since this is a ratio question, draw a Ratio Box. You know the ratio for the votes forSkinnerandWhitehouse,andthetotalnumberofvotescast.Fillinthetotalbyaddingtheratio(4+3=7),andthenfindthemultiplierbyseeinghowmanytimes7goesinto140,000(140,000÷7=20,000).
Skinner Whitehouse Total4 3 7
×20,000 ×20,000 ×20,00080,000 60,000 140,000
ThequestionwantstoknowhowmanyvotesWhitehousereceived,whichis60,000,(C).
23. B Thisisahardquestion,soyouhavetostayonyourtoes.Iftheownerbuys3poundsofeachspice,thatmeansshepaysthefollowingamountsforeachspice:
cinnamon:$8×3=$24nutmeg:$9×3=$27ginger:$7×3=$21
cloves:$10×3=$30
Soshepaysatotalof24+27+21+30,or$102for12poundsofspices.Shethensellsthespicesperounce,soyouhavetofigureoutfirsthowmanyouncesofspicesshehas.If1poundis16ounces,then12poundsis12×16,or192ounces.Shesellsallthespicesat$2
perounce,soshemakes192×$2,or$384.Tofigureoutherprofit,subtracttheamountshepaidforthespicesfromtheamountshemadesellingthem:$384−$102=$282,(B).
25. D Theaveragegoldcontentinthegranitesamplescanbecalculatedasfollows:
Theaveragegoldcontentinthegneisssamplescanbecalculatedas
Becausetheaveragegoldcontentinthegranitesamplesishigher,youcaneliminate(A)and(C).Ballparktofindtherightanswer:0.782isalmosttwiceasmuchas0.418.Therefore,granitecontains,onaverage,almost100%moregoldthangneissdoes.Thecorrectansweris(D).
26. D Startbyfiguringoutwhatpercentofthehousesdonothavetwo-cargarages.Since60%of
thehouseswithgarageshavetwo-cargarages,40%ofthehouseswithgaragesdonothave
two-cargarages.Inotherwords,40%of80%ofthehousesdonothavetwo-cargarages.
Translatethatintomathtoget =0.32,or32%ofthehouses.Theproblemstates
that 56houses donot have two-car garages,whichmeans32%of the houses equals 56.
Translatingintomathgives ×x=56.Solveforx,andyou’llget175,whichis(D).
28. D Tryouttheanswersandseewhichoneworks.Startwith(B).Ifthewatchmakermade21
watches onTuesday, then hemust havemade 17watches onMonday.You know that he
should have made 16% more watches on Tuesday than on Monday, so use the percent
change formula to see if you get 16% : ≈ 23.5%, which is too big.
Eliminate(B).Youwantthe4watchestobeasmallerpercentofthetotal,soyouneeda
biggertotal.Tryabiggeranswerchoice,like(D).Ifhemade29watchesonTuesday,then
hemade25watches onMonday.Now the percent change is =0.16= 16%,which is
exactlywhatyouwant.Therefore,(D)isthecorrectanswer.
Summary◦ Aratiocanbeexpressedasafraction,butratiosarenotfractions.Aratiocomparespartstoparts;a
fractioncomparesaparttothewhole.
◦ YoucanuseaRatioBoxtosolvemostratioquestions.
◦ Directproportionis .Indirectproportionisx1y1=x2y2.
◦ Apercentageisjustaconvenientwayofexpressingafractionwhosebottomis100.
◦ Toconvertapercentagetoafraction,putthepercentageover100andreduce.
◦ Toconvert a fraction toapercentage,useyourcalculator todivide the topof the fractionby thebottomofthefraction.Thenmultiplytheresultby100.
◦ Toconvertapercentagetoadecimal,movethedecimalpointtwoplacestotheleft.Toconvertadecimaltoapercentage,movethedecimalpointtwoplacestotheright.
◦ Inproblemsthat requireyou tofindaseriesofpercentage increasesordecreases, remember thateachsuccessiveincreaseordecreaseisperformedontheresultofthepreviousone.
◦ Ifyouneedtofindthepercentincreaseordecreaseuse%change= ×100.
◦ Tofindtheaverage(arithmeticmean)ofseveralvalues,addupthevaluesanddividethetotalbythenumberofvalues.
◦ Use theAveragePie tosolveproblemsinvolvingaverages.Thekey tomostaverageproblemsisfindingthetotal.
◦ Themedianofagroupofnumbersisthenumberthatisexactlyinthemiddleofthegroupwhenthegroup is arranged from smallest to largest, as on a number line. If there is an even number ofnumbers,themedianistheaverageofthetwomiddlenumbers.
◦ Themodeofagroupofnumbersisthenumberinthegroupthatappearsmostoften.
◦ Therangeofagroupofnumbersisthedifferencebetweenthegreatestnumberinthegroupandtheleastnumber.
◦ Onquestionsaboutrates,usetheRate,orWork,Pie.Becarefulwiththeunits—theSATwilloftenrequireyoutodoaunitconversionsuchasminutestohoursorinchestofeet.
◦ Probabilityisexpressedasafraction:
Chapter15FunctionsandGraphsInthelastchapter,welookedatafewdifferenttypesofchartsandgraphslikelytoshowupontheMathTest.Anotherwaydatacanberepresentediswithagraphinthexy-plane.Thischapterwillgiveyouthetoolsyouneedtounderstandthesegraphsandotherrepresentationsoffunctions.
FUNCTIONFUNDAMENTALSThinkofafunctionasjustamachineforproducingorderedpairs.Youputinonenumberandthemachinespitsout another.Themost common function is an f(x) function.You’veprobablydealtwith it inyouralgebraclass.
Let’slookataproblem.
3. Iff(x)=x3−4x+8,thenf(5)=A) 67B) 97C) 113D) 147
Here’sHowtoCrackItAnytimeyouseeanumberinsidetheparentheses,suchasf(5),pluginthatnumberforx.ThequestionisactuallytellingyoutoPlugIn!Let’sdoit:
f(5)=53−4(5)+8f(5)=125−20+8f(5)=113
That’s(C).
Trythenextone.
What’sThis?Anytimeyouseethenotation
f(x),knowthatfisn’tavariable;it’sthename
ofthefunction.Whenyousayitoutloudit’s“fof
x.”Thoughf(x)isthemostcommonwaytoshowthat
anequationisamathematicfunction,anylettercanbeused.Soyou
mayseeg(x)orh(d).Knowthatyou’restilldealing
withafunction.
14. Iff(x)=x2+2,whichofthefollowingcouldbeavalueoff(x)?
A) −1B) 0C) 1D) 2
Here’sHowtoCrackItNotethattheproblemisaskingwhichoftheanswerscouldbeequaltof(x)—inotherwords,theproblemisaskingwhichofthesevaluescouldbespitoutofthe f(x)machine.Thinkaboutwhatisgoingin:Nomatterwhatyouputinasavalueforx,thevalueofx2hastobepositiveorzero.So,thelowestpossiblevalueofx2+2is2,whichis(D).
NotethatyoucouldalsoapproachthisquestionbyPluggingIntheAnswers.Ifyoupluggedin1forf(x),forinstance,youwouldget1=x2+2,whichbecomesx2=−1,whichisimpossible.
Sometimes you’ll getmore complicated questions.As long as you know thatwhen you put in x, yourfunctionwillspitoutanothernumber,you’llbefine.Nowtryanotherone:
20. Letthefunctiongbedefinedbyg(x)=5x+2.If =6,whatisthevalueofa?
A)
B)
C)
D)
PITA!Don’tforgetthat
youcanoftenplugintheanswerchoiceson
functionquestions!Noticingapatternyet?
Justafeweasytrickscanunlockalotof
easypoints.
Here’sHowtoCrackIt
Thismaylookcomplicated,butjustfollowthedirections.Youknowthatg(x)=5x+2.Youalsoknow
that =6.First,getridofthesquarerootbysquaringbothsides.Nowyouhave =36.Usually
there’sanxinsidetheparentheses.Treatthisthesame.Thisstatementsaysthatgofsomenumberequals
6.Youalsoknowthatgofsomenumberisthesameas5x+2.So5x+2=36.Simplifyandyouget .
Becarefulhere;you’renotdone.Younowknowthat = ,soa= ,or(D).
Anotherway theSAT canmake functionsmore complicated is to give you two functions to dealwithtogether.Ifyouapproachtheseproblemsonepieceatatime,theywillbeeasiertohandle.
Here’sanexample:
15. Iff(g(a))=6,f(x)= +2,andg(x)=|x2−10|,whichofthefollowingisapossiblevalue
ofa?A)
B) 2C) 6D) 18
Here’sHowtoCrackIt
ThisisagreatopportunitytoPlugIntheAnswers!Takeoneofthemiddleanswerchoicesandplugitin
fora,thenworktheproblemonestepatatimetoseeiff(g(a))=6.Try(B):Ifa=2,theng(a)=|(2)2−
10|=|4−10|=|−6|=6.So,f(g(a))=f(g(2))=f(6)= +2=3+2=5.Sincetheproblemstatesthat
f(g(a))issupposedtoequal6,(B)isnotcorrect.
Ifyoudon’tknowwhichwaytogonext,justpickadirection.Try(A):Ifa= ,theng(a)=|( )2−10|=|2−10|=|−8|=8.So,f(g(a))=f(g( ))=f(8)= +2=4+2=6.Choice(A)iscorrect.
15. Rockclimbingroutesareratedonanumberedscalewiththehighestnumberrepresentingthemostdifficultroute.Sallytriedarangeofshoesizesoneachofseveralroutesofvaryingdifficultyandfoundthatwhensheworesmallershoes,shecouldclimbroutesofgreaterdifficulty.IfDrepresentsthedifficultyratingofarouteSallysuccessfullyclimbedandsrepresentsthesizeoftheshoessheworeonsucharoute,thenwhichofthefollowingcouldexpressDasafunctionofs?
Sometimesyoumayseeawordproblemthatdescribesafunctionandthenasksyouto“buildafunction”that describes the real-world situation presented in the problem. Take the following question, forexample.
A) D(s)=s2
B) D(s)=C) D(s)=s−3.5
D) D(s)=
Here’sHowtoCrackItStartby thinkingabout the relationshipdescribed in thequestion: the smaller the shoes, thegreater thedifficulty. This is an inverse relationship. So, look for an inverse function. Only (D) is an inversefunction.
Ifyouaren’tsure,tryplugginginnumberstotryitout.Plugins=8thens=10toseeiftheresultforDissmallerwhenyouusealargershoesize.Sinceonly(D)resultsinasmallerdifficultyforalargershoesize,thecorrectresponseis(D).
WHAT’STHEPOINT?Whydidmathfolkscomeupwithfunctions?Tographthem,ofcourse!Whenyouputinavalueforx,andyour machine (or function) spits out another number, that’s your y. You now have an ordered pair.Functionsarejustanotherwaytoexpressgraphs.Knowingtheconnectionbetweenfunctionsandgraphsisuseful,becauseyouwillmostlikelyseequestionsinvolvinggraphsontheSAT.
TheCoordinatePlaneAcoordinateplane,orthexy-plane,ismadeupoftwonumberlinesthatintersectatarightangle.Thehorizontalnumberlineiscalledthex-axis,andtheverticalnumberlineisthey-axis.
Thefourareasformedbytheintersectionoftheaxesarecalledquadrants.Thelocationofanypointcanbe described with a pair of numbers (x, y), just the way you would point on a map: (0, 0) are thecoordinatesoftheintersectionofthetwoaxes(alsocalledtheorigin);(1,2)arethecoordinatesofthepointonespacetotherightandtwospacesup;(−1,5)arethecoordinatesofthepointonespacetotheleftandfivespacesup;(−4,−2)arethecoordinatesofthepointfourspacestotheleftandtwospacesdown.Allofthesepointsarelocatedonthefollowingdiagram.
Someof thequestionsontheSATmayrequireyoutoknowcertainpropertiesof linesonthexy-plane.Let’stalkaboutthem.
QuadrantsAcoordinateplane
hasfourdistinctareasknownasquadrants.Thequadrantsarenumbered
counterclockwise,startingfromthetopright.Theyhelpdeterminegenerally
whetherxandyarepositiveornegative.
Sometimesknowingwhatquadrantapointisinandwhatthatmeansisallyouneedtofindtheanswer.
PointsonaLineYoumaybeaskedifapointisonalineoronthegraphofanyotherequation.Justplugthecoordinatesofthepointintotheequationofthelinetodetermineifthatpointmakestheequationatruestatement.
3. Inthexy-plane,whichofthefollowingorderedpairsisapointontheliney=2x−6?A) (6,7)B) (7,7)C) (7,8)D) (8,7)
WaystoRememberHavingtrouble
rememberingthatthex-coordinatecomes
beforethey-coordinateinanorderedpair?Justrememberthephrase“xbeforey,walkbeforeyoufly.”Theletterxcomes
beforeyinthedictionary.
Here’sHowtoCrackItPlug In theAnswers, startingwith (B).The (x,y) point is (7, 7), so plug in 7 for x and 7 for y. Theequationbecomes7=2(7)−6or7=8.Thisisn’ttrue,soeliminate(B).Theresultwasveryclosetoatruestatement,andthepointin(C)hasthesamex-coordinateandalargery-coordinate,sotrythatnext.Because8=2(7)−6,(C)isthecorrectanswer.
SlopeYoualwaysreadagraphfromlefttoright.Asyoureadthegraph,howmuchthelinegoesupordownisknownastheslope.Slopeistherateofchangeofalineandiscommonlyknownas“riseoverrun.”It’sdenotedbytheletterm.Essentially,it’sthechangeinthey-coordinatesoverthechangeinx-coordinatesandcanbefoundwiththefollowingformula:
m=
Thisformulausesthepoints(x1,y1)and(x2,y2).
Forexample,ifyouhavethepoints(2,3)and(7,4),theslopeofthelinecreatedbythesepointswouldbe
Sotheslopeofalinewithpoints(2,3)and(7,4)wouldbe ,whichmeansthateverytimeyougoup1
unit,youtraveltotheright5units.
EquationofaLine—Slope-InterceptFormThe equation of a line can take multiple forms. The most common of these is known as the slope-interceptform.Ifyouknowtheslopeandthey-intercept,youcancreatetheequationofagivenline.Aslope-interceptequation takes theformy=mx+b,wherem is the slopeandb is they-intercept (thepointwherethefunctioncrossesthey-axis).
Let’ssaythatweknowthatacertainlinehasaslopeof5(whichisthesameas )anday-interceptof3.
Theequationofthelinewouldbey=5x+3.Youcouldgraphthislinesimplybylookingatthisformof
the equation. First, draw they-intercept, (0, 3).Next, plug in a number for x and solve fory to get a
coordinate pair of a point on the line. Then connect the point you just foundwith the y-intercept you
alreadydrew, and voilà, you have a line. If youwantmore points, you can create a table such as the
following:
x y
−2 −7
−1 −2
0 3
1 8
Takealookatthefinishedproduct:
OnewaytheSATcantestyourunderstandingoflinesistoshowyouagraphandaskyouwhichequationdescribesthatgraph.
Here’sanexample:
4.
Whichofthefollowingcouldbetheequationofthelinerepresentedinthegraphabove?A) y=2x+4B) y=2x−4C) y=−2x−1D) y=−2x+4
Here’sHowtoCrackItRememberthattheequationofalineisy=mx+b,wheremistheslopeandbisthey-intercept.Lookatthe graph and think about what the equation should look like. Since the line is sloping downward, itshouldhaveanegative slope, soyoucaneliminate (A)and (B).Next, since the linehasapositivey-
intercept,youcaneliminate(C),andonly(D)remains.
EquationofaLine—StandardFormAnotherwaytheequationofalinecanbewrittenisthestandardformofAx+By=C,whereA,B,andCareconstantsandAandBdonotequalzero.The testwriterswill sometimespresentequations in thisforminthehopesthatyouwillwastetimeputtingitinslope-interceptform.Ifyouknowwhattolookfor,thestandardformcanbejustasusefulastheslope-interceptform.
InstandardformAx+By=C:
Theslopeofthelineis− .
They-interceptofthelineis .
Thex-interceptofthelineis .
Theequationinthepreviousexamplewouldbe−5x+y=3whenwritteninthestandardform.Usingtheinformationabove,youcanseethat
slope=− =5
y-intercept= =3
x-intercept= =−
Theanswersfortheslopeandthey-interceptwerethesameaswhentheslope-interceptformwasused.Dependingontheformoftheequationinthequestionorintheanswers,knowingtheselineequationfactscanhelpsavetimeonthetest.
Let’slookathowthismaybetested.
15. Thegraphofwhichofthefollowingequationsisparalleltothelinewithequationy=−3x−6?
A) x−3y=3
B) x− y=2
C) x+ y=4
D) x+ y=5
Here’sHowtoCrackItThequestionasksfortheequationofalinethathasaslopeparalleltotheslopeofthelinegivenintheproblem. In the form y=mx+ b,m represents the slope. So, the slope of the equation given in theproblem,y=−3x−6,is−3.Allyouneedtodonowisfindwhichchoicealsohasaslopeof−3.
Onewaytodothatwouldbetorewriteeachanswerintothey=mx+bform.However,ifyounotice
thateachequationispresentedintheAx+By=Cform,youknowthattheslopeinthatformisequalto−
.So,checkeachanswerchoice:Theslopeof(A)is− ,or− ;theslopeof(B)is− or3;the
slopeof (C) is− , or−6; and the slopeof (D) is− ,which equals−3. So, (D) is the correct
answer.
ParallelandPerpendicularLinesSonowweknow thatparallel lines have the sameslope.Whenever theSATbringsupperpendicular
lines,justrememberthataperpendicularlinehasaslopethatisthenegativereciprocaloftheotherline’s
slope.Forinstance,iftheslopeofalineis3,thentheslopeofalineperpendiculartoitwouldbe− .
Combinethiswiththeskillsyou’vealreadylearnedtoattackaproblemaboutperpendicularlines.
Here’sanexample:
Parallelvs.Perpendicular
Parallellineshavethesameslopeandnever
intersect.Perpendicularlineshaveslopesthatarenegativereciprocalsandintersectatarightangle.
18. Whichofthefollowingisthegraphofalineperpendiculartothelinedefinedbythe
equation2x+5y=10?A)
B)
C)
D)
Here’sHowtoCrackIt
Sincethequestionasksforalineperpendiculartotheline2x+5y=10,youneedtofindtheslopeofthe
lineandthentakethenegativereciprocaltofindtheslope.Youcanconverttheequationintothey=mx+
bformatinordertofindtheslope,orsimplyrememberthatwhenanequationispresentedintheformAx
+By=C,theslopeisequalto− .Sotheslopeofthislineis− ,andtheslopeofaperpendicular
linewouldbe .
Look at the answer choices for one with a positive (upward) slope. Choices (B) and (C) slopedownward,soeliminatethem.Next,usepointsinthegraphtofindtheslopeofeachanswer.Eliminate(A);ithaspointsat(1,0)and(2,5),foraslopeof5—toosteep.Theonlyremainingchoiceis(D),whichisthecorrectanswer.
TwoEquationswithInfinitelyManySolutionsInthepreviouschaptersonalgebra,wediscussedequationswithoneormultiplesolutions.Nowimagineanequationinwhichanyvalueofxwouldcreateaviablesolutiontotheequation.
x+3=x+3
Inthiscase,itisfairlyobviousthatanynumberyouchoosetoputinforxwillcreateatrueequation.Butwhatdoesitmeanwhentwolineshaveinfinitelymanysolutions?Let’slookatanexample.
20.
gx−hy=78
4x+3y=13
Inthesystemofequationsabove,gandhareconstants.Ifthesystemhasinfinitelymanysolutions,whatisthevalueofgh?A) −432B) −6C) 6D) 432
ToInfinity…andBeyond!Whengiventwoequationswithinfinitelymanysolu-tions,findawaytomake
themequal.Theequationsrepresentthesameline.
Here’sHowtoCrackItThisquestionmayhaveyouscratchingyourheadandmovingontothenextquestion,butexplorewhatyoucandotosolvethisbeforeyoudecideit’snotworthyourtime.Youmaybesurprisedbyhoweasyitistosolveaproblemlikethis.
Whentheysaythattheseequationshaveinfinitelymanysolutions,whattheyarereallysayingisthatthesearethesameequation,orthatoneequationisamultipleoftheotherequation.Inotherwords,thesetwoequationsrepresentthesameline.Withthatinmind,trytodeterminewhatneedstobedonetomaketheseequationsequal.Sincetherightsideoftheequationisdealingwithonlyaconstant,firstdeterminewhatyouwouldneedtodotomake13equalto78.
Inthiscase,youneedtomultiply13by6.Sinceyouareworkingwithequations,youneedtodothesamethingtobothsidesoftheequationinorderfortheequationtoremainequal.
6(4x+3y)=6×13
24x+18y=78
Sincebothequationsarenowequalto78,youcansetthemequaltooneanother,givingyouthisequation:
24x+18y=gx−hy
Youmayknow thatwhenyouhave equationswith the samevariableson each side the coefficientsonthosevariablesmustbeequal,soyoucandeducethatg=24andh=−18.(Becautiouswhenyouevaluatethis equation. The test writers are being sneaky by using addition in one equation and subtraction inanother.)Therefore,ghequals24×−18=−432.Choice(A)iscorrect.
TwoEquationswithNoSolutionsYousawabovethatasystemofequationscanhaveinfinitelymanysolutions.Whensolvingequations,youlikelyassume,asmostpeopledo, that therewillbeat leastonesolutiontotheequation,butthat isnotalwaysthecase.Lookatthefollowingexample.
3x−6=3x+7
Ifyousolvethisequation,youwillfindthat−6=7.Since−6canneverequal7,thereisnovalueofxthatcanbeputintothisequationtomakeittrue.Inthiscase,theequationhasnosolutions.
Whatdoesitmeaniftwoequationsoflineshavenosolutions?Here’sonetotry.
15. Whichofthefollowingaccuratelyrepresentsthesetofsolutionsforthelines6x+12y=−24and ?
A) (0,−4)B) (0,4)C) Therearenosolutions.D) Thereareinfinitelymanysolutions.
There’sJustNoSolutionWhengiventwoequations
withnosolutions,findawaytocompareslopes.Theequationsrepresent
parallellines.
Here’sHowtoCrackIt
Startbyputtingthefirstlineintoy=mx+bform:12y=−6x−24.Dividethewholeequationby12,so
.Sincetheselineshavethesameslopebutdifferenty-intercepts,thelinesareparallel,and
theywillneverintersect.Therefore,(C)isthecorrectanswer.
If two lines had different slopes, the lineswould intersect at a single point such as (A) or (B). If theequationswereidentical,thentheywouldbethesamelineandthereforehaveinfinitelymanysolutions.
PointsofIntersectionEarlierinthisbookyoulearnedhowtofindthesolutiontoasystemofequations.Thereareseveralwaysto do this, including stacking up the equations and adding or subtracting, setting them equal, or evenPlugging In theAnswers. The SATmay also ask about the intersection of two graphs in the xy-plane,whichisasimilaridea.
Let’stryone:
14. Inthexy-plane,whichofthefollowingisapointofintersectionbetweenthegraphsofy=x+2andy=x2+x−2?A) (0,−2)B) (0,2)C) (1,0)D) (2,4)
Here’sHowtoCrackItThinkaboutwhatthequestionisasking:Apointofintersectionmeansapoint that ison thegraphsofbothequations.Therefore,thepointwouldactuallyworkifpluggedintotheequationofthelineandtheequationoftheparabola.
So,usePITAbytestingtheanswerchoices:Startwithoneoftheanswersinthemiddleandpluginthepointtoeachequationtoseeifitistrue.Thecorrectpointofintersectionwillworkinbothfunctions.Try(C)inthefirstequation:Does0=(1)+2?No.So,(C)isnottheanswer.Try(D)inthefirstequation:Does4= (2)+2?Yes.So, try (D) in thesecondequation:Does4= (2)2+2−2?Yes.Because (D)worksinbothequations,itisthecorrectanswer.
OtherThingsYouCanDotoaLineThemidpoint formula gives themidpoint ofST, with points S (x1, y1) andT (x2, y2). It’s simply the
average of the x-coordinates and the y-coordinates. In our example, the midpoint would be
.
Let’sseeanexampleofamidpointproblem.
2. Inthexy-plane,whatisthemidpointofthelinesegmentwithendpointsat(3,4)and(0,0)?A) (1.5,2)B) (5,0)C) (2.5,0)D) (3.5,3.5)
Here’sHowtoCrackIt
You can use the formula for themidpoint of a line segment: . If you forget it, try to
rememberthatyouarejusttakingtheaverageofthex-coordinatesofthetwopointstogetthex-coordinate
ofthemidpoint,anddoingthesameforthey-coordinates.Forthex-coordinates,theaverageof3and0is
(3+0)÷2=1.5.Onlyoneanswerhasthisforthex-coordinate:(A).Don’twastetimecalculatingthey-
coordinateifyoudon’thaveto!
3. Whichofthefollowingpointsliesthegreatestdistancefromtheorigininthexy-plane?
Thedistanceformulalooksquitecomplicated.Theeasiestwaytosolvethedistancebetweentwopointsis to connect them and form a triangle. Then use the Pythagorean Theorem.Many times, the triangleformedisoneofthecommonPythagoreantriplets(3-4-5or5-12-13).
Let’stryadistanceformulaquestion.
A)
B) (−1,−1)
C)
D) (0,1)
Here’sHowtoCrackItDrawthe linebetween theoriginand thepoint ineachanswerchoiceanduse the techniquedescribedabovetoseewhichhasthelongesthypotenuse.Choice(A)wouldlooklikethis:
Thiscreatesatrianglewithlegsof1.5and1.5;thehypotenuse(thedistancefromtheorigin)wouldthenbe ,orabout2.12.Dothesamewith(B),(C),and(D).Thedistanceof(B)wouldbe ,orabout 1.4. Choices (C) and (D) lie in a straight line left and up from the origin, respectively, so the
distanceof(C) is0.5,andthedistanceof(D) is1.Thedistancefarthest fromtheorigin isabout2.12,whichis(A).
Roots,Solutions,andx-interceptsWe’ve talked about y-intercepts in the discussion of the slope-intercept form of a line, andwe talkedaboutsolutionswhenwecoveredsystemsofequations.Butwhataboutx-intercepts,or thesolutionforjust one equation? A solution, sometimes called a root, is simply any point where a line or curveintersectsthex-axis.Similarly,justasthey-interceptwasthepointwherealinecrossedthey-axis,anx-interceptisapointwherealineorcurveintersectsthex-axis.
Keepthesetermsstraightandyou’llbeingreatshape!
Let’stryaquestionthatrequiresknowledgeofinterceptsanddistanceinthexy-plane.
15. Whatisthedistancebetweenthex-interceptandthey-interceptoftheliney= x−6?
A) 9B) 15C) (approximately9.43)
D) (approximately10.82)
Here’sHowtoCrackIt
Startbyfindingthex-andy-interceptsoftheline.Whenanequationisiny=mx+bform,they-intercept
isb.So,they-interceptisatthepoint(0,−6).Tofindthex-intercept,youneedapointwheretheyvalue
is0,justlikehowthey-intercepthasanxvalueof0.So,plugin0foryintheequation:0= x−6,so,
x=6,andx=6 =9.Thex-intercept,then,is(9,0).
Nowdrawarighttrianglewithabaseof9(thedifferencebetweenthex-coordinates)andaheightof6(thedifferencebetween they-coordinates), anduse thePythagoreanTheorem (moreon this in thenextchapter)tocalculatethedistance:62+92=c2,soc2=117,andthedistanceis ,whichis(D).
y=f(x)Sometimes,insteadofseeingthetypicaly=mx+bequation,orsomethingsimilar,you’llseef(x)=mx+b.Lookfamiliar?Graphsarejustanotherwaytoshowinformationfromafunction.Functions
showinformationalgebraicallyandgraphsshowfunctionsgeometrically(aspictures).
Here’sanexample.Thefunctionf(x)=3x−2isshowngraphicallyasthefollowing:
ThereasontheSATincludesfunctionquestionsistotestwhetheryoucanfigureouttherelationshipbetweenafunctionanditsgraph.Totacklethesequestions,youneedtoknowthattheindependentvariable,thex,isonthex-axis,andthedependentvariable,thef(x),isonthey-axis.Forexample,ifyouseeafunctionoff(x)=7, thenyouneedtounderstandthat thisisagraphofahorizontal linewherey=7.
GraphingFunctionsOnetypeoffunctionquestionyoumightbeaskedishowthegraphofafunctionwouldshiftifyouaddedavaluetoit.
Hereisaquickguide(cisaconstant)forthegraphoff(x)=x2:
Forf(x)+c,thegraphwillshiftupcunits,asshowninthediagrambelow:
Conversely,f(x)−cwillshiftthegraphdownbycunits:
Youmayhaverealizedhoweasytheseproblemswouldbecomeifyousimplyputthemintoyourgraphingcalculator. If calculatoruse is allowed, type in the function; ifnot, remember the four simple rules fortransforminggraphs.
Youcanalsopluginpointstofindthecorrectgraph.
FormsofEquationsTheSATwillaskquestionsusingtwodifferentformsoftheequationforaparabola.
Thestandardformofaparabolaequationis:
y=ax2+bx+c
Inthestandardformofaparabola,thevalueofatellswhetheraparabolaopensupwardsordownwards(ifaispositive,theparabolaopensupwards,andifaisnegative,theparabolaopensdownwards).
Thevertexformofaparabolaequationis:
y=a(x−h)2+k
Inthevertexform,thepoint(h,k)isthevertexoftheparabola.
Simply knowingwhat the vertex form looks likemay help you answer a question, like the followingexample.
29. Whichofthefollowingisanequivalentformoftheequationofthegraphshowninthexy-planeabove,fromwhichthecoordinatesofvertexVcanbeidentifiedfromconstantsintheequation?
A) y=(x−2)2−16B) y=x(x−4)−12C) y=(x−6)(x+2)D) y=(x+6)(x−2)
Here’sHowtoCrackItThegraphtellsyouthatthevertexoftheparabolaisatabout(2,−16).Only(A)hasthenumbers2and16in it, so itmustbe thecorrectanswer. Ifmore thanonechoicehad theseconstants,youcoulduseyourknowledgeofthevertexform.Ifyourecognizethatthequestionasksforthevertexformoftheequationoftheparabola,youcansimplyselect(A),theonlychoicethatactuallyusesthatform.Finally,ifyouforget
26. Whichofthefollowingistheequationofacirclewithcenter(2,0)andaradiuswith
theform,youcanmultiplyouttheanswerstoseewhichofthemmatchtheoriginalequation.Ofcourse,thetestwritershavewrittentheanswerssuchthatallbut(D)areequivalent,soyouwouldstillhavetoguessfromamongtheremainingthreeanswerchoices.
Knowing the vertex of a parabola can help you more easily answer questions about the minimum ormaximumvalueaparabolicfunctionwillreach,orthex-valuethatresultsinthatminimumormaximumy-value.SaythelastquestionwasaGrid-InontheNoCalculatorsectionthataskedforthex-coordinateofthevertex.Youcouldn’tgraphittofindthevertex,soyou’dhavetogetitintovertexform.Herearethestepstodothat.
Toconvertaparabolaequationinthestandardformtothevertexform,completethesquare.
1. Makey=0,andmoveanyconstantsovertotheleftsideoftheequation.2. Takehalfofthecoefficientonthex-term,squareit,andaddittobothsidesoftheequation.3. Convertthextermsandthenumberontherighttosquareform:(x−h)2.4. Movetheconstantontheleftbackovertotherightandsetitequaltoyagain.
Fortheequationinthelastquestion,youwouldmakeit0=x2−4x−12,then12=x2−4x.You’dadd4tobothsidestoget16=x2−4x+4,thenconverttherightsidetothesquareformtoget16=(x−2)2.Finally,you’dmovethe16backoverandsetitequaltoytogety=(x−2)2−16.
TheSATwillalsoaskquestionsabouttheequationofacircleinthexy-plane.
Theequationofacircleis:
(x−h)2+(y−k)2=r2
Inthecircleequation,thecenterofthecircleisthepoint(h,k),andtheradiusofthecircleisr.
Let’slookataquestionthatteststheuseofthecircleequation.
endpoint ?
A) (x−2)2+y2=4B) (x+2)2+y2=4C) (x−2)2+y2=16D) (x+2)2+y2=16
Here’sHowtoCrackItStart by buildingwhat you know of the circle formula: If the center is at point (2, 0), then the circleequationwillbe(x−2)2+(y−0)2=r2,ormoresimply,(x−2)2+y2=r2.Choices(B)and(D)donotmatch,soeliminatethem.
Nowcalculatetheradiusofthecircle.Findthedistancebetweenpoints(2,0)and bydrawingarighttriangle.Thebaseoftherighttrianglewillbethedifferencebetweenthexvaluesof5and2,sothebaseoftherighttriangleis3.Theheightoftherighttrianglewillbethedifferencebetweentheyvalues,which is . Use the Pythagorean Theorem to find the hypotenuse of the triangle, which will be thedistancebetweenthepoints(and, therefore, thelengthof theradius).So,r2=32+ =9+7=16.Sinceyouhavethevalueofr2,whichis16,usePOEtoeliminate(A)andselect(C).
Justasyoumaybegivenaparabolainstandardformandexpectedtoconvertitintovertexform,youmayalsobegivenanequationforacirclethatisnotintheform(x−h)2+(y−k)2=r2andexpectyoutofigureouttheradiusorcenter.Todoso,youjustneedtocompletethesquareasyoudidabovewiththeequationofaparabola.Youwillneedtodoit twice,though—onceforthex-termsandagainfor they-terms.
Gotallofthat?Nowtestyourknowledgeoffunctionsandgraphingwiththefollowingdrills.
FunctionsandGraphsDrill1:NoCalculatorSectionUse your new knowledge of functions and graphs to complete these questions, but don’t use yourcalculator!Answersandexplanationscanbefoundonthispage.
3. Letthefunctionfbedefinedsuchthatf(x)=x2−c,wherecisaconstant.Iff(−2)=6,whatisthevalueofc?A) −10B) −2C) 0D) 2
7.
Thegraphaboveshowsy=2x.Whichofthefollowinggraphsrepresentsy=|2x|?A)
B)
C)
D)
10. Thegraphoflinelinthexy-planepassesthroughthepoints(2,5)and(4,11).Thegraphoflinemhasaslopeof−2andanx-interceptof2.Ifpoint(x,y)isthepointofintersectionoflineslandm,whatisthevalueofy?
A)
B)
C) 1D) 2
15.
Thefiguresaboveshowthegraphsofthefunctionsfandg.Thefunctionfisdefinedbyf(x)=2x3+5x2−x.Thefunctiongisdefinedbyg(x)=f(x−h)−k,wherehandkareconstants.Whatisthevalueofhk?A) −2
FunctionsandGraphsDrill2:Calculator-PermittedSectionCalculatoruseisallowedonthesequestions,souseitwisely.Answersandexplanationscanbefoundonthispage.
6. Iff(x)= ,whatisthesmallestpossiblevalueoff(x)?A) 0
B)
C) 1D) 2
10.x y−3 −7−1 −32 3
Basedonthechartabove,whichofthefollowingcouldexpresstherelationshipbetweenxandy?A) y=x−4B) y=2x−1C) y=2x+2D) y=3x−3
13. Linelcontainspoints(3,2)and(4,5).Iflinemisperpendiculartolinel,thenwhichofthefollowingcouldbetheequationoflinem?A) x+5y=15B) x+3y=15C) 3x+y=5
D) −5x+y=
18. Iff(x)=2x2+4forallrealnumbersx,whichofthefollowingisequaltof(3)+f(5)?A) f(4)
B) f(6)C) f(10)D) f(15)
21.
Thegraphofy=g(x)isshowninthefigureabove.Ifg(x)=ax2+bx+cforconstantsa,b,andc,andifabc≠0,thenwhichofthefollowingmustbetrue?A) ac>1B) c>1C) ac>0D) a>0
26. CarlosandKatherineareestimatingaccelerationbyrollingaballfromrestdownaramp.At1second,theballismovingat5meterspersecond(m/s);at2seconds,theballismovingat10m/s;at3seconds,theballismovingat15m/s;andat4seconds,itismovingat20m/s.Whengraphedonanxy-plane,whichequationbestdescribestheball’sestimatedaccelerationwhereyexpressesspeedandxexpressestime?A) y=5x+5B) y=25xC) y=5xD) y=(4x+1)2+5
CHAPTERDRILLANSWERSANDEXPLANATIONS
FunctionsandGraphsDrill1:NoCalculatorSection3. B Startbyplugginginwhatyouknowintothegivenfunction.Iff(x)=x2−c,andf(−2)=6,then
plugin−2forxinthefunction:f(−2)=(−2)2−c.Solveandreplacef(−2)with6:6=4−c;2=−c;andc=−2.Ifyoupicked(A),youforgotthat(−2)2ispositive4.
7. A Tryplugginginavalueforxtoseeifthegraphsincludethatpoint.Ifx=0,theny=0,so(0,0)should be a point on the graph.Unfortunately, this doesn’t eliminate any answer choices; tryanothervalue.Ifx=1,theny=2,so(1,2)shouldbeapointonthegraph.Eliminate(B),(C),and(D).Thecorrectansweris(A).
10. D First,findtheslopeoflinelbyusingtheslopeformula: .Plugthisslope
andoneofthepointsonlinelintotheslope-interceptformy=mx+btosolveforb,givingyou
thefullequationoftheline.Ifyouusethepoint(2,5),youget5=3(2)+bor5=6+b,sob=
−1.Therefore,theequationforlinelisy=3x−1.Forlinem,theslopeisgivenas−2,andthe
x-interceptis2.Beverycarefulnottojumptotheconclusionthattheequationoflinemisy=
−2x+2.Intheformy=mx+b,thebisthey-intercept,notthex-intercept.Thex-intercept is
wherey=0,soyouknowthat(2,0)isapointonlinem.Usethispointandtheslopetofindthe
equationoflineminthesamewayyoudidforlinel.0=−2(2)+b,sob=4andtheequationis
y=−2x+4.Nowsetthexpartsoftheequationsequaltofindthepointofintersection.If3x−1
=−2x+4,then5x=5andx=1.Again,becareful!Thequestionaskedforthevalueofy!Plug
x=1intooneofthelineequationstofindy.Forlinel,theequationbecomesy=3(1)−1=3−
1=2,whichis(D).
15. B Thesecondgraphmovesdown1andtotheleft1.Rememberthatwhenagraphmovestotheleft,itisrepresentedby(x+h),whichwouldbethesameasx−(−1).Soh=−1.Becauseanegativek representsmovingdown,k=1.Therefore,hk= (−1)× (1)=−1, and thecorrectansweris(B).
FunctionsandGraphsDrill2:Calculator-PermittedSection
6. A On this question you can use Plugging In the Answers. The numbers in the answer choices
replacethef(x)portionoftheequation,soyoucanjustwriteouttherestofit, ,nextto
eachtoseeifitcanbetrue.Startwith(A)sinceyouarelookingforthesmallestvalueoff(x).If
0= ,then0=3x−2whenyousquarebothsides.Add2tobothsidestoget2=3x,and
thendividebothsidesby3.Yougetx= .Sincethisisarealvalue,theequationworks,sothe
smallestvalueoff(x)is0.Choice(A)iscorrect.
10. B Pluginthevaluesfromthechart.Usethepair(−3,−7)fromthetopofthechartandeliminateanswersthatarenottrue:Choice(A)becomes−7=−3−4,whichistrue.Keepit.Keep(B):−7=2(−3)−1istrue.Getridof(C),whichbecomes−7=2(−3)+2:−7doesnotequal−4.Getridof(D):−7=3(−3)−3.−7doesnotequal−12.Nowuseanotherpairjusttotest(A)and(B).Using(−1,−3),(A)gives−3=−1−4,whichisnottrue,soeliminateit,leavingonly(B).Thevalues(−1,−3)work:−3=2(−1)−1.
13. B First, find the slope of line l by using the slope formula: . A line
perpendicular to line lmust have a slope that is the negative reciprocal of l’s slope. So, its
slopeshouldbe− InthestandardformofalineAx+By=C,theslopeis− .Only(B)has
a slope of − . If you didn’t remember the rule about the slope of perpendicular lines in
standardform,youcouldhaveconvertedtheanswerstoslope-interceptformandsketchedout
eachofthelinestolookfortheanswerthatlookedperpendiculartol.
18. B Tofindthevalueoff(3)+f(5),findthevaluesoff(3)andf(5)separately:f(3)=2(3)2+4=22andf(5)=2(5)2+4=54.Sof(3)+f(5)=76.Youcantellthatf(4)willbebetween22and54,soyoucancrossout(A).IfyouBallpark(C)and(D),putting10or15inthefunctionwillgiveyou a number bigger than 100, and you’re looking for 76, so (C) and (D) are too big. Thatmeanstheansweris(B)byPOE.
21. C Rememberyourtransformationrules.Wheneveraparabolafacesdown,thequadraticequation
hasanegativesigninfrontofx2term.ItalwayshelpstoPlugIn!Forexample,ifyouroriginal
equation was (x − 2)2, putting a negative sign in front would make the parabola open
downward,soyou’llhave−(x−2)2.Ifyouexpanditout,youget−x2+4x−4.Noticethatthe
value of a in this equation is −1.Also notice that the value of c is −4. This allows you to
eliminate(B)and(D).Nowyoumustplugindifferentlytodistinguishbetween(A)and(C).Be
warned:Youmustusefractionstohelpdiscernwhichiscorrect.Saythex-interceptstakeplace
atx= andx= .Rewritingthosetwoexpressionsmeansthatthefactorsare and
.IfyouFOILouttheterms,youendupwithx2− x+ .Remember,theparabolaopens
downward,soyoumustmultiplyby−1toeachtermtoyield−x2+ x− .Yourvaluesofaand
carenow−1and− ,respectively.Multiplythetwovaluesandyouget ,whichallowsyouto
eliminate (A) and confidently choose (C). (And that was worth only 1 point! Embrace the
POOD!)
26. C Figureoutthepointsthatwillbeonthegraphfromthedatagiven:(0,0),(1,5),(2,10),(3,15),(4,20).Drawalinethroughorclosetothesepointstogetanideaofwhatthegraphwilllooklike.ThenusePOE.Thelineislinear,notquadratic,soyoucaneliminate(D).Itisalsoclearthatthelinebeginsattheorigin,sothey-interceptwillbe0.Thiswilleliminate(A).Aslopeof25isfartoobig—Ballpark—soyoucaneliminate(B),leaving(C).
Summary◦ Givenafunction,youputanx-valueinandgetanf(x)ory-valueout.
◦ LookforwaystousePluggingInandPITAonfunctionquestions.
◦ Forquestionsaboutthegraphsoffunctions,rememberthatf(x)=y.
◦ Ifthegraphcontainsalabeledpointorthequestiongivesyouapoint,plugitintotheequationsintheanswersandeliminateanythataren’ttrue.
◦ Theequationofalinecantaketwoforms.Ineitherform,(x,y)isapointontheline.• Inslope-interceptform,y=mx+b,theslopeismandthey-interceptisb.
• Instandardform,Ax+By=C,theslopeis− andthey-interceptis .
◦ Giventwopointsonaline,(x1,y1)and(x2,y2),theslopeis .
◦ Twolinearequationswithinfinitelymanysolutionsactuallyrepresentthesameline.
◦ Parallellineshavethesameslopesandnopointsofintersection.
◦ Perpendicularlineshaveslopesthatarenegativereciprocalsandintersectatarightangle.
◦ Tofindapointofintersection,plugthepointintobothequationstoseeifitworksorgraphthelinesonyourcalculatorwhenitisallowed.
◦ Tofindthemidpointbetweentwopoints,averagethex-coordinatesandaveragethey-coordinates.
◦ To find the distance between two points, make them the endpoints of the hypotenuse of a righttriangleandusethePythagoreanTheorem.
◦ Therootsofafunction,alsoknownassolutions,zeroes,orx-intercepts,are thepointswhere thegraphcrossesthex-axisandwherey=0.
◦ Graphs of functions can be moved up or down if a number is added to or subtracted from thefunction,respectively.Theycanmoveleftifanumberisaddedinsidetheparenthesesofthefunctionormoverightifanumberissubtractedinsidetheparentheses.
◦ Thevertexformofaparabolaequation isy=a(x−h)2+k,where(h,k) is thevertex.Togetaparabolainthestandardformintovertexform,completethesquare.
◦ Thestandardformofacircleequationis(x−h)2+(y−k)2=r2,where(h,k)isthecenterandristheradius.Togetacircleequationintothestandardform,completethesquareforboththex-terms
Chapter16GeometryNow that you’ve had some review and practice in coordinate geometry, it’s time to learn a fewmoregeometryrules.TheSATMathTestcontainsfiveorsixquestionsthattestyourbasicgeometryknowledgeontopicslikelinesandangles,triangles,andcircles.Thischaptercoverseachofthesetopicsandmoreandprovidesastep-by-stepwalk-throughforeachtypeofproblem.
GEOMETRYONTHESATWecoveredcoordinategeometryinChapter15.Butinadditiontocoordinategeometryquestions, therewillbefiveorsixquestionsontheSATthattestyourknowledgeofbasicgeometryrules.Well,kinda.AtthebeginningofeachMathsection,youareprovidedwiththefollowingreferencetable:
Thisboxofinformationcontainssomeofwhatyou’llneedtotacklegeometryontheSAT.Inthischapter,we’llcoverhowtoapproachgeometryquestionsandotherinformationyouwillneedtoknowinordertohandlegeometryquestionsontheSAT.
Geometry:BasicApproachFor the handful of non-coordinate geometry questions that appear on the SAT, we recommend thefollowingstep-by-stepapproach:
1. Drawafigureifafigureisnotprovided.Also,ifthereisafigureprovided,butthequestioncontainsthenote“Figurenotdrawntoscale,”youmightwanttoredrawthefigureusingtheinformationinthequestion.
2. Labelthefigurewithanyinformationgiveninthequestion.SometimesyoucanPlugInforpartsofthefigureaswell.
3. Writedownformulasthatyoumightneedforthequestion.4. Ballparkifyou’restuckorrunningshortontime.
Thesefoursteps,combinedwiththetechniquesyou’velearnedintherestofthisbookandthegeometryconceptsthischapterwillcover,willenableyoutotackleanygeometryquestionyoumightrunacrossontheSAT.
Beforewediveintothenitty-gritty,let’stryaproblemusingthisapproach.
25. InΔABC(notshown), ABC=60°andAC BC.IfAB=x,thenwhatistheareaof
ΔABC,intermsofx?
A)
B)
C)
D) x2
Here’sHowtoCrackItFollowthestepsoutlinedonthepreviouspage.Startbydrawingthefigure.IfAC BC,thenΔABCisarighttrianglewiththerightangleatpointC:
Thenextstepistolabelwhatyouknow. ABC=60°cangorightintothediagram.BecauseAB=x,youcanpluginforx;makex=4.Labelthisinformationinthediagram:
Next,figureoutwhatotherinformationyouknow.Becausethereare180°inatriangle, BAC=180−90
−60=30°.Thisisa30°-60°-90°specialrighttriangle,whichyouaregiveninformationaboutinthebox
atthestartofeachMathTestsection.Basedonthefiguregiveninthebox,thehypotenuseisequalto2x.
(Notethatthisisadifferentxthanwhatyoupluggedinfor;thetestwritersaretryingtoconfuseyou.)So,
ifthehypotenuseis4,thenx= =2;thisisthesideoppositethe30°angle,BC.Theremainingside,AC,
isx ,whichis2 .Labelthisinformationinyourdiagram:
Nowwritedowntheformulayouneed.Thequestionisaskingforthearea,sousetheareaofatriangle
formulafromthebox:A= bh.Fillinwhatyouknow.Becausethisisarighttriangle,youcanusethetwo
legsofthetriangleasthebaseandtheheight.Makeb=2 andh=2intheequationandsolve:A= (2
)(2)=2 .Thisisyourtarget;circleit.Nowpluginx=4(that’sthexfromtheproblem,NOTthex
fromtheinformationinthebox!)intoeachanswerchoiceandeliminatewhatdoesn’tequal2 .Theonly
choicethatworksis(A).
Now thatwe’ve covered how to approach geometry questions, let’s lookmore closely at someof thegeometryconceptsyou’llneedfortheseproblems.
LinesandAnglesHerearethebasicrulesyouneedtoknowforquestionsaboutlinesandanglesontheSAT.
1. Acirclecontains360degrees.
Everycirclecontains360degrees.Eachdegreeis ofthetotaldistancearoundtheoutside
ofthecircle.Itdoesn’tmatterwhetherthecircleislargeorsmall;itstillhasexactly360
degrees.
2. Whenyouthinkaboutangles,remembercircles.Anangleisformedwhentwolinesegmentsextendfromacommonpoint.Ifyouthinkofthepointasthecenterofacircle,themeasureoftheangleisthenumberofdegreesenclosedbythelineswhentheypassthroughtheedgeofthecircle.Onceagain,thesizeofthecircledoesn’tmatter;neitherdoesthelengthofthelines.Refertothefollowingfigure.
3. Alineisa180-degreeangle.Youprobablydon’tthinkofalineasanangle,butitisone.Thinkofitasaflatangle.Thefollowingdrawingsshouldhelp:
4. Whentwolinesintersect,fouranglesareformed.Thefollowingdiagramshouldmakethisclear.Thefouranglesareindicatedbyletters.
5. Whentwolinesintersect,theanglesoppositeeachotherwillhavethesamemeasures.Suchanglesarecalledverticalangles.Inthefollowingdiagram,anglesaandcareequal;soareanglesbandd.
a+b+c+d=360°a=c,b=d
Themeasuresofthesefouranglesaddupto360degrees.(Rememberthecircle.)
a+b+c+d=360°
Itdoesn’tmatterhowmanylinesyouintersectthroughasinglepoint.Thetotalmeasureofalltheanglesformedwillstillbe360degrees.
a+b+c+d+e+f+g+h=360°a=e,b=f,c=g,d=h
6. Iftwolinesareperpendiculartoeachother,eachofthefouranglesformedis90degrees.A90-degreeangleiscalledarightangle.
Perpendicular:Meetingatright
(90°)angles
Anglesa,b,c,anddallequal90degrees.
FlipandNegate
Iftwolinesareperpendicular,
thentheirslopes
arenegativereciprocals;
i.e.,ifl1hasaslopeof
2andl2isperpendicular
tol1,thenl2musthavea
slopeof− .
The little box at the intersection of the two lines is the symbol for a right angle. If the lines are notperpendiculartoeachother,thennoneoftheangleswillberightangles.Don’tassumethatanangleisarightangleunlessyouarespecificallytoldthat it isarightangle,eitherintheproblemorwiththe90°symbol.
7. Whentwoparallellinesarecutbyathirdline,allofthesmallanglesareequal,allofthebiganglesareequal,andthesumofanybigangleandanysmallangleis180degrees.Parallellinesaretwolinesthatneverintersect,andtherulesaboutparallellinesareusuallytaughtinschoolwithlotsofbigwords.Butweliketoavoidbigwordswheneverpossible.Simplyput,whenalinecutsthroughtwoparallellines,twokindsofanglesarecreated:biganglesandsmallangles.Youcantellwhichanglesarebigandwhicharesmalljustbylookingatthem.Allthebigangleslookequal,andtheyare.Thesameistrueofthesmallangles.Lastly,anybigangleplusanysmallanglealwaysequals180degrees.(Thetestwriterslikerulesaboutanglesthataddupto180or360degrees.)
ParallelLinesParallellineshavethesameslope.
Inanygeometryproblem,neverassumethattwolinesareparallelunlessthequestionordiagramspecificallytellsyouso.Inthefollowingdiagram,angleaisabigangle,andithasthesamemeasureasanglesc,e,andg,whicharealsobigangles.Anglebisasmallangle,andithasthesamemeasureasanglesd,f,andh,whicharealsosmallangles.
a=c=e=gb=d=f=hl2=l3
Youshouldbeabletoseethatthedegreemeasuresofanglesa,b,c,anddaddupto360degrees.Sodothoseofanglese,f,g,andh.Ifyouhavetroubleseeingit,drawacirclearoundtheangles.Whatisthedegreemeasureofacircle?Also,thesumofanysmallangle(suchasd)andanybigangle(suchasg)is180°.
Let’sseehowtheseconceptsmightbetestedontheSAT.
12.
Note:Figurenotdrawntoscale.
Inthefigureabove,l2||l3.Whichofthefollowingcouldbefalse?
A) a=eB) b+e=180C) l1 l4D) c=d
Here’sHowtoCrackItStartbymarkingl2andl3asparallellines.Next,becauseyou’relookingforwhatcouldbefalse,considereachanswerchoiceandusePOE.For(A),ifl2andl3areparallel,thenl4transectsbothlinesandcreatessetsofequalangles.Allsmallanglesaroundl4whichareformedbyl2orl3areequal,soamustbeequaltoe;eliminate(A).Choice(B)isbasedonthesamesetofintersectinglines;becausel2andl3areparallelandl4 transectsbothlines,thenanybigangleplusanysmallangleequals180°.Therefore,(B)mustbetrue;eliminateit.For(C),youdon’tknowthevalueofanyangles,soyoucannotdetermineiftheselinesareperpendicular.Since(C)couldbefalse,choose(C).Choice(D)mustbetruebecauseoppositeanglescreatedbytwolinesarealwaysequal.
ConvertingDegreestoRadiansSomegeometryquestionswillaskyoutoconvertananglemeasurementfromdegreestoradians.Whilethismaysoundscary,doingthisconversionrequiresonlythatyourememberthat180degrees=πradians.Usethisrelationshiptosetupaproportion(seeChapter14)andconverttheunits.
27. πradiansisapproximatelyequaltohowmanydegrees?
A) 8°B) 694°C) 1,389°D) 2,777°
Here’sHowtoCrackItUsetherelationshipbetweenradiansanddegreestosetupaproportion.If180degrees=πradians,thentheproportionwilllooklikethefollowing:
Cross-multiplytoget180× π=πx.Dividebothsidesbyπ:180× =x.Finally,useyourcalculator,
andyoufindthatxisapproximately1,389,whichis(C).
TrianglesHerearesomebasictrianglerulesyou’llneedtoknowfortheSAT.
1. Everytrianglecontains180degrees.Thewordtrianglemeans“threeangles,”andeverytrianglecontainsthreeinteriorangles.Themeasureofthesethreeanglesalwaysaddsuptoexactly180degrees.Youdon’tneedtoknowwhythisistrueorhowtoproveit.Youjustneedtoknowit.Andwemeanknowit.
2. Anisoscelestriangleisoneinwhichtwoofthesidesareequalinlength.Theanglesoppositethoseequalsidesarealsoequalbecauseanglesoppositeequalsidesarealsoequal.
AB=ACAB≠BCc=bc≠a
YourFriendtheTriangleIfyouareeverstumpedbyageometryproblemthatdealswithaquadrilateral,
hexagon,orotherpolygon,lookforthetrianglesthatyoucanformbydrawinglinesthroughthefigure.
3. Anequilateraltriangleisoneinwhichallthreesidesareequalinlength.Becausetheanglesoppositeequalsidesarealsoequal,allthreeanglesinanequilateraltriangleareequaltoo.(Theirmeasuresarealways60degreeseach.)
EquilateralTrianglesAnequilateraltriangle
isalsoisosceles.
AB=BC=AC
4. Arighttriangleisatriangleinwhichoneoftheanglesisarightangle(90degrees).Thelongestsideofarighttriangle,whichisalwaysoppositethe90-degreeangle,iscalledthehypotenuse.
ACisthehypotenuse.
Somerighttrianglesarealsoisosceles.Theanglesinanisoscelesrighttrianglealwaysmeasure45°,45°,and90°.
AB=BC
5. Theperimeterofatriangleisthesumofthelengthsofitssides.
perimeter=4+6+6=16
6. Theareaofatriangleis (base×height).
InorOutTheheightcanbefoundwithalinedroppedinsideoroutsidethetriangle—
justaslongasit’sperpendiculartothebase.
Tryaquestiontestingsomeoftheseconcepts:
3.
Theregularhexagonshownaboveisdividedintosixcongruentequilateraltriangles.Whatisthemeasure,indegrees,ofoneoftheinterioranglesofthehexagon?A) 60°
B) 120°C) 180°D) 360°
Here’sHowtoCrackItFirst,youcanBallparkandeliminate(C)and(D);(C)wouldbeastraight line,and(D)isall thewayaroundacircle,soneitherofthosecanbetheinteriorangleofthisfigure.Next,labelwhatyouknow.Ifeachofthetrianglesinthefigureisequilateral,thenalloftheangleswithinthetrianglesareequalto60°.Theinterioranglesofthehexagonarecomprisedoftwoanglesofthetriangles,sotheinterioranglesofthehexagonmustbe2×60=120°,whichis(B).
SOHCAHTOATrigonometrywill likelyappearon theSATMathTest.But fearnot!Many trigonometryquestionsyouwill see mostly require you to know the basic definitions of the three main trigonometric functions.SOHCAHTOAisawaytorememberthethreefunctions.
Checkoutthisnextexample.
11.
Inthetriangleabove,sinx=0.8andcosx=0.6.Whatistheareaofthetriangle?A) 0.48B) 4.8C) 24D) 48
Here’sHowtoCrackIt
Usethedefinitionsofsineandcosinetofindthetwolegsofthetriangle.Sineis ,soifsinx=
0.8,then0.8= .Multiplybothsidesby10andyoufindthesideoppositetheanglewithmeasure
x°is8.Similarly,cosineis ,soifcosx=0.6,then0.6= .Multiplybothsidesby10to
determine thesideadjacent to theanglewithmeasurex° is6.With those twosides, find thearea.The
formulaforareaisA= bh,soA= (6)(8)=24,whichis(C).
PythagoreanTheoremThePythagoreanTheoremstatesthatinarighttrianglethesquareofthehypotenuseequalsthesumofthe squares of the other two sides.Asmentioned earlier, the hypotenuse is the longest side of a righttriangle;it’sthesideoppositetherightangle.Thesquareofthehypotenuseisitslengthsquared.ApplyingthePythagoreanTheoremtothefollowingdrawing,wefindthatc2=a2+b2.
PythagoreanTheorema2+b2=c2,wherecisthehypotenuseofarighttriangle.Learnit;loveit.
IfyouforgetthePythagoreanTheorem,youcanalwayslookitupintheboxatthebeginningoftheMathsections.
ThetestwriterslovetoaskyouquestionsinvolvingthePythagoreanTheoremalongwithSOHCAHTOA.Seethefollowingsamplequestion.
15. InΔABC(notshown),AC BCandcos ABC= .Whatisthevalueoftan ABC?
A)
B)
C)
D)
Here’sHowtoCrackItStartbydrawingtriangleABC.
Next,labelwhatyoucan.Youdon’tknowtheactualsidelengths,butbecausecos ABC= ,youdo
knowtherelationshipbetweenthesideadjacenttoangleABCandthehypotenuse.YoucanPlugInforthis
relationship:MakeBC(thesideadjacenttotheangle)12andAB(thehypotenuse)13:
Youneedtofindtan ABC,whichmeansyouneed .Youalreadyknowtheadjacentsideis12,
butyoustillneedthesideopposite,AC.UsethePythagoreanTheoremtofindthemissingside:
a2+b2=c2122+b2=132
144+b2=169b2=25b=5
Therefore,AC=5,andtan ABC= ,whichis(B).
SpecialRightTrianglesBothofthepreviousquestionsyouworkedalsousedspecialrighttriangles.Whileinthelastquestionwe
usedthePythagoreanTheoremtofindthemissingside,ifyoumemorizethesespecialtrianglesyoucanavoidusingthePythagoreanTheoreminalotofcases.
YourFriendtheRectangle
Beonthelookoutforproblemsinwhichthe
applicationofthePythagoreanTheoremisnotobvious.Forexample,everyrectanglecontains
tworighttriangles.Thatmeansthatifyouknowthelengthand
widthoftherectangle,youalsoknowthelength
ofthediagonal,whichisthehypotenuseof
bothtriangles.
When it comes to geometry questions involving right triangles, the SAT Math Test is often fairlypredicable, as questions tend to focus on certain relationships. In these questions the triangles haveparticular ratios.Thereare twodifferent typesofspecial right triangles.Thefirst involves theratioofsidesandthesecondinvolvestheratioofangles.
ThemostcommonspecialrighttriangleswithsideratiosareknownasPythagoreantriplets.Herearethetestwriters’favorites:
IfyoumemorizethesetwosetsofPythagoreantriplets(3-4-5and5-12-13),you’lloftenbeabletofindthe answer without using the Pythagorean Theorem. If you’re given a triangle with a side of 3 and ahypotenuseof5,youknowrightawaythattheothersidehastobe4.Likewise,ifyouseearighttrianglewithsidesof5and12,youknowthehypotenusemustbe13.
Relax;It’sJustaRatioA3-4-5trianglemaybe
hiding,disguisedas6-8-10or18-24-30.It’sallthe
sameratio,though,sobeonthelookout.
The test writers also like to use right triangles with sides that are simply multiples of the commonPythagoreantriplets.Forexample,youmightseea6-8-10ora10-24-26triangle.Thesesidesaresimplythesidesofthe3-4-5and5-12-13trianglesmultipliedby2.
There are two types of special right triangles that have a specific ratio of angles. They are the30°-60°-90°triangle and the45°-45°-90°triangle.The sidesof these triangles alwayshave the samefixedratiotoeachother.Theratiosareasfollows:
Let’s talkabouta45°-45°-90°trianglefirst.Didyounoticethat this isalsoanisoscelesright triangle?Thesideswillalwaysbethesame.Andthehypotenusewillalwaysbethesidetimes .Itsratioofsidetosidetohypotenuseisalways1:1: .Forexample,ifyouhavea45°-45°-90°trianglewithasideof3,thenthesecondsidewillalsobe3andthehypotenusewillbe3 .
Now let’s talk about a 30°-60°-90° triangle. The ratio of shorter side to longer side to hypotenuse is
always1: :2. For example, if the shorter side of a 30°-60°-90° triangle is 5, then the longer side
wouldbe5 andthehypotenusewouldbe10.
SymbolsHere’salistofsymbolsyoumightseeontheSATMathTest,alongwithatranslationofeachoneintoEnglish.Learnthesesymbolsandkeepaneyeoutforthem!
Symbol Meaning
∆ABC triangleABC
AB linesegmentAB
AB thelengthoflinesegmentAB
SimilarTrianglesSimilartriangleshavethesameshape,buttheyarenotnecessarilythesamesize.Havingthesameshapemeansthattheanglesofthetrianglesareidenticalandthatthecorrespondingsideshavethesameratio.Lookatthefollowingtwosimilartriangles:
Thesetwotrianglesbothhavethesamesetofangles,buttheyaren’tthesamesize.Wheneverthisistrue,
the sides of one triangle are proportional to those of the other.Notice that sidesNO andST are both
oppositetheanglethatisa°.Thesearecalledcorrespondingsides,becausetheycorrespondtothesame
angle.SothelengthsofNOandSTareproportionaltoeachother.Inordertofigureoutthelengthsofthe
othersides,setupaproportion: .Nowfillintheinformationthatyouknow: = .Cross-
multiplyandyoufindthatx=21.Youcouldalsofigureoutthelengthofy: .So, = ,and
y=36.Wheneveryouhavetodealwithsidesofsimilartriangles,justsetupaproportion.
Finally,there’saspecialrelationshipbetweensimilartrianglesandtrigonometry.Sidelengthsinsimilartrianglesareproportional,andthetrigonometricfunctionsgivetheproportionsofthesidesofatriangle.Therefore,iftwotrianglesaresimilar,thecorrespondingtrigonometricfunctionsareequal!Let’slookathowthismightworkinaproblem.
16.
Inthefigureabove,ΔABCissimilartoΔXYZ.WhatisthevalueofcosA?
A)
B)
C)
D) 2
Here’sHowtoCrackItBecausethetwotrianglesaresimilar,thevalueofcorrespondingtrigonometricfunctionswillbeequal.
Therefore, cosA = cos X. The value of cos X is or . You could use the Pythagorean
Theorem to find XY, but it’s easier to use the special right triangle discussed earlier. Because thehypotenuseistwiceoneofthelegs,youknowthisisa30°-60°-90°triangle.YZistheshortestside(x),so
XY isx or2 .Therefore,cosX= ,whichreduces to .BecausecosX= cosA,cosA also
equals ,whichis(B).
CirclesHerearetherulesyou’llneedtotacklecirclequestionsontheSAT.
1. Thecircumferenceofacircleis2πrorπd,whereristheradiusofthecircleanddisthediameter.You’llbegiventhisinformationinyourtestbooklet,sodon’tstressovermemorizingtheseformulas.Youwillalwaysbeabletorefertoyourtestbookletifyouforgetthem.Justkeepinmindthatthediameterisalwaystwicethelengthoftheradius(andthattheradiusishalfthediameter).
AFewFormulasArea=πr2
Circumference=2πrorπdDiameter=2r
Inmathclassyouprobablylearnedthatπ=3.14(oreven3.14159).OntheSAT,π=3+(alittlemorethan3)isagoodenoughapproximation.Evenwithacalculator,usingπ=3willgiveyoualltheinformationyouneedtosolvedifficultSATmultiple-choicegeometryquestions.
LeaveThatπAlone!Mostofthetime,youwon’tmultiplyπoutin
circleproblems.Becausetheanswerchoiceswillusuallybeintermsofπ
(6πinsteadof18.849…),youcansaveyourself
sometroublebyleavingyourworkintermsofπ.
2. Theareaofacircleisπr2,whereristheradiusofthecircle.
area=π42=16π
3. Atangentisalinethattouchesacircleatexactlyonepoint.Aradiusdrawnfromthattangentpointformsa90-degreeangle.
Let’sseehowtheserulescanshowupontheSAT.
CirclesHaveNames?Ifaquestionrefersto
CircleR,itmeansthatthecenterofthecircle
ispointR.
22.
Thecircledefinedbytheequation(x−4)2+(y−4)2=25hasitscenteratpoint(4,4)andincludespoint(7,8)onthecircle.Thisisshowninthefigureabove.Whatistheareaofthecircleshown?A) 5πB) 10πC) 16πD) 25π
15. PointsAandBlieoncircleO(notshown).AO=3and AOB=120°.WhatistheareaofminorsectorAOB?
Here’sHowtoCrackItYouwant the area, sowrite down the formula for area of a circle:A =πr2. Thatmeans you need todetermine the radius of the circle. If you remember the circle formula from the previous chapter, yousimplyneedtorecallthatr2=25andjustmultiplybyπtofindthearea.Ifnot,youcanfindthedistancebetween(4,4)and(7,8)bydrawingarighttriangle.Thetriangleisa3-4-5righttriangle,sothedistancebetween(4,4)and(7,8)(andthustheradius)is5.Iftheradiusis5,thentheareaisπ(5)2,or25π.Theansweris(D).
ArcsandSectorsManycirclequestionsontheSATwillnotaskaboutthewholecircle.Rather,you’llbeaskedaboutarcsor sectors.Both arcs and sectors are portions of a circle: arcs are portions of the circumference, andsectorsareportionsofthearea.Luckily,botharcsandsectorshavethesamerelationshipwiththecircle,basedonthecentralangle(theangleatthecenterofthecirclewhichcreatesthearcorsector):
Notethattheserelationshipsareallproportions.Arcsandsectorsareproportionaltothecircumferenceandarea,respectively,asthecentralangleisto360°.
QuestionsontheMathTestsometimesreferto“minor”or“major”arcsorsectors.Aminorarcorsectorisonethathasacentralangleoflessthan180°,whereasamajorarcorsectorhasacentralanglegreaterthan180°(inotherwords,itgoesthelongwayaroundthecircle).Let’sseehowarcsandsectorsmightshowupinaproblem.
A)
B) πC) 3πD) 9π
Here’sHowtoCrackIt
BecauseO isthenameofthecircle,it’salsothecenterofthecircle,soAOistheradius. AOB is thecentral angle of sectorAOB, so you have all the pieces you need to find the sector. Put them into aproportion:
Cross-multiplytoget360x=1,080π(remembertonotmultiplyoutπ).Dividebothsidesby360andyougetx=3π,whichis(C).
RelationshipBetweenArcandAngleinRadiansSometimesyou’llbeaskedforanarclength,butyou’llbegiventheangleinradiansinsteadofdegrees.Fearnot!Rather thanmaking theproblemmorecomplicated, the testwritershaveactuallygivenyouagift!Allyouneedtodoismemorizethisformula:
s=rθ
Inthisformula,sisthearclength,ristheradius,andθisthecentralangleinradians.Ifyouknowthisformula,thesequestionswillbeasnap!
RectanglesandSquaresHerearesomerulesyou’llneedtoknowaboutrectanglesandsquares:
1. Theperimeterofarectangleisthesumofthelengthsofitssides.Justaddthemup.
perimeter=10+4+10+4=28
2. Theareaofarectangleislength×width.Theareaoftheprecedingrectangle,therefore,is10×4,or40.
LittleBoxesHere’saprogressionofquadrilateralsfromleastspecifictomostspecific:
quadrilateralisany4-sidedfigure
↓parallelogramisa
quadrilateralinwhichoppositesidesareparallel
↓rectangleis
aparallelograminwhichallangles=90degrees
↓squareisarectangleinwhichallsidesareequal
3. Asquareisarectanglewhosefoursidesareallequalinlength.Theperimeterofasquare,therefore,isfourtimesthelengthofanyside.Theareaisthelengthofanysidesquared.
perimeter=4(3)=12area=32=9
4. Inrectanglesandsquaresallanglesare90-degreeangles.Itcan’tbeasquareorarectangleunlessallanglesare90degrees.
Let’scheckoutanexample.
6. Iftheperimeterofasquareis28,whatisthelengthofthediagonalofthesquare?
A) 2
B) 7
C) 7
D) 14
Here’sHowtoCrackItTheperimeterofasquareis4s.So,28=4s.Divideby4tofinds=7.Thediagonalofasquaredividesthesquareintotwo45°-45°-90°triangles,withsidesintheratioofx:x:x: .Ifthesideis7,thediagonalis7 .Theansweris(B).
PolygonsPolygonsaretwo-dimensionalfigureswiththreeormorestraightsides.Trianglesandrectanglesarebothpolygons.Soarefigureswithfive,six,seven,eight,oranygreaternumberofsides.Themostimportantfacttoknowaboutpolygonsisthatanyoneofthemcanbedividedintotriangles.Thismeansthatyoucanalwaysdeterminethesumofthemeasuresoftheinterioranglesofanypolygon.
For example, the sumof the interior angles of any four-sided polygon (called aquadrilateral) is 360degrees.Why?Becauseanyquadrilateralcanbedividedintotwotriangles,andatrianglecontains180degrees.Lookatthefollowingexample:
Inthispolygon,a+b+c=180degrees;sodoesd+e+f.Thatmeansthatthesumoftheinterioranglesofthequadrilateralmustbe360degrees(a+b+c+d+e+f).
Aparallelogram is a quadrilateralwhose opposite sides are parallel. In the following parallelogram,sideABisparalleltosideDC,andADisparalleltoBC.Becauseaparallelogramismadeoftwosetsofparallellinesthatintersecteachother,weknowthatthetwobiganglesareequal,thetwosmallanglesareequal,andabigangleplusasmallangleequals180degrees.Inthefigurebelow,biganglesAandCareequal,andsmallanglesBandDareequal.Also,becauseAisabigangleandDisasmallangle,A+D=180degrees.
NeedtheFormula?Youmayhavelearnedthe
formulaforthisinmathclass.Ifso,youcanuse
it:Thesumofthedegreesinann-sidedpolygonis
180(n−2).Ifyoudon’tknowtheformula,don’t
worryaboutmemorizingit.Itdoesn’tcomeupmuch,
andwhenitdoescomeup,youcanalwaysbreakupthepolygonintotriangles.
Let’stryanexample.
12.
Note:Figurenotdrawntoscale.
InparallelogramABCDabove,AC=3andAD=5.WhatistheareaofABCD?A) 12B) 15C) 18D) 20
Here’sHowtoCrackItThetrickistonoticethatthisparallelogramisactuallymadeoftwoequaltriangles.Byfindingtheareaofthetriangles,youcanfindtheareaoftheparallelogram.Thetrianglesarebothrighttriangles,andthetwosidesgiven in thefigurefollowthe3-4-5pattern. Ifyou lookat triangleACDwithACas thebase, thebaseis3andtheheightis4.Nowusetheformulaforareaofatriangle:
A= ×3×4=6
Thatmeanstheparallelogramis2×6=12.
Also,ifyouestimatethearea,thebaseis5andtheheightislessthan3,sotheareaislessthan15.Theonlyanswerlessthan15is(A).
VolumeVolumequestionsontheSATcanseemintimidatingattimes.Thetestwriterslovetogiveyouquestionsfeaturingunusualshapessuchaspyramidsandspheres.Luckily,atthebeginningoftheMathsections(andthebeginningof thischapter),you’regivenaboxwithall the formulasyouwilleverneed forvolumequestionsontheSAT.SimplyapplytheBasicApproachforgeometryusingthegivenformulasandyou’llbeingoodshape(punentirelyintended)!
Let’slookatanexample.
15. Aspherehasavolumeof36π.Whatisthesurfaceareaofthesphere?(ThesurfaceareaofasphereisgivenbytheformulaA=4πr2.)A) 3πB) 9πC) 27πD) 36π
Here’sHowtoCrackIt
Startbywritingdowntheformulaforvolumeofaspherefromthebeginningofthechapter:V= πr3.Put
whatyouknowintotheequation:36π= πr3.Fromthisyoucansolveforr.Dividebothsidesbyπtoget
36= r3.Multiplybothsidesby3toclearthefraction:36(3)=4r3.Noteweleft36as36,becausethe
nextstepistodividebothsidesby4,and36dividedby4is9,so9(3)=r3or27=r3.Takethecuberoot
ofbothsidestogetr=3.Nowthatyouhavetheradius,usetheformulaprovidedtofindthesurfacearea:
A=4π(3)2,whichcomesoutto36π,whichis(D).
BallparkingYoumaybethinking,“Waitasecond,isn’tthereaneasierway?”Bynow,youshouldknowthatofcoursethereis,andwe’regoingtoshowyou.OnmanySATgeometryproblems,youwon’thavetocalculateanexactanswer.Instead,youcanestimateananswerchoice.WecallthisBallparking,astrategymentionedearlierinthisbook.
Ballparking is extremely useful on SAT geometry problems. At the very least, it will help you avoidcareless mistakes by immediately eliminating answers that could not possibly be correct. In manyproblems,Ballparkingwillallowyoutofindtheanswerwithoutevenworkingouttheproblematall.
RocketScience?TheSATisacollege
admissionstest,notanexerciseinprecision.
Because45ofits58Mathquestionsaremultiple-choice,
youcanaffordtoapproximatenumberslikeπ, ,and (3+,1.4,and1.7+,respectively).
For example, onmanySATgeometry problems, youwill be presentedwith a drawing inwhich someinformationisgivenandyouwillbeaskedtofindsomeoftheinformationthatismissing.Inmostsuchproblems,you’reexpected toapplysomeformulaorperformsomecalculation,oftenanalgebraicone.Butyou’llalmostalwaysbebetteroffifyoulookatthedrawingandmakearoughestimateoftheanswer(basedonthegiveninformation)beforeyoutrytoworkitout.
Thebasicprinciplesyoujustlearned(suchasthenumberofdegreesinatriangleandthefactthatπ≈3)will be enormously helpful to you inBallparking on the SAT.You should also know the approximatevaluesofseveralcommonsquareroots.Besuretomemorizethembeforemovingon.Knowingthemcoldwillhelpyousolveproblemsandsavetime,especiallywhencalculatoruseisnotallowed.
SquareRoots
=1
≈1.4
≈1.7+
=2
HappyHolidays!February14(2/14)isValentine’sDay,so
=1.4.March17(3/17)is
St.Patrick’sDay,so=1.7.
Youwillalsofinditveryhelpfulifyouhaveagoodsenseofhowlargecertaincommonanglesare.Studythefollowingexamples.
HowHighIstheCeiling?If your friend stoodnext to awall in your living roomand askedyouhowhigh the ceilingwas,whatwouldyoudo?Wouldyougetoutyourtrigonometrytextbookandtrytotriangulateusingtheshadowcastbyyourpal?Ofcoursenot.You’dlookatyourfriendandthinksomethinglikethis:“Dave’sabout6feettall.Theceiling’sacoupleoffeethigherthanheis.Itmustbeabout8feethigh.”
YourBallparkanswerwouldn’tbeexact,butitwouldbeclose.Ifsomeonelaterclaimedthattheceilinginthelivingroomwas15feethigh,you’dbeabletotellherwithconfidencethatshewasmistaken.
You’llbeabletodothesamethingontheSAT.Everygeometryfigureonyourtestwillbedrawnexactlyto scale unless there is a note in that problem telling you otherwise. That means you can trust theproportionsinthedrawing.IflinesegmentAhasalengthof2andlinesegmentBisexactlyhalfaslong,thenthelengthoflinesegmentBis1.AllsuchproblemsareidealforBallparking.
TheCorrectChoiceRememberthattheSAT
isamultiple-choicetest.Thismeansthat
youdon’talwayshavetocomeupwithananswer;
youjusthavetoidentifythecorrectonefromamongthefour
choicesprovided.
20. ThebaseoftriangleTis40percentlessthanthelengthofrectangleR.TheheightoftriangleTis50percentgreaterthanthewidthofrectangleR.TheareaoftriangleTiswhatpercentoftheareaofrectangleR?
PluggingInAsyoulearnedalready,PluggingInisapowerfultechniqueforsolvingSATalgebraproblems.Itisalsoveryusefulongeometryproblems.Forsomequestions,youwillbeable toplug inballparkvaluesformissinginformationandthenusetheresultseithertofindtheanswerdirectlyortoeliminateanswersthatcannotpossiblybecorrect.
Here’sanexample:
A) 10B) 45C) 90D) 110
Here’sHowtoCrackItThisisareallyhardproblem.Don’tworry—you’llstillbeabletofindtherightanswerbysketchingandpluggingin.
WhenPluggingIn,alwaysusenumbersthatareeasytoworkwith.Saythelengthoftherectangleis10;thatmeansthatthebaseofthetriangle,whichis40percentsmaller,is6.Ifyouplug4inforthewidthofrectangleR,theheightoftriangleTis6.Youshouldcomeupwithtwosketchesthatlooklikethis:
Thasanareaof bh,or18.Rhasanareaof40.Nowsetup the translation:18= (40),wherex
representswhatpercentthetriangleisoftherectangle.
Solveforxandyouget45.Thecorrectansweris(B).
GeometryDrill1:NoCalculatorSectionWorktheseGeometryquestionswithoutyourcalculator.Answersandexplanationscanbefoundonthispage.
2.
Inthefigureabove,circleOhasaradiusof8,andangleXOYmeasures πradians.What
isthemeasureofminorarcXY?
A) π
B) π
C) 5π
D) 16π
3.
Whatisthevalueoftan XZY?
A)
B)
C)
D)
10.
Inthefigureabove,sina=x.Whatisthevalueofcosb?A) x
B)
C) |1−x|
D)
15.
Note:Figurenotdrawntoscale.
ThecircleabovewithcenterAhasanareaof21.BCistangenttothecirclewithcenterAatpointB.IfAC=2AB,thenwhatistheareaoftheshadedregion?A) 3.5B) 15.75C) 17.5D) 21
GeometryDrill2:Calculator-PermittedSectionCalculatoruseisallowedonthesequestions,souseittothebestofyourability,butbesuretosetuptheproblemsonpaperfirst.Answersandexplanationscanbefoundonthispage.
1. Ifarectangularswimmingpoolhasavolumeof16,500cubicfeet,auniformdepthof10feet,andalengthof75feet,whatisthewidthofthepool,infeet?A) 22B) 26C) 32D) 110
8.
Inthefigureabove,whatisthelengthofBD?A) 8B) 9C) 12D) 15
12.
Martinwantstoknowhowtallacertainflagpoleis.Martinwalks10metersfromtheflagpole,liesontheground,andmeasuresanangleof70°fromthegroundtothebaseoftheballatthetopoftheflagpole.Approximatelyhowtallistheflagpolefromthegroundtothebaseoftheballatthetopoftheflagpole?A) 3mB) 9mC) 27mD) 29m
26.
ΔABCisequilateraland AEFisarightangle.DandFarethemidpointsofABandAC,respectively.Whatisthevalueofw?A) 1B)
C) 2D) 2
29. Atoypyramid(notshown)ismadefrompoly(methylmethacrylate),betterknownbyitstradetermLucite.Thetoypyramidhasaregularhexagonalbaseof15cm2andaheightof4cm.Inthebaseofthepyramid,thereisasemisphericalindentation2cmindiameter.Ifthepyramidweighs21.129g,thenwhatisthedensityofLucite?(Densityequalsmassdividedbyvolume.)A) 1.06g/cm3
B) 1.18g/cm3
C) 2.09g/cm3
D) 6.51g/cm3
CHAPTERDRILLANSWERSANDEXPLANATIONS
GeometryDrill1:NoCalculatorSection2. B Becausethequestionwantsarclengthandgivesyouthemeasureofthecentralangleinradians,
youcanusetheformulas=rθtofindthearclength:s=(8)( π)= π,whichreducesto π,
whichis(B).
3. C Tangentisdefinedas .ThesideoppositeangleXZYis7,andthesideadjacenttothis
angleis8,sothetangentof XZY= ,whichis(C).
10. A YoucanPlug Inwhenyou’redealingwithageometryproblemwithunknowns.Whenyou’re
PluggingInforaright triangle,useoneof thespecialright triangles tomakeyour lifeeasier.
Use a 3-4-5 right triangle. Make the side opposite a 3, the side adjacent to a 4, and the
hypotenuse5.Becausesineis ,sina= ,sox= .Cosineis ,socosb=
.Thisisyourtarget;circleit.Makex= ineachanswerchoiceandlookfortheanswerwhich
equals .Only(A)works.
15. C ThetrickistorecognizethatDABCisa30°-60°-90°righttriangle. ABCmustequal90°since
a tangent linemustbeperpendicular to the radiusofacircledrawn to thepointof tangency.
Onlya30°-60°-90°hasahypotenuse(AC)equaltodoublethelengthofoneofthesides(AB).
(YoucanalsousethePythagoreanTheoremtoshowthis.)Thismeansthat BAC=60°,sothe
shaded region has a central angle measure of 360° − 60° = 300°. To get the area, use the
proportion Reduce,cross-multiply,andsolvetogets=
17.5.Thismatches(C).
GeometryDrill2:Calculator-PermittedSection
1. A Forthisquestion,youneedtoknowthatvolumeequalslength×width×height.Youknowthatthevolumeis16,500,thedepth(orheight)is10,andthelengthis75.Justputthosenumbersin
theformula:16,500=75×w×10.Useyourcalculatortosolveforw,whichequals22.Choice(A)iscorrect.
8. C The 5 equal lengths that make up the two sides of the largest triangle tell you that you aredealingwith5similartriangles.Thelargesttrianglehassides15:25:30,andthesidesofall5triangleswill have an equivalent ratio.Reduced, the ratio is 3:5:6,whichhappens tobe thedimensionsof thesmallest triangle.Youwant to find the lengthofBD, thebaseofa trianglewithsidesof6and10.Thisistwiceasbigasthesmallesttriangle,sothebaseBDmustbe6×2=12,whichis(C).
12. C UseSOHCAHTOAandyourcalculatortofindtheheightoftheflagpole.Fromthe70°angle,
youknowtheadjacentsideofthetriangle,andyouwanttofindtheoppositeside,soyouneed
tousetangent.Tangent= ,sotan70°= ,wherexistheheightoftheflagpoleupto
theball.Isolatexbymultiplyingbothsidesby10:10tan70°=x.Useyourcalculatortofind
that10tan70°=27.47,whichisclosestto(C).
26. D Don’tforget thatyoucanpluginnumbersongeometryquestions.Makeb=70°anda=30°.Therefore, the thirdangle in the triangle is80°.Youknow thatcwouldbe80°because it isoppositean80°angle.Yourtargetanswerisa=30°,soplugin80°and70°tofindit.Theonlypossibleansweris(D).
28. B There’sa lotgoingoninthisproblem!UseBite-SizedPiecesandstartfillingininformation.First,theproblemsaysisthattriangleABCisequilateral.Mark60degreeanglesonthefigure.Next, you see that angle AEF is a right angle. Write that in as well. The problem alsoconvenientlytellsyouthatDandFarethemidpointsofABandAC,respectively.Therefore,ADandAFare2.Finally,thelastpieceofinformationrevealsthatEisthemidpointofDF;markDEandEFasequal.
Now,whatdoyouhave?TriangleAEFisarighttriangle,withahypotenuseof2andalegof1.Hmm,perhapsthegoodol’PythagoreanTheoremcanhelp.Plugthenumbersintotheformula,andyou’llfindthattheansweris(B).
You may have also noticed that triangle ADE is a 30°-60°-90° triangle with hypotenuse 2,whichmeansthatDEis1andw,oppositethe60°,isthesquarerootof3.IngeometryquestionsontheSAT,therewilloftenbemultiplewaystogettotheanswer.Onthedayofthetest,usewhichevermethodyouaremostcomfortablewith.
29. B Work the problem in steps. You are given themass, so to find density you need to find the
volumeofthepyramid.Theformulaatthebeginningofthesectiontellsyouthat,forapyramid,
V= Bh,whereB is the areaof thebaseof thepyramid andh is the height.Therefore, the
volume of the pyramid is (15)(4) = 20. However, you need to subtract the volume of the
semisphericalindentationinthebase.Onceagain,thereferencetablefoundatthebeginningof
eachMathTestsectiontellsyouthatthevolumeofasphereisgivenbytheequationV= πr3.
Becausethediameteroftheindentationis2cm,theradiusofthehemisphereis1cm.Ifitwere
awholesphere,thevolumeoftheindentationwouldbe π(1)3=4.189;youwantonlyhalf,so
dividingby2givesyou2.094cm3forthehemisphere.Subtracting2.094cm3fromthe20cm3of
thepyramidgivesyoua totalvolumeof20−2.094=17.906cm3. Finally, you can find the
densityofLucitebyusingthedefinitionofdensity:Density= ≈1.18g/cm3,which
is(B).
Summary◦ Degreesandangles
• Acirclecontains360degrees.• Whenyouthinkaboutangles,remembercircles.• Alineisa180-degreeangle.• Whentwolinesintersect,fouranglesareformed;thesumoftheirmeasuresis360degrees.• Whentwoparallellinesarecutbyathirdline,thesmallanglesareequal,thebiganglesare
equal,andthesumofabigangleandasmallangleis180degrees.
◦ Triangles• Everytrianglecontains180degrees.• Anisoscelestriangleisoneinwhichtwoofthesidesareequalinlength,andthetwoangles
oppositetheequalsidesareequalinmeasure.• Anequilateraltriangleisoneinwhichallthreesidesareequalinlength,andallthreeangles
areequalinmeasure(60degrees).
• Theareaofatriangleis bh.
• Theheightmustformarightanglewiththebase.• ThePythagoreanTheoremstatesthatinarighttriangle,thesquareofthehypotenuseequalsthe
sumofthesquaresofthetwolegs.Rememberthetestwriters’favoritePythagoreantriplets(3-4-5and5-12-13).
• Remembertheotherspecialrighttriangles:45°-45°-90°and30°-60°-90°.• Similartriangleshavethesameanglesandtheirlengthsareinproportion.
• Fortrigonometryquestions,rememberSOHCAHTOA:
• sin=
• cos=
• tan=
◦ Circles• The circumferenceof a circle is 2πr or πd,where r is the radius of the circle andd is the
diameter.• Theareaofacircleisπr2,whereristheradiusofthecircle.• Atangenttouchesacircleatonepoint;anyradiusthattouchesthattangentformsa90-degree
angle.
• Arcsareproportionaltothecircumferencebasedonthecentralangle: = .
• Sectorsareproportionaltotheareabasedonthecentralangle: = .
• Ifthecentralangleisgiveninradians,themeasureofthearcisgivenbys=rθ.
◦ Rectanglesandsquares• Theperimeterofarectangleisthesumofthelengthsofitssides.• Theareaofarectangleislength×width.• Asquareisarectanglewhosefoursidesareallequalinlength.• Anypolygoncanbedividedintotriangles.• Thevolumeof a rectangular solid is length ×width ×height. The formulas to compute the
volumesofotherthree-dimensionalfiguresaresuppliedintheinstructionsatthefrontofbothMathsections.
◦ WhenyouencounterageometryproblemontheSAT,Ballparktheanswerbeforetryingtoworkitout.
◦ Youmustbefamiliarwiththesizeofcertaincommonangles.
◦ MostSATgeometrydiagramsaredrawntoscale.Useyoureyesbeforeyouuseyourpencil.Trytoeliminateimpossibleanswers.
◦ Whenadiagramisnotdrawntoscale,redrawit.
◦ Whennodiagramisprovided,makeyourown;whenaprovideddiagramisincomplete,completeit.
◦ Wheninformationismissingfromadiagram,BallparkandPlugIn.
Chapter17Grid-InsOn theSAT, 13 of the 58Math questionswill require you to produce your own answer.Although theformatofthesequestionsisdifferentfromthatofthemultiple-choicequestions,themathematicalconceptstestedaren’tallthatdifferent.Inthischapter,wewillshowyouhowtoapplywhatyouhavelearnedinthepreviouschapterstothesenewquestions.
WHATISAGRID-IN?Bothof theMathsectionson theSATwillcontainagroupofproblemswithoutanswerchoices.Therewillbe5oftheseintheNoCalculatorsectionand8intheCalculatorsection.ETSandtheCollegeBoardcalltheseproblems“student-producedresponses.”WecallthemGrid-Insbecauseyouhavetomarkyouranswersonagridprintedonyouranswersheet.Thegridlookslikethis:
Despite their format, Grid-Ins are just like any other Math questions on the SAT, and many of thetechniquesthatyou’velearnedsofarstillapply.YoucanstillusePluggingInandothergreattechniques,suchastheRatioBoxandAveragePie.Yourcalculatorwillstillhelpyououtonmanyoftheseproblemsaswell.So,Grid-Insarenothingtobescaredof.Infact,manyofthesearesimplyregularSATmultiple-choicemathproblemswith the answer choices loppedoff, soyouhave to arrive at your answer fromscratchratherthanchoosefromfourpossibilities.
Youwillneed tobeextracarefulwhenansweringGrid-Inquestions,however,because thegridformatincreases the likelihood of careless errors. It is vitally important that you understand how theGrid-Informatworksbeforeyou take the test. Inparticular, you’ll need tomemorizeETS’s rules aboutwhichkindsofanswersreceivecreditandthosethatdonot.Theinstructionsmaylookcomplicated,butwe’veboiledthemdowntoafewrulesforyoutomemorizeandpractice.
Beforewegetintospecifics,herearesomebasicrulesaboutGrid-Instokeepinmind.
OrderofDifficulty:Grid-Ins
Aswiththemultiple-choicequestions,Grid-Ins
willbeinalooseorderofdifficulty.
• MostanswersforGrid-Insareintegers.Takealookatthegridagain.Becauseofthewayit’sarranged,onlycertaintypesofproblemscanbeusedforGrid-Ins.Forexample,you’llneverseevariablesinyouranswer(thoughtherecanbevariablesinthequestion)becausethegridscanaccommodateonlynumbers.Youwillalsoneverhaveaπ,squareroot,ornegativenumberinyouranswer.
• Yourcalculatorcanhelpyou—ifyouuseitcarefully.Thismeansthatyourcalculatorwillbeusefulonseveralquestions.Asalways,becarefultosetuptheproblemonpaperbeforeyou(carefully)punchthenumbersintoyourcalculator.Becauseyouhavetowriteintheansweronthegridyourself,youneedtobemorecarefulthanevertoavoidcarelessmistakes.
• Beaggressive.Justaswiththemultiple-choicequestions,thereisnopenaltyforwronganswersontheGrid-Ins.Anincorrectanswerononeofthesequestionsisnoworseforyourscorethanaquestionleftblank.And,bythesametoken,ablankisjustascostlyasanerror.Therefore,youshouldbeveryaggressiveinansweringthesequestions.Don’tleaveaquestionblankjustbecauseyou’reworriedthattheansweryou’vefoundmaynotbecorrect.ETS’sscoringcomputerstreatincorrectanswersandblankslikethey’reexactlythesame.Ifyouhavearrivedatananswer,youhaveashotatearningpoints;andifyouhaveashotatearningpoints,youshouldtakeit.We’renotsayingyoushouldguessblindly.Butifyouworkaproblemandareunsureofyouranswer,enteritanyway.Thereisnopenaltyforgettingitwrong.
TakeaGuessJustlikethemultiple-choice
questions,thereisnopenaltyforwronganswersontheGrid-In
questions.
THEINSTRUCTIONSHerearetheinstructionsfortheGrid-InsectionastheywillappearintheNoCalculatorsectionoftheMathTest.TheinstructionsfortheCalculatorsectionwilllookjustlikethis,excepttheywillstart“Forquestions31–38…”
WhattheInstructionsMeanOfalltheinstructionsontheSAT,thesearethemostimportanttounderstandthoroughlybeforeyoutakethe test.Pity theunpreparedstudentwho takes theSATcoldandspends10minutesofpotentialpoint-scoring time readingandpuzzlingover theconfusing instructions.We’ve translated theseunnecessarilycomplicatedinstructionsintoafewimportantrules.Makesureyouknowthemallwell.
WatchOutNegatives,π,and%
cannotbegriddedin!ForaGrid-Inquestioninvolving%or$,theSATwilltellyoutoignorethe%or$
symbol.Butnegativenumbers,non-integer
squareroots,andπcan’tbegriddedin,sothey’llneverbeananswerfor
thistypeofproblem.
FillIntheBoxesAlwayswriteyouranswer in theboxesat the topof thegridbeforeyoudarken theovalsbelow.Yourwrittenanswerswon’taffectthescoringofyourtest;ifyouwritethecorrectanswerintheboxesandgridinthewrongovals,youwon’tgetcreditforyouranswer(andyouwon’tbeabletoappealtoETSandtheCollegeBoard).However,writingintheanswersfirstmakesyoulesslikelytomakeanerrorwhenyougridin,anditalsomakesiteasiertocheckyourwork.
FillIntheOvalsCorrectlyAswejustpointedout,youreceivenocreditforwritingintheansweratthetopofthegrid.Thescoringcomputercaresonlywhethertheovalsarefilledincorrectly.Foreverynumberyouwriteintothegrid,makesurethatyoufillinthecorrespondingoval.
StaytotheLeftAlthoughyou’llreceivecreditnomatterwhereyouputyouransweronthegrid,youshouldalwaysbeginwritingyouranswerinthefarleftcolumnofthegrid.Thisensuresthatyouwillhaveenoughspaceforlonger answers when necessary. You’ll also cut down on careless errors if you always grid in youranswersthesameway.
KeepLeftNomatterhowmany
digitsareinyouranswer,alwaysstartgriddingin
theleft-mostcolumn.Thatway,you’llavoidomittingdigitsandlosingpoints.
FRACTIONSORDECIMALS:YOURCHOICEYoucangridinananswerineitherfractionordecimalform.Forexample,ifyouranswertoaquestionis
,youcaneithergridin or.5.Itdoesn’tmattertoETSbecause equals.5;thecomputerwillcredit
either form of the answer. That means you actually have a choice. If you like fractions, grid in your
answers in fraction form. Ifyou likedecimals,youcangrid in thedecimal. Ifyouhavea fraction that
doesn’tfitinthegrid,youcansimplyconvertittoadecimalonyourcalculatororonpaperandgridin
thedecimal.
Here’s thebottomline:Whengriddinginfractionsordecimals,usewhicheverformiseasierandleastlikelytocausecarelessmistakes.
DecimalPlacesandRoundingWhenyouhaveadecimalanswerofavaluelessthan1,suchas .45or .678,manyteachersaskyoutowriteazerobeforethedecimalpoint(forexample,0.45or0.678).OnGrid-Inquestions,however,ETSdoesn’twantyou toworry about the zero. In fact, there is no0 in the first columnof thegrid. If youranswer is a decimal less than 1, just write the decimal point in the first column of the grid and thencontinuefromthere.
LopWhydoextrawork?Afterall,itwon’tgive
youextrapoints.Ifyourdecimaldoesn’tfit
inthegrid,lopofftheextradigitsandgridin
whatdoesfit.
Youshouldalsonoticethatifyouputthedecimalpointinthefirstcolumnofthegrid,youhaveonlythreeplaceslefttowriteinnumbers.Butwhatifyourdecimalislongerthanthreeplaces,suchas.87689?Inthesecases,youwillgetcreditifyouroundoffthedecimalsothatitfitsinthegrid.Butyou’llalsogetcreditifyoujustenterasmuchofthedecimalaswillfit.
Forexample,ifyouhadtogridin.87689,youcouldjustwrite.876(whichisallthatwillfit)andthenstop.Youneedtogridinonlywhateverisnecessarytoreceivecreditforyouranswer.Don’tbotherwithextraunnecessarysteps.Youdon’thavetoroundoffdecimals,sodon’tbother.
If youhave a longor repeatingdecimal, however, be sure to fill up all the spaces in thegrid. If yourdecimalis.666666,youmustgridin.666.Justgriddingin.6or.66isnotgoodenough.
Note:Verylongdecimalanswersaresomewhatrare.Youranswershouldusuallybeintegersorsimplefractions.
ReducingFractionsIfyoudecidetogridinafraction,ETSdoesn’tcareifyoureducethefractionornot.Forexample,ifyour
answertoaproblemis ,youwillgetcreditifyougridin orreduceitto .Soifyouhavetogridina
fraction, and the fraction fits in the grid, don’t bother reducing it.Why give yourselfmorework (and
anotherchancetomakeacarelesserror)?
RelaxIfyouranswerisafraction
anditfitsinthegrid(fractionbarincluded),don’treduceit.Why
bother?Youwon’tgetanextrapoint.However,ifyourfractiondoesn’tfit,reduceitorturnitintoa
decimalonyourcalculator,dependingonthesection
you’reworkingon.
The only time youmight have to reduce a fraction is if it doesn’t fit in the grid. If your answer to a
questionis ,itwon’tfitinthegrid.Youhavetwooptions:Eitherreducethefractionto andgridthat
in,oruseyour calculator to convert the fraction to .6.Choosewhicheverprocessmakesyou themost
comfortablewhencalculatoruseisallowed,andmakesureyouknowhowtoreducefractionsfortheNo
Calculatorsection.
MixedNumbersThescoringcomputerfortheSATdoesnotrecognizemixednumbers.Ifyoutrytogridin2 bywriting
“21/2,” thecomputerwill read thisnumberas .Youhave toconvertmixednumbers to fractionsor
decimalsbeforeyougridthemin.Togridin2 ,eitherconvertitto oritsdecimalequivalent,whichis
2.5. If you have to convert a mixed number to grid it in, be very careful not to change its value
accidentally.
Don’tMixNevergridinamixed
number.Changeitintoatop-heavyfractionorits
decimalequivalent.
Don’tWorryThevastmajorityofGrid-Inanswerswillnotbedifficulttoenterinthegrid.Thetestwriterswon’ttrytotrickyoubypurposelywritingquestionsthatareconfusingtogridin.Justpayattentiontotheseguidelinesandwatchoutforcarelesserrors.
GRIDDINGIN:ATESTDRIVETogetafeelforthisformat,let’sworkthroughtwoexamples.Asyouwillsee,Grid-InproblemsarejustregularSATMathproblems.
16. Ifa+2=6andb+3=21,whatisthevalueof ?
Here’sHowtoCrackItYouneedtosolvethefirstequationforaandthesecondequationforb.Startwiththefirstequation,andsolvefora.Bysubtracting2frombothsidesoftheequation,youshouldseethata=4.
Now move to the second equation, and solve for b. By subtracting 3 from both sides of the secondequation,youshouldseethatb=18.
Thequestionaskedyoutofindthevalueof .That’seasy.Thevalueofbis18,andthevalueofais4.
Therefore,thevalueof is .
That’sanugly-lookingfraction.Howintheworlddoyougriditin?Askyourselfthisquestion:“Does
fit?”Yes!Gridin .
Yourmathteacherwouldn’tlikeit,butthescoringcomputerwill.Youshouldn’twastetimereducing
34. Fortypercentofthemembersofthesixth-gradeclassworewhitesocks.Twentypercentworeblacksocks.Iftwenty-fivepercentoftheremainingstudentsworegraysocks,whatpercentofthesixth-gradeclassworesocksthatwerenotwhite,black,orgray?(Disregardthe%whengriddingyouranswer.)
toaprettierfractionorconvertingittoadecimal.Spendthattimeonanotherprobleminstead.Thefewer
stepsyoutake,thelesslikelyyouwillbetomakeacarelessmistake.
Here’sanotherexample.Thisoneisquiteabitharder.
Here’sHowtoCrackItTheproblemdoesn’ttellyouhowmanystudentsareintheclass,soyoucanpluginanynumberyoulike.This isapercentageproblem,so theeasiestnumber toplug in is100.Fortypercentof100 is40; thatmeans40studentsworewhitesocks.Twentypercentof100is20.Thatmeansthat20studentsworeblacksocks.
Yournextpieceofinformationsaysthat25percentoftheremainingstudentsworegraysocks.Howmanystudents remain? Forty, because 60 students wore either white or black socks, and 100 − 60 = 40.Therefore,25percentofthese40—10students—woregraysocks.
Howmanystudentsareleft?30.Therefore,thepercentageofstudentsnotwearingwhite,black,orgraysocksis30outof100,or30percent.Griditin,andremembertoforgetaboutthepercentsign.
36. Grow-Uppottingsoilismadefromonlypeatmossandcompostinaratioof3poundsofpeatmossto5poundsofcompost.IfabagofGrow-Uppottingsoilcontains12poundsofpottingsoil,howmanypoundsofpeatmossdoesitcontain?
ORDEROFDIFFICULTYLikeallotherquestionsontheMathTest,Grid-Inproblemsarearrangedina looseorderofdifficulty.Sincethisorderisnotstrict,however, it ismuchmoreimportanttopayattentiontoyourownstrengthsandweaknesses.Remembertofocusonthequestionsyouknowhowtoanswerfirst.Don’tspendtimeonquestionsthatyouhavenoideahowtowork.
Keepinmind,ofcourse,thatmanyofthemathtechniquesthatyou’velearnedarestillveryeffectiveonGrid-Inquestions.PluggingInworkedverywellonthepreviousquestion.Ifyou’reabletopluginortakeaneducatedguess,goaheadandgridinthatanswer.Again,thereisnopenaltyforgettingitwrong.
Here’s another difficult Grid-In question that you can answer effectively by using a technique you’velearnedbefore.
Here’sHowtoCrackItTosolvethisproblem,setupaRatioBox.
Whatdoyoumultiplyby8toget12?Ifyoudon’tknow,divide12by8onyourcalculator.Theansweris1.5.Write1.5ineachoftheboxesontheMultiplyByrowofyourRatioBox.
Theproblemasksyouhowmanypoundsofpeatmossareinabag.Tofindout,multiplythenumbersinthePeatMosscolumn.Thatis,multiply3×1.5,andyouget4.5.
Griditinlikethis:
CarelessMistakesOnGrid-Inquestions,youobviouslycan’tuseProcessofEliminationtogetridofbadanswerchoices,and techniques like Plugging In the Answers won’t work either. In order to earn points on Grid-Inquestions,you’regoing tohave to find theansweryourself, aswell asbe extremelycarefulwhenyouenteryouranswersontheanswersheet.Ifyouneedto,double-checkyourworktomakesureyouhavesolvedcorrectly.Ifyoususpectthatthequestionisadifficultoneandyougetananswertooeasily,youmayhavemadeacarelessmistakeorfallenintoatrap.
RANGEOFANSWERSSomeGrid-Inproblemswillhavemanypossiblecorrectanswers.Itwon’tmatterwhichcorrectansweryouchoose,aslongastheoneyouchoosereallyiscorrect.
Here’sanexample.
17. If4<3x+2<5,whatisonepossiblevalueofx?
MoreThanOneSomeGrid-Inquestionshaveseveralpossiblecorrectanswers.None
ismorecorrectthananyother,sogridinthefirst
oneyoufindandmoveon.
Here’sHowtoCrackItWithdoubleinequalitiesorequations,don’ttrytodotheentireproblematonce.It’smucheasiertosplitthisproblemintotwosmallerproblems:
4<3x+2and3x+2<5
Solveeachone.Forthefirstinequality,startbysubtracting2frombothsides,leaving2<3x.Divideby3,leaving(approximately)0.666<x.Fortheotherinequality,start,asbefore,bysubtracting2frombothsides,leaving3x<3.Divideby3togetx<1.Combiningbothinequalitiesbacktogether,you’llgetthatxisbetween0.666and1.
So,whatdoyouenterasyouranswer?Anythingbetween .666and1.Really.Anything. .8, .954, .667,.999,5/6,7/8,9/10,whatever.
EXTENDEDTHINKINGThelasttwoquestionsintheCalculatorsectionwillbeapairofGrid-InsthatETSandtheCollegeBoardrefertoasExtendedThinkingquestions.Itclaimsthatthesequestions,drawnfromreal-worldcontexts,willassessastudent’sabilitytoapply“complexcognitiveskills.”Don’tpanic,though.Asidefrombeingpaired and sometimesmore difficult, they are not any different than otherGrid-Ins.Many of the samestrategies will apply to the Extended Thinking questions. They can be drawn from pretty much anymathematicalcontent,fromproblemsolvingtofunctions,andtheyareonlyworthonepointeach.
ExtendedWhat?ThelasttwoGrid-Inswill
beapairofquestionsbasedonthesameinformation.
Theycancoveranyofthepreviousmathcontent,andtheyarestillworthjustonepointeach.
Useyourknowledgeofyourowntest-takingskillstodecidewhichoftheseyouwanttotry,ifyoudo
thematall.
Let’slookataset.
Questions37and38refertothefollowinginformation.
37. Ifthereactioninitiallystartswith2mol/LofspeciesA,andtheactivationenergyofthereactionis10,082J/mol,at310Kelvin,howmanysecondswillittakefortheconcentrationofAtoreach0.4mol/L?
38. Ifrateconstantktriplesforthereactiondescribedinquestion37,whatistheconcentrationofspeciesAafter50seconds,inmol/L?
k=Ce
r=k[A]2
=kt+
Thekineticsofachemicalreactioncanbedescribedbytheequationsabove,whereeisaconstantapproximatelyequalto2.718,kistherateconstantinL/mol-s,EaistheactivationenergyinJ/mol-K,TistemperatureinKelvin,risthereactionrateinmol/s,and[A]istheconcentrationofaspeciesinmols/L,eitherinitiallyas[A]0,oratagiventimeoftas[A]t.Cisaconstantequalto4,andRisaconstantof8.314J/mol.
Here’sHowtoCrackItAsyoucansee,inordertohaveachanceatsolvingquestion38,youfirstmustsolvequestion37.Inmostcases,thetwoExtendedThinkingquestionswillbemoreindependentofeachother.Inthatcase,ifoneiseasier than theother,maybe try thatoneandskip theotherone.Only ifyouareaimingfora topscoreshouldyouattemptbothExtendedThinkingquestions.
TacklingExtendedThinkingQuestions
MostExtendedThinkingquestionscanbesolved
independentofoneanother,andoneisoften
easierthantheother.Considerdoingthemorestraightforwardoneand
skippingthemoredifficult
ortime-consumingone.
Startwithquestion37.Therearethreeequations,soitishardtoknowwheretobegin.Startbywriting
downthevaluesforthevariablesyouknow.Thequestiontellsyouthat[A]0=2and[A]t=0.4.Youwant
tofindthetime,t,soplugthesevaluesintothelastequationtoget =kt+ .Simplifythisequationto
get2.5=kt+0.5,andkt=2.Tosolvefort,youfirstneedtofigureoutthevalueofk.Youneedtousethe
first equation to find the value of k, since the value of r in the second equation is never defined.
According to thequestion,C andR are constants,whereC = 4 andR = 8.314.Also according to the
question,Ea=10,082,andT=310.Plugallofthesevaluesintothefirstequationtogetk=4 .
Simplifytheexponent togetk=4e−3.9118.Useyourcalculatortofindthatk=4(0.02)=0.08.Plug this
valueintotheearlierequationkt=2toget0.08t=2,andt=25.Thecorrectansweris25.Griditin!
Notice how the second equation was completely useless in solving this problem. That will happenoccasionallyontheSAT,sodon’tgetdistractedbytheextraneousinformation.
Nowthatyouhavethevalueofrateconstantk,crackquestion38.Inquestion37,k=0.08,soifktriples,
the new value for k is 0.08 × 3 = 0.24. According to the information in question 37, [A]0 = 2, and
accordingtoquestion38,t=50.Plugallofthesevaluesintothelastequation,whichhas[A]tinit,toget
=(0.24)(50)+ .Simplifytherightsideoftheequationtoget =12.5.Multiplybothsidesby[A]t
toget1=12.5[A]t.Finally,dividebothsidesby12.5toget0.08=[A]t.Thecorrectansweris0.08.
Grid-InDrill1:NoCalculatorSectionWorktheseGrid-Inswithoutyourcalculator.Answersandexplanationscanbefoundonthispage.
16. Ifab=4,and3b=2,whatisthevalueofa?
17. If4x+2y=24and =7,whatisthevalueofx?
Grid-InDrill2:Calculator-PermittedSectionWork these Grid-Ins using your calculator as needed and applying the skills you’ve learned so far.Answersandexplanationscanbefoundonthispage.
32.
n=12×2
Thenumberofmiceinacertaincolonyisshownbytheformulaabove,suchthatnisthenumberofmiceandtisthetime,inmonths,sincethestartofthecolony.If2yearshavepassedsincethestartofthecolony,howmanymicedoesthecolonycontainnow?
33.
Inthefigureabove,ifdisparalleltoe,whatisthevalueofy?
35. IfAlexandrapays$56.65foratable,andthisamountincludesataxof3%onthepriceofthetable,whatistheamount,indollars,thatshepaysintax?(Disregardthedollarsignwhengriddingyouranswer.)
36.
Inthefigureabove,ABisthearcofthecirclewithcenterO.PointAliesonthegraphofy=x2−b,wherebisaconstant.IftheareaofshadedregionAOBisπ,thenwhatisthevalueofb?
Questions37and38refertothefollowinginformation.
Agarden,measuring10feetby12feet,containsindividualplotsthatmeasure1footby1foot.30%oftheplotscontainbellpeppers,30%containcherrytomatoes,25%containsquash,andtheremaining15%containeggplants.Eachbellpepperplotproduces2bellpeppersevery5days,atomatoplotproduces4cherrytomatoesevery6days,asquashplotproduces1squashevery15days,andaneggplantplotproduces3eggplantsevery10days.
37. Ina30-daymonth,howmanyvegetablesareproducedbythe10×12footgarden?
38. Anunusuallywarmandwetmonthcausesthemonthlyproductionofeggplantstodouble.Whatisthedailyaveragenumberofeggplantsproducedinthegardenduringa30-daymonthatthenewrate?
CHAPTERDRILLANSWERSANDEXPLANATIONS
Grid-InDrill1:NoCalculatorSection
16. 8 Using3b=2,solveforbbydividingbothsidesby3 togetb= .Thatmeansa = 4.
Fractionalexponentstellyoutousethedenominatorastherootandusethenumeratorasa
regularexponent.So, =4.First,cubebothsidestofinda2=43=64.Next, take the
squarerootofbothsidestofinda=8.
17. 3 Youcansolvethisquestionusingsimultaneousequationsbecauseyouhavetwoequations
withtwovariables.First,youneedtorearrangetheequationsabit:4x+2y=24divided
by2onbothsidesbecomes2x+y=12. ,=7multipliedby2xonbothsides,becomes
7y=14x.This,dividedby7onbothsides,becomesy=2x,whichcanbemanipulatedinto
2x−y=0.Nowyoucanaddtheequations:
Therefore,x=3.
18. 9 Factorthenumeratorandthedenominatorinto =4.The(x−2)cancelsoutof
thetopandbottomtoleave =4.Multiplybothsidesby(x−6)togetx+3=4x−24.
Subtractxfrombothsides:3=3x−24.Add24tobothsides:27=3x.Divideby3togetx
=9.
19. 9 Thislookssuspiciouslylikeaquadraticequation,andifyoumultiplyitout,itsequivalentis
b2−a2.Youwanttomakethisaslargeaspossible,soyouwantb2tobelargeanda2tobe
small.Ifb=−3,b2=9;ifa=0,a2=0.Sob2−a2canbeaslargeas9.
Grid-InDrill2:Calculator-PermittedSection32.3,072
Becausethetinn=12× represents thenumberofmonths,youcannotuse the2-year
timeframegiveninthequestioninplaceoft.Thecolonyhasbeengrowingfor24months,
whichisevenlydivisiblebythe3inthefractionalexponent.Theequationismucheasier
nowthatthefractionalexponentisgone.n=12× =12×28=12×256=3,072.
33. 148 Alinecrossingtwoparallel linescreatesbiganglesandsmallangles.Thebigangle thatmatchesyissplitbyalineperpendiculartodande.Thebigangleis58+90=148,whichisalsothevaluefory.Anotherwaytosolvethisistofindthethirdangleofthetriangle:180−90−58=32.The32°angleandthey°anglemakeupastraightline,so180−32=148.
35. 1.65 Thebestwaytoapproachthisproblemistosetupanequation.Thereissomepricesuchthatifyouadd3%ofthepricetothepriceitself,youget$56.65.Thismeansthatyoucansetupanequation:x+3%ofx=56.65,orx+0.03x=56.65.Nowyoucanjustsolveforx,and you get the original price, whichwas $55. Subtract this from $56.65 to get the tax$1.65.
36. 4 This question looks tough, sowork it one step at a time, and startwithwhat you know.SectorAOBisaquarter-circle(itcoversanangleof90outof360degrees),somultiplyingitsarea(π)by4givesyoutheareaofthewholecircle(4π).Pluggingthisintotheequationfortheareaofacircle,A=πr2,givesyou4π=πr2,andtheradiusmustbeapositivevalue,sor=2.ThismeansthatthecoordinatesofpointAmustbe(−2,0).BecauseAisonboththecircleandtheparabola,youcanplugitsx-andy-coordinatesintothegivenequationoftheparabola,y=x2−b.Thisbecomes0=(−2)2−b,sob=4.
37. 1,374
First,calculatethenumberofplotsinthegarden.Giventhatthegardenmeasures10feetby12 feet and each plot is one foot by one foot, there are 10× 12= 120 total plots.Nextcalculatethenumberofeachtypeofvegetableplotasfollows:
120×0.3=36bellpepperplots
120×0.3=36cherrytomatoplots
120×0.25=30squashplots
120×0.15=18eggplantplots
Accordingtothequestion,2bellpeppersaregrownevery5daysoneachofthe36pepperplots.Thatmeansthatallthepepperplotstogethergrow2×36=72peppersin5days.Todeterminehowmanypepperswouldgrowinamonth,setupaproportion.
Cross-multiply,andthendivideby5tofindthatthegardenproduces432peppersforthemonth.Repeat these stepswith theother3vegetables.The36 tomatoplotsproduce144tomatoesevery6days.Together, theyproduce720 tomatoes in themonth.The30squashplotsproduce30squashevery15days,foratotalof60squashinamonth.Finally,the18eggplantplotsgrow54eggplantsevery10days,whichmeansduringa30-dayperiodthegardenwill produce162 eggplants.The total number of vegetables canbe calculated as432bellpeppers+720cherrytomatoes+60squash+162eggplants=1,374vegetables.
38. 10.8 Duringanormalmonth,eacheggplantplotproduces3eggplantsevery10days.Therefore,if the production were to double, each plot would produce 6 eggplants every 10 days.Given that thegardenmeasures10 feetby12 feet andeachplot isone footbyone foot,thereare10×12=120totalplots,15%ofwhichareeggplantplots.Therefore,thereare120×0.15=18eggplantplots.Calculatethetotalnumberofeggplantsproducedin10daysas18×6=108. Ina30-daymonth, thereare three10-dayperiods, so theentiregardenwouldproduce108×3=324totaleggplants.Tofindthedailyaverageproduction,divide324by30togetanaverageof10.8eggplantseachday.
Summary◦ Bothof theMath sectionson theSATwill contain agroupofproblemswithout answer choices.
ETSandtheCollegeBoardcalltheseproblems“student-producedresponses.”WecallthemGrid-Ins,becauseyouhavetomarkyouranswersonagridprintedonyouranswersheet.
◦ Despitetheirformat,Grid-InsarereallyjustlikeotherMathquestionsontheSAT,andmanyofthesametechniquesthatyouhavelearnedstillapply.
◦ Thegridformatincreasesthelikelihoodofcarelesserrors.Knowtheinstructionsandcheckyourworkcarefully.
◦ Justliketherestoftheexam,thereisnoguessingpenaltyforGrid-Ins,soyoushouldalwaysgridinyouranswer,evenifyou’renotsurewhetherit’scorrect.
◦ Always write the numbers in the boxes at the top of the grid before you (carefully) fill in thecorrespondingovals.
◦ Gridinyouranswerasfartotheleftaspossible.
◦ IftheanswertoaGrid-Inquestioncontainsafractionoradecimal,youcangridintheanswerineitherform.Whengriddinginfractionsordecimals,usewhicheverformiseasierandleastlikelytocausecarelessmistakes.
◦ There’snoneedtorounddecimals,eventhoughitispermitted.
◦ Ifyouhavealongorrepeatingdecimal,besuretofillupallthespacesinthegrid.
◦ Ifafractionfitsinthegrid,youdon’thavetoreducethefractionbeforegriddingitin.
◦ The scoringcomputerdoesnot recognizemixednumbers.Convertmixednumbers to fractionsordecimalsbeforegriddingthemin.
◦ SomeGrid-Inquestionswillhavemorethanonecorrectanswer.Itdoesn’tmatterwhichansweryougridin,aslongasit’soneofthepossibleanswers.
◦ LikeallotherquestionsontheSATMathTest,Grid-Inproblemsarearrangedinalooseorderofdifficulty. Use your knowledge of your own strengths and weaknesses to decide which ones totacklefirstandwhichones,ifany,toskip.
◦ ThelasttwoGrid-InsintheCalculatorsectionareExtendedThinkingquestions,asetofquestionson thesame information.Usually, theycanbeanswered independently,and theyareworthonly1pointeach.Attemptbothonlyifyouareaimingforatopscore.
◦ Negatives,π,squareroots,%,anddegreesymbolscannotbegriddedin.
Chapter18ReadingandAnalyzingtheEssayPassageTheSATincludesanoptionalrhetoricalanalysisessay.Yourjobistoreadatext(typicallyaspeechoreditorialofsomesort)anddiscusshowtheauthorbuildsanargumenteffectively.Thismightbeafamiliartask if you’ve done it in school. If not, don’t worry. The format is straightforward, and with somepractice,youcanlearnhowtowriteasolidSATessay.Inthischapterwe’lllookattwoofthethreetasksyouwillneedtodofortheessay—readingandanalysis—andshowyouhowtoapproacheachtaskinthemosteffectivewaypossible.
THE“OPTIONAL”ESSAYTheessayusedtobearequiredpartoftheSAT,butnotallcollegesfoundthisscoretobeuseful.Thisiswhytheessayisnow“optional.”Youressayscoreisnowcompletelyseparatefromyourtotalscore,soopting out of the essay will not have any effect on your 400–1600 score. Notice how we’re usingquotationmarkswheneverwesaytheessayis“optional,” though?Youshouldconsider theessaytobeoptionalforcollegesbutnotoptionalforyou.
The problem is that some schools require the essay while others do not, and you can’t do the essayindependentlyoftherestoftheSAT.Thatmeansifyouoptoutoftheessayandlateryourealizeyouneeditforyourapplication,youcan’tsimplyredojusttheessay:YouhavetoredotheentireSAT.Sogoaheadandwritetheessay.You’vealreadykilledaSaturdaymorning,you’resittinginthetestingroom,andit’snotridiculouslychallengingtoprepareforthisessay.Justwriteit.
Writingtheessaycanmakeyourcollegeapplicationlookmoreattractive.Youressayscorewillappearonevery score reportyou send to colleges, regardlessofwhetherornot the school requires anessay.Everyschooltowhichyouapplywillseethatyoutooktheinitiativetowritetheessay,whichisagoodthing.
YOURESSAYMISSIONIn 50minutes, you’ll be required to read a text and write a logical, well-constructed analysis of theauthor’sargument.Thethingtorememberhereisthatyouarenotbeingaskedforyouropiniononatopicoratext.Youressaywillbeanobjectiveanalysisofaspeechorargument.
Thepromptwillbenearlythesameeverytime,justwithadifferentsourcetext,andwillbesomethinglikethis:
Asyoureadthepassagebelow,considerhowtheauthoruses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
Writeanessay inwhich youexplainhow [theauthor] buildsanargument topersuade[his/her]audiencethat[author’sclaim].Inyouressay,analyzehow[theauthor]usesoneormoreofthefeatureslistedabove(orfeaturesofyourownchoice)tostrengthenthelogicandpersuasivenessof [his/her] argument.Besure that youranalysis focusesonthemostrelevantaspectsofthepassage.
Youressayshouldnotexplainwhetheryouagreewith [theauthor’s]claims,but ratherexplainhowtheauthorbuildsanargumenttopersuade[his/her]audience.
Intheessay,youwill:
• carefullyreadatext• understandhowanauthorappealstoareader’slogic,emotions,ormorals• writealogicalanalysisofanargument• explainhowstylechoicescanaffectanauthor’spersuasiveness
Intheessay,youwillNOT:
• giveyouropinionaboutatext• memorizeexamplesfromhistoryorliterature• havepreviousexperiencewiththetext
Twograderswillreadandscoretheessayona1–4scaleinthreedifferentcategories:Reading,Analysis,andWriting.
4=Advanced3=Proficient2=Partial1=Inadequate
Thescoreswillbedeterminedusingthefollowingrubric.Thereisalotofinformationhere.Youdon’tneedtomemorizethis,butitmayhelpyouunderstandthescoringalittlemore.We’llgothroughthefirsttwotasksinthischapter,followedbythethirdtask—Writing—inChapter19.
EssayScoringReading,Analysis,andWritingscoreswillbe
combinedforatotalscoreof3–12.(Eachcategorywillreceiveatotalscoreof2–8,whichisfoundbyaddingtheindividual
1–4scoresfromyourtworeaders.)Eachtask
(Reading,Analysis,andWriting)isscored
individually,soahighscoreinonedoes
notguaranteeahighscoreinanother.
ETS’sEssayRubricReading
Scoreof4:Advanced
• Demonstratesthoroughcomprehensionofthesourcetext.• Showsanunderstandingofthetext’scentralidea(s)andofmostimportantdetailsandhowtheyinterrelate,demonstratingacomprehensiveunderstandingofthetext.
• Isfreeoferrorsoffactorinterpretationwithregardtothetext.• Makesskillfuluseoftextualevidence(quotations,paraphrases,orboth),demonstratingacompleteunderstandingofthesourcetext.
Scoreof3:Proficient
• Demonstrateseffectivecomprehensionofthesourcetext.• Showsanunderstandingofthetext’scentralidea(s)andimportantdetails.• Isfreeofsubstantiveerrorsoffactandinterpretationwithregardtothetext.• Makesappropriateuseoftextualevidence(quotations,paraphrases,orboth),demonstratinganunderstandingofthesourcetext.
Scoreof2:Partial
• Demonstratessomecomprehensionofthesourcetext.• Showsanunderstandingofthetext’scentralidea(s)butnotofimportantdetails.• Maycontainerrorsoffactand/orinterpretationwithregardtothetext.• Makeslimitedand/orhaphazarduseoftextualevidence(quotations,paraphrases,orboth),demonstratingsomeunderstandingofthesourcetext.
Scoreof1:Inadequate
• Demonstrateslittleornocomprehensionofthesourcetext.• Failstoshowanunderstandingofthetext’scentralidea(s),andmayincludeonlydetailswithoutreferencetocentralidea(s).
• Maycontainnumerouserrorsoffactand/orinterpretationwithregardtothetext.• Makeslittleornouseoftextualevidence(quotations,paraphrases,orboth),demonstratinglittleornounderstandingofthesourcetext.
ETS’sEssayRubricAnalysis
Scoreof4:Advanced
• Offersaninsightfulanalysisofthesourcetextanddemonstratesasophisticatedunderstandingoftheanalyticaltask.
• Offersathorough,well-consideredevaluationoftheauthor’suseofevidence,reasoning,and/orstylisticandpersuasiveelements,and/orfeature(s)ofthestudent’sownchoosing.
• Containsrelevant,sufficient,andstrategicallychosensupportforclaim(s)orpoint(s)made.
• Focusesconsistentlyonthosefeaturesofthetextthataremostrelevanttoaddressingthetask.
Scoreof3:Proficient
• Offersaneffectiveanalysisofthesourcetextanddemonstratesanunderstandingoftheanalyticaltask.
• Competentlyevaluatestheauthor’suseofevidence,reasoning,and/orstylisticand
persuasiveelements,and/orfeature(s)ofthestudent’sownchoosing.• Containsrelevantandsufficientsupportforclaim(s)orpoint(s)made.• Focusesprimarilyonthosefeaturesofthetextthataremostrelevanttoaddressingthetask.
Scoreof2:Partial
• Offerslimitedanalysisofthesourcetextanddemonstratesonlypartialunderstandingoftheanalyticaltask.
• Identifiesandattemptstodescribetheauthor’suseofevidence,reasoning,and/orstylisticandpersuasiveelements,and/orfeature(s)ofthestudent’sownchoosing,butmerelyassertsratherthanexplainstheirimportance,oroneormoreaspectsoftheresponse’sanalysisareunwarrantedbasedonthetext.
• Containslittleornosupportforclaim(s)orpoint(s)made.• Maylackaclearfocusonthosefeaturesofthetextthataremostrelevanttoaddressingthetask.
Scoreof1:Inadequate
• Offerslittleornoanalysisorineffectiveanalysisofthesourcetextanddemonstrateslittleornounderstandingoftheanalytictask.
• Identifieswithoutexplanationsomeaspectsoftheauthor’suseofevidence,reasoning,and/orstylisticandpersuasiveelements,and/orfeature(s)ofthestudent’schoosing.
• Numerousaspectsoftheresponse’sanalysisareunwarrantedbasedonthetext.• Containslittleornosupportforclaim(s)orpoint(s)made.orsupportislargelyirrelevant.
• Maynotfocusonfeaturesofthetextthatarerelevanttoaddressingthetaskortheresponseoffersnodiscernibleanalysis(e.g.,islargelyorexclusivelysummary).
ETS’sEssayRubricWriting
Scoreof4:Advanced
• Cohesiveanddemonstratesahighlyeffectiveuseandcommandoflanguage.• Includesaprecisecentralclaim.• Includesaskillfulintroductionandconclusion.Theresponsedemonstratesadeliberateandhighlyeffectiveprogressionofideasbothwithinparagraphsandthroughouttheessay.
• Widevarietyinsentencestructures.Theresponsedemonstratesaconsistentuseofprecisewordchoice.Theresponsemaintainsaformalstyleandobjectivetone.
• ShowsastrongcommandoftheconventionsofstandardwrittenEnglishandisfreeorvirtuallyfreeoferrors.
Scoreof3:Proficient
• Mostlycohesiveanddemonstrateseffectiveuseandcontroloflanguage.• Includesacentralclaimorimplicitcontrollingidea.• Includesaneffectiveintroductionandconclusion.Theresponsedemonstratesaclearprogressionofideasbothwithinparagraphsandthroughouttheessay.
• Varietyinsentencestructures.Theresponsedemonstratessomeprecisewordchoice.Theresponsemaintainsaformalstyleandobjectivetone.
• ShowsagoodcontroloftheconventionsofstandardwrittenEnglishandisfreeofsignificanterrorsthatdetractfromthequalityofwriting.
Scoreof2:Partial
• Demonstrateslittleornocohesionandlimitedskillintheuseandcontroloflanguage.• Maylackaclearcentralclaimorcontrollingideaormaydeviatefromtheclaimorideaoverthecourseoftheresponse.
• Mayincludeanineffectiveintroductionand/orconclusion.Theresponsemaydemonstratesomeprogressionofideaswithinparagraphsbutnotthroughouttheresponse.
• Limitedvarietyinsentencestructures;sentencestructuresmayberepetitive.• Demonstratesgeneralorvaguewordchoice;wordchoicemayberepetitive.Theresponsemaydeviatenoticeablyfromaformalstyleandobjectivetone.
• ShowsalimitedcontroloftheconventionsofstandardwrittenEnglishandcontainserrorsthatdetractfromthequalityofwritingandmayimpedeunderstanding.
Scoreof1:Inadequate
• Demonstrateslittleornocohesionandinadequateskillintheuseandcontroloflanguage.
• Maylackaclearcentralclaimorcontrollingidea.• Lacksarecognizableintroductionandconclusion.Theresponsedoesnothaveadiscernibleprogressionofideas.
• Lacksvarietyinsentencestructures;sentencestructuresmayberepetitive.Theresponsedemonstratesgeneralandvaguewordchoice;wordchoicemaybepoororinaccurate.Theresponsemaylackaformalstyleandobjectivetone.
• ShowsaweakcontroloftheconventionsofstandardwrittenEnglishandmaycontainnumerouserrorsthatunderminethequalityofwriting.
TASK1:READINGInordertowriteanessaythatanalyzesasourcetext,youmustfirstreadthetext.UnlikewiththeReadingpassages,therearenotrickstoshortenyourreadingtimeorcutoutpiecesofthetext.However,knowingwhat to look forasyou readcanhelp streamline the readingprocessandgiveyouagoodstarton thesecondtaskofanalysis.
PlanAccordinglyPlanfor25–30minutesforReadingandAnalysis,and20–25minutesforWriting.
AccordingtoETSandtheCollegeBoard,yourReadingscoreontheessaywillbebasedonyour
• comprehensionofthesourcetext• understandingofcentralideas,importantdetails,andhowthesethingsarerelated• accuracyinrepresentationofthesourcetext(i.e.,noerrorsoffactorinterpretationintroduced)• useoftextualevidence(quotations,paraphrases,orboth)todemonstrateunderstandingofthe
sourcetext
Whenyoustartthistask,theveryfirstthingyouhavetodoisreadthetext.Obvious,right?Butreadingfortheessayisunlikeleisurereading,whenallyouneedtoworryaboutiswhetherornotKatnissisgoingtomake it to the endof theGames.Asyou read the essayprompt, youneed to consider the central idea(SOAPS)andimportantdetailsthatsupportthatidea(typesofappealsandstyleelements).
SOAPS—LikeintheTub?SOAPSisanacronymtohelpyourememberthefivethingsyouneedtolookforinordertoestablishthecentralideaofapassageorargument.
SpeakerOccasionAudiencePurposeSubject
SOAPStone:EverHearofIt?Youmayhavelearned
SOAPStoneinyourEnglishclass.It’salmostthesame
thingasSOAPS.
Speaker
Whoisspeakingorwriting?
Knowingwhosevoiceyouarereadingisveryimportantforunderstandingthetextthoroughly.Itwillhelpyouunderstandtheirmotivationsaswellasthereason(s)theyarespeakingorwritinginthefirstplace.Asyouread,askwhatmakesthispersoncredible?Whatarethespeaker’scredentials?
• Whatgivesadoctortheauthoritytospeakaboutmedicalissues,orapoliticiantheauthoritytospeakaboutpoliticalissues?(Bespecific.)
For thedoctor,youmightmentionmedicalschoolandmanyyearsstudyingmedicine.Passing testsandacquiringhands-onexperiencegiveadoctorcredibilityonmedicalissues.Thelongeradoctorhasbeenpracticingmedicine, themoreexperiencehehas, lendingevenmorecredibility.For thepolitician,youmightmentionexperienceworkingingovernmentandpolicy.Manystudypoliticalscienceincollege.Thepoliticianmayhaverunsuccessfulcampaignspreviously.
• Wouldyouratherhearastockbrokeroranathletespeakaboutfinancialinvesting?Why?
Probablythestockbroker!Astockbrokerhasexperienceinthefieldofinvestmentsandknowsimportantinformationtohelpeducateyou.Anathletedoesn’tnecessarilyknowthe typeoffiscal informationyouwouldwanttohear.
So,remember!Thespeakerofthesourcetextisveryimportant.Thenexttimeyoureadanarticleonlineabout the five foods you should never eat, consider the speaker or writer. Does that person have thecredentials to give advice on nutrition?On the SATEssay, youwill not see a speaker unqualified todiscussthegiventopic.
Occasion
Whathappenedthatrequiresthisspeechortext?
Theeventthatcausedtheauthortowanttoexpressherthoughtsisanintegralpartofanalyzingthework.Itmightbeassimpleasthetypeofeventinwhichthespeechwasgiven.Itmight,however,besomethinglargersuchasasignificanttimeinawar.Youwillneedtothinkaboutthehistoricalcontextofthetext.
• Whattypeofelementswouldyouexpecttohearinacoach’sspeechbeforeabiggame?
Youmightexpectelementssuchasmotivationalsupport(examples:“GoTeam!”;“Keepyourheadinthegame!”; “Victorywill be ours!”) and strategy (examples: “Remember thatWilkins isweak on his leftside.”;“Keepyoureyesopenforthegapintheline.”;“FakeapasstoJenkins.”).
• Whattypeofelementswouldyouexpecttohearinapolitician’sspeechthedaybeforeElectionDay?
Youmight expect sweeping statementswith fewdetails, such as a reminder to “goout andvote” or apatriotic reminder about that politician’s values. Youmight even hear a cheer of confidencemeant toinspire.
• Howmightaminister’smessageataweddingdifferfromhermessageatafuneral?
Atawedding, aminister is likely tobeoptimisticandcheerful,whileat a funeral, aminister ismorelikelytobesolemnandcomforting.Inthiscase,sincethespeakeristhesame,theoccasionmakesallthedifference.
ChangeofOccasion=ChangeinSpeech
Eventhoughthespeakeristhesame,achangeofoccasioncantotallychangethespeech.
So, remember to take note of the occasion of the speech or piece of writing; doing sowill help youunderstandwhytheauthorusesacertaintoneaswellassomeofhisorhermotivations.
Audience
Whoistheintendedaudience?
Considering your audience is criticalwhen you arewriting a speech.Therefore, it is critical that youconsiderwho the author’s audience is in order to understand the text.What doyouknowabout them?What’s the relationshipbetween thespeaker/authorand the intendedaudience?What sortofvaluesorpriorideasmighttheaudiencehave?Howmightthataffecttheirperceptionofthespeaker/author?
• Howmightapolitician’sElectionEvespeechtoaconservativegroupdifferfromhisspeechtoaliberalgroup?
TakeNote!Samespeaker…same
occasion…differentaudience!
Whenspeakingtogroupsthatareverydifferent,apoliticianisgoingtocaterhisspeechtoeachgroup’svalues.Totheconservatives,shewillspeakonconservativeissuesandtotheliberals,theliberalissues.Thepoliticianlikelyhasdifferentgoalsforeach.
• Howwouldaprincipal’smessagetoagroupofnewteachersbedifferentfromamessagetoagroupofexperiencedteachers?
Aprincipalismorelikelytobemoreinformalintonetoexperiencedteachersandprovidelessdetailedinformation.Withnew teachers,however, theprincipalwill likelywant tomakeagood impressionaswell as make sure the teachers understand her role as a supportive authority.With new teachers theprincipalwill also need to give very clear information and perhaps repeat that informationmore thanonceandexplainallthethingstheexperiencedteachersalreadyknowabouttheschool.
So,rememberthattheaudiencecanentirelychangeawork.Whenreadingyoursourcetextfortheessay,makesuretoconsiderwhotheaudienceisandhowthisaffectshowtheauthorbuildshisorherargument.
Purpose
Whatistheauthororspeaker’sintention?
Occasion,Subject,andAudienceallcontributetoPurpose.Whatistheauthortryingtoaccomplishwiththiswork?Isitanattack?Defense?Persuasion?Doesitaimtogivepraiseorblame?Isitsgoaltoteach,orsomethingelse?
Subject
Whatisthemainidea?
Ofcourse,youneedtoknowwhattheworkisabout.Whatisthetopic?Whatistheauthor’smainpoint?Whatarethemainlinesofreasoningused?
AppealsArhetoricalappealisapersuasivestrategythatanauthororspeakerusestosupporthisclaims(orinadebate,torespondtoopposingarguments).Whenaspeakerorauthorwantstoconvinceanaudienceofsomething,therearethreemaintypesofrhetoricalappealsthatcanbeused:appealtocredibility,appealtoemotion,andappealtologic.
AppealtoCredibility:“WhyShouldIBelieveYou?”This is the author’sway of establishing trustwith his audience.We tend to believe peoplewhomwerespect,andagoodwriterknowsthis!Oneofthecentraltasksofpersuasionistoprojectanimpressiontothereaderthattheauthorissomeoneworthlisteningto,aswellassomeonewhoislikableandworthyofrespect.RememberwhenwetalkedaboutthespeakerinSOAPSandhiscredibility?Thisishowanauthormightusehisowncredentialstohisbenefit.
Considerthefollowing:
• Adoctorwritesanarticleabouthealthissues.Whatdoessheneedtoincludeinordertoestablishtrustfromheraudience?
Howdidyourespond?Sheshouldprobablyincludeabriefbiographyaboutherpracticeandhermedicalexperience, as well as information about whether she has been practicing for a long time, has doneimportantresearch,orwenttoatopschool.
• Aspeakercallsintoatalkradioprogramaboutmilitarystrategy.Whatshouldhementioninordertoestablishcredibilitywithotherlisteners?
Herearesomepossibilities:anyexperiencehehashad(andhowmuch)inthemilitaryorwithmilitarystrategy,andwhathehasdonetoenablehimtoknowwhatheistalkingabout.A4-stargeneralismore
likelytobefairlylistenedtoandbelievedthanthesoon-to-beCallofDutytristateareachampion.
AppealtoEmotion:“Gee,ThatMadeMeFeelAllWarmandFuzzy.”This iswhen the author tries to appeal to the reader’s emotions. This allows an author or speaker toconnectwithanaudiencebyusingfear,humor,happiness,disgust,andsoon.Imageryandlanguagechoiceareoftenbigcomponentsofappealstoemotion.
• Anarticleaboutworldhungerrunsinamagazine.Whatdecisionscouldthemagazineeditormaketoappealtoherreaders’emotions?
Picturesofstarvingchildrenorvisualchartsshowinghowmuchfoodtheaveragefamilythrowsawayaretwopossiblewaystheeditorcouldattempttotugonheartstrings.
• Amotivationalspeakerwantstomakeanenergeticentrance.Whatcouldhedo(andwhy)?
Somepossibilities:Playupbeatmusicandrunin,havecertainpeopleintheaudiencecheerridiculously,haveacheesyannouncerandballoonsfallingfromtheceiling.
Peoplegetexcitedwhenotherpeoplegetexcited.Certainthings, likeballoons,confetti,andfireworks,triggerhappinessinus,perhapsduetoourchildhood.Ifthespeakerrunsoutwithahugesmileonhisfaceanddozens(hundreds?)ofscreamingfans,itisverylikelygoingtoexcitehisaudience—or,attheveryleast,makethemsitupalittlestraighterandbeinterestedinwhathewillsaynext.
AppealtoLogic:“Well,ThisJustMakesSense!”This connects with an audience’s reason or logic. This isn’t logic like the formal logic in math,philosophy,orevencomputerscience;itistheconsistencyandclarityofanargumentaswellasthelogicofevidenceandreasons.
Instead of simply saying, “This is a good idea,” an author of amagazine article about environmentalprotectioncouldconvinceherreadersofherpointbydoingwhat?
Some possibilities: Providing proof of some sort, in the form of data, statistics, expert opinions,testimonials,orotheroptions.
• Asalesmanwantsahusbandandwifetobuyawasher/dryerpairinsteadofasingleappliance.Howmightheappealtotheirlogic?
Discuss thecostbenefitsofbuying twoatonceversuseachoneatadifferent timesuchashaving twobrandnewappliancesthatwon’tneedtobeworriedaboutforyears,andbenefitsordiscountsthatapplyonlyif theybuyboththewasheranddryer,forexample.Hecouldalsotell themabout themoneybackguaranteetoshowthattheappliancesmustbequalityifthestoreiswillingtorefundtheirmoneyiftheyaren’t satisfied.All of these are examples of appeals to logic and reasoning.These are all things thatmakethecouplethink,“Well,gee,thisjustmakessense!”
OnceyoufindalltheSOAPSpointsandexamplesofappeals,you’vegotwhatyouneedfortheReading
task.Remember,fortheReadingtask,thetestwriterswanttoseethatyouunderstandthetext,canidentifythecentralidea/themeofthetext,andknowhowdetailsandexamplessupportthatcentralidea.
SOAPSANDAPPEALSDRILLRead the following prompt and highlight anything that references SOAPS points. There’s aworksheetstartingonthispageforyoutotrackyournotes,andyoucancheckyouranswersonthispage.
Asyoureadthepassagebelow,considerhowPresidentJohnF.Kennedyuses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
1 Wesetsailonthisnewseabecausethereisnewknowledgetobegained,andnewrightstobewon,andtheymustbewonandusedfortheprogressofallpeople.Forspacescience,likenuclearscienceandalltechnology,hasnoconscienceofitsown.Whetheritwillbecomeaforceforgoodorilldependsonman,andonlyiftheUnitedStatesoccupiesapositionofpre-eminencecanwehelpdecidewhetherthisnewoceanwillbeaseaofpeaceoranewterrifyingtheaterofwar.Idonotsaythatweshouldorwillgounprotectedagainstthehostilemisuseofspaceanymorethanwegounprotectedagainstthehostileuseoflandorsea,butIdosaythatspacecanbeexploredandmasteredwithoutfeedingthefiresofwar,withoutrepeatingthemistakesthatmanhasmadeinextendinghiswritaroundthisglobeofours.
2 Thereisnostrife,noprejudice,nonationalconflictinouterspaceasyet.Itshazardsarehostiletousall.Itsconquestdeservesthebestofallmankind,anditsopportunityforpeacefulcooperationmanynevercomeagain.Butwhy,somesay,themoon?Whychoosethisasourgoal?Andtheymaywellaskwhyclimbthehighestmountain?Why,35yearsago,flytheAtlantic?WhydoesRiceplayTexas?
3 Wechoosetogotothemoon.Wechoosetogotothemooninthisdecadeanddotheotherthings,notbecausetheyareeasy,butbecausetheyarehard,becausethatgoalwillservetoorganizeandmeasurethebestofourenergiesandskills,becausethatchallengeisonethatwearewillingtoaccept,oneweareunwillingtopostpone,andonewhichweintendtowin,andtheothers,too.
4 ItisforthesereasonsthatIregardthedecisionlastyeartoshiftoureffortsinspacefromlowtohighgearasamongthemostimportantdecisionsthatwillbemadeduringmyincumbencyintheofficeofthePresidency…
5 Tobesure,wearebehind,andwillbebehindforsometimeinmannedflight.Butwedonot
intendtostaybehind,andinthisdecade,weshallmakeupandmoveahead.
6 Thegrowthofourscienceandeducationwillbeenrichedbynewknowledgeofouruniverseandenvironment,bynewtechniquesoflearningandmappingandobservation,bynewtoolsandcomputersforindustry,medicine,thehomeaswellastheschool.Technicalinstitutions,suchasRice,willreaptheharvestofthesegains.
7 Andfinally,thespaceeffortitself,whilestillinitsinfancy,hasalreadycreatedagreatnumberofnewcompanies,andtensofthousandsofnewjobs.Spaceandrelatedindustriesaregeneratingnewdemandsininvestmentandskilledpersonnel,andthiscityandthisState,andthisregion,willsharegreatlyinthisgrowth.WhatwasoncethefurthestoutpostontheoldfrontieroftheWestwillbethefurthestoutpostonthenewfrontierofscienceandspace.Houston,yourCityofHouston,withitsMannedSpacecraftCenter,willbecometheheartofalargescientificandengineeringcommunity.Duringthenext5yearstheNationalAeronauticsandSpaceAdministrationexpectstodoublethenumberofscientistsandengineersinthisarea,toincreaseitsoutlaysforsalariesandexpensesto$60millionayear;toinvestsome$200millioninplantandlaboratoryfacilities;andtodirectorcontractfornewspaceeffortsover$1billionfromthisCenterinthisCity…
8 ManyyearsagothegreatBritishexplorerGeorgeMallory,whowastodieonMountEverest,wasaskedwhydidhewanttoclimbit.Hesaid,“Becauseitisthere.”
9 Well,spaceisthere,andwe’regoingtoclimbit,andthemoonandtheplanetsarethere,andnewhopesforknowledgeandpeacearethere.And,therefore,aswesetsailweaskGod’sblessingonthemosthazardousanddangerousandgreatestadventureonwhichmanhaseverembarked.
Thankyou.
(JohnF.Kennedy.September12,1962.RiceStadium,Houston,TX)
Write an essay in which you explain how President Kennedy builds an argument toexpand and move forward with the United States’ space program. In your essay,analyzehowKennedyusesoneormoreofthefeatureslistedabove(orfeaturesofyourownchoice) to strengthen the logicandpersuasivenessofhisargument.Besure thatyouranalysisfocusesonthemostrelevantaspectsofthepassage.
Your essay should not explain whether you agree with Kennedy’s claims, but ratherexplainhowtheauthorbuildsanargumenttopersuadehisaudience.
SOAPS:
1. Speaker:Whoisspeaking?Whatcredentialsdoesthispersonhavetomakehisspeech
believable?
2. Occasion:WhatwasthereasonforPresidentKennedytogivethisparticularspeech?
3. Audience:Whoistheaudienceforthisspeech?Whatdoyouknowaboutthem?
CanyoufigureanythingoutabouttheirvaluesbasedonhowPresidentKennedyspeakstothemandwhathesays?
4. Purpose:WhatisJFK’sgoal?
5. Subject:Whatisthemainideaofthespeech?
Appeals:
1. AppealtoEmotion:WhatdoesPresidentKennedysaytoappealtohisaudience’semotions?
Thesewords/phraseswouldappealtowhichemotion(s)?
2. AppealtoLogic:WhatdoesPresidentKennedysaytoappealtohisaudience’slogicandreason?
Howmightthesewords/phrasesappealtologicorreason?
Awesome job!Now take a look at thispage to see howyour ideas comparewith ours and if there isanythingyoumissed.Onceyouhavethemainpointsofthespeech,it’stimetostartanalyzing.
TASK2:ANALYSISRemember:Agoodscoreononetaskdoesnotguaranteeagoodscoreonanother.Doingagoodjobofexplaining themain ideaof the speech and the details that support thatmain ideawill get you a goodReadingscore,butnowweneedtotalkaboutAnalysis.
For the Analysis task, you’ll have to determine the pieces of evidence, stylistic elements, or logicalreasoningtheauthorusestoeffectivelyachievehisorherobjective.
AccordingtoETSandtheCollegeBoard,yourAnalysisscorewillbebasedonyourabilityto
• analyzethesourcetextandunderstandtheanalyticaltask• evaluatetheauthor’suseofevidence,reasoning,and/orstylisticandpersuasiveelements,and/or
featureschosenbythestudent• supportclaimsorpointsmadeintheresponse• focusonfeaturesofthetextmostrelevanttoaddressingthetask
Forthistask,youwillneedtoexplaintheauthor’schoiceanduseofspecificelementsintheessay.It’snotenoughtosay,“Theauthorusesaquotetoappealtotheaudience’sreason.”Youhavetoexplainhowthe quote appeals to the audience’s reason. This task is all about the how andwhy. Look for facts,
evidence,literarydevices,persuasiveelements,andotherelementstheauthorhasusedtoformhisorherargument.
Herearesomecommonstyleelementsthatmayshowupinthetext.
StyleDetail Definition ExampleAllusion Abriefreferencetoaperson,
thing,orideafromhistory,literature,politics,orsomethingwithculturalsignificance
“Don’t ask him for a donation;he’satotalScrooge.”“ChocolatewasherKryptonite.”
Comparison Comparingtwodistinctthings;theauthor/speakermakesaconnectionbetweenthem
“Julietisthesun.”“Myloveislikearedrose.”
Diction Theauthor’schoiceofwords “Skinny” instead of “slender”soundslessflattering.Slangorvernaculargivesatextaninformalfeel,whileaprofessionalvocabularymakesatextfeelmoreformal.
Hyperbole Exaggerationnotmeanttobetakenliterally
“I’msohungryIcouldeatahorse.”
Imagery Usinglanguagethatappealstooursenses.Visualrepresentationofanobjectorideaisacommonperceptionofimagery,butimageryactuallycancreateideasthatappealtoallfivesenses.
“Thewomanwalkedby,trailingathick,cloyingcloudofperfume.”“The percussive thump of thelarge drums vibrated in her chestasthebandmarchedby.”
Juxtaposition Placingtwoideasside-by-sideinorderfortheaudiencetomakeacomparisonorcontrast
“Itwasthebestoftimes,itwastheworstoftimes…”
Repetition Deliberaterepetitionofaletter,word,orphrasetoachieveaspecificeffect
“Weshallnotflagorfail.Weshallgoontotheend.WeshallfightinFrance,weshallfightontheseasandoceans,weshallfightwithgrowingconfidenceandgrowingstrengthintheair…”
Statisticsorquotes Awriterorspeakermayaddcredibilitytohisorherargumentbyaddingdataorquotesfromarespected/recognizedsource.
AquotefromtheAmericanAcademyofPediatricsinaspeechaboutbestpracticesforcarseatuse.
Syntax Howwordsareputtogethertoachieveacertaineffect.Firstandlastwordsofanideacanbeparticularlyimportant.
Anauthorwhowantstoconveyamessagequicklyorurgentlymightchoosetouseshort,directsentences,whileanauthorwhowantstodeliberatelyslowdowna
textmayuselonger,moreconvolutedsentences.
Tone Theattitudeoftheauthor/speakertowardthesubject
Sarcastic,professional,critical
Note:Thesedevicesaredeliberatelyusedbytheauthor/speakerforaspecificpurpose.Youwillneedtoknowthepurposesofthedevicesandtheireffectsonatext,butyouwillnotneedtoknowthespecificnames.
SpottheElementLet’sreadthefollowingpiecesoftextandthenidentifytherhetoricaldeviceusedineach.
“…raised herself on one round elbow and looked out on a tiny river like a gleaming blue snakewindingitselfaroundapurplehill.Rightbelowthehousewasafieldwhiteassnowwithdaisies,andtheshadowofthehugemapletreethatbentoverthelittlehousefelllacilyacrossit.FarbeyonditwerethewhitecrestsofFourWindsHarbourandalongrangeofsunwasheddunesandredcliffs.”
—L.M.Montgomery,TheRoadtoYesterday
• WhichofthefivesensesisappealedtomoststronglyinMontgomery’sdescriptionofthesetting?
If you are thinking vision, then you are correct!Montgomery uses imagery (detailed descriptions) toallowthereaderto“see”thesetting.
• WhatliterarydevicedoesMontgomeryusetodescribetheriverandthefieldofdaisies?
Comparisons!Montgomery compares the river to a “gleaming blue snake” and the daisies to a “fieldwhiteassnow.”Thesecomparisonsallowthereader toconnect theimagestosomethingalreadyinhismindtocreatemorevibrantimage.
“Wellnow,onewinteritwassocoldthatallthegeeseflewbackwardandallthefishmovedsouthandeventhesnowturnedblue.Lateatnight,itgotsofrigidthatallspokenwordsfrozesolidaforetheycouldbeheard.Peoplehadtowaituntilsunuptofindoutwhatfolksweretalkingaboutthenightbefore.”
• InthisexcerptfromatalltaleaboutPaulBunyan,whichliterarydeviceisusedtogreateffect?
If you are thinking hyperbole, then you are correct! Think aboutwhat the author’s goal for using thatparticulardevicemightbe.Hyperbolehelpstheauthorcommunicatetothereaderthatitwasn’tjustplainoldcold.Itwasincrediblycold.However,insteadofjustusingitalicslikewejustdid,theauthorusedthemuchmorecreativeexaggerationofwordsfreezinginmidairtogethispointacross.
“Jacksonpulledback thecurtain to lookat therain. ‘Betterstartbuilding thatArk,’hesaidoverhisshoulder.”
• WhatdoesJacksonmean?
Hemeansthatitisrainingreallyhard.Howwouldyouknowthat?Jacksonsaystostartbuildingan“ark,”areferencetoNoah’sArk,whichhehadtobuildtosurviveagreatflood.Whatliterarydeviceisthis?Allusion.Anallusionisareferencetosomething(usuallyanothergreatwork,event,orperson)withoutexplicitmentionofit.
LITERARYDEVICESDRILLNowlet’sthinkbacktothespeechbyPresidentKennedy.Gobackandreadforstylisticelements.Takenotesonthepassage.Whenyouaredone,turntothenextpagetocheckyourwork.
Herearesomeexamplesofstyledevicesandrhetoricalelementsyoumayhavefoundinthespeech.
• Metaphor:JFKusesthemetaphorofspaceastheoceanwhenhesays,“Wesetsailonthisnewsea”inthefirstparagraph.Thismetaphoriscontinuedlaterintheparagraphwith“whetherthisnewoceanwillbeaseaofpeace.”
Intheseventhparagraph,JFKsaysthatHoustonwill“becometheheart”ofalargescientificcommunity.
Ricewill“reaptheharvest”ofthenewadvancementsintechnology.
Imagery:JFKmentions“feedingthefiresofwar”whichcreatestheimageofwarasadangerous,uncontrollableelementofnature.
• Syntax:JFK(whoiswidelyrememberedforhisdistinctsyntaxinhisspeeches)usesrhetoricalquestionssuchas“Whychoosethisasourgoal?”Healsousesrepetitionfrequently.Heasksseveralrhetoricalquestionsinarowinthesecondparagraph.Inthethirdparagraph,herepeatsthephrase“Wechoosetogotothemoon.”
• Allusion:JFKmakesanallusiontoCharlesLindberghflyingacrossfromNewYorktoParisonhisSpiritofSt.Louisplane,completingthefirstsolocrossingoftheAtlanticwiththewords“Why,35yearsago,flytheAtlantic?”
JFKmakesanallusiontoTexasbeing“thefurthestoutpostontheoldfrontieroftheWest.”ThisreferstotheouterlineofsettlementintheUnitedStatesmovingsteadilywestandthefactthatthelocationofhisspeechwas,atonepoint,thefurthestwestthatthecountryextended.
• StatisticsandQuotes:JFKmentionsspecificfiguresforspendingonthenewspaceprogramsuchas“$60millionayear”forsalariesandexpenses,“$200million”inplantandlaboratoryfacilities,and“over$1billion”tocontractfornewspaceefforts.
• Diction:We“choose”togotothemooninsteadof“Wearegoingtothemoon.”
JFKdescribestheentireplantogothemoonasan“adventure”insteadof“budgetlineitem”or“task”oreven“journey.”
PUTTINGITALLTOGETHERNowthatyouhaveidentifiedthepartsofthespeech,appeals,andtheliterarydevicesusedinthepassageonthispage,youhavetofigureouthowthosecometogethertocreateaneffectiveargument.
Thischapterendswithadrillthatallowsyoutodojustthat.RereadPresidentKennedy’sspeechandlookoveryournotes,andthenanswerthequestionsstartingonthispage.Whenyou’redone,turntothispagetoseehowyouranswerscomparewithours.
ReadingandAnalysisDrillAnswersandexplanationscanbefoundonthispage.
1. Howdidthepresident’sappealshelpmakehisspeechmoreeffectiveforhislisteners?Whatwouldhavebeenmotivatingforthem,andwhy?
2. Ifhehadbeenspeakingtoadifferentaudience,wouldsomeofthesestrategieshavebeenlesseffective?Explain.
3. Whatisthetoneofthepassage?Howdoyouknow?
4. Whataresomespecificexamplesofwordchoice(diction)thatmakethespeechconvincing?Canyouexplainwhy?Whatwordchoiceswouldhavemeantthesamethingbutbeenlessconvincing?
5. Howdoesthestructureofthespeechimpacthisaudience?Doestheorderinwhichtheideasarepresentedaffecttheargument?Whyorwhynot?
6. Whatwouldyouconsiderthethreemosteffectivepartsofthespeech?(Thesewillbethebasisforyouressaybodyparagraphs.)
CHAPTERDRILLANSWERSANDEXPLANATIONS
SOAPSandAppealsDrill
SOAPS
1. Speaker:Whoisspeaking?Whatcredentialsdoesthispersonhavetomakehisspeechbelievable?
Thespeakeristhecurrent(1962)PresidentoftheUnitedStates,JohnF.Kennedy.Thejobofthepresidencyalonecarriesenoughweightforpeopletolisten.However,Kennedydoesmentionhispresidencyinlinessuchas“duringmyincumbencyintheofficeofthePresidency,”probablytokeepthatauthorityinthemindsofhislisteners.
2. Occasion:WhatwasthereasonforPresidentKennedytogivethisparticularspeech?
JFKwantedtopromoteandrousesupportfortheUnitedStates’newspaceprogram.Inparagraph4hesays,“…Iregardthedecisiontoshiftoureffortsinspacefromlowtohighgearasamongthemostimportantdecisionsmade…”
3. Audience:Whoistheaudienceforthisspeech?Whatdoyouknowaboutthem?
JFKmentionsbothRiceUniversityandHoustoninhisspeech,makingseveralreferencesthatwouldbesignificanttothosepeople.Weknowthattheycareabouttheiruniversityandtheircity,andweknowtheyhaveschoolspirit!(Inparagraph2,JFKasksseveralquestionsincludingwhyclimbamountain,whyflyacrosstheAtlantic,and“WhydoesRiceplayTexas?”Youcanalmostimaginethelistenerscheeringatthisreference.)
CanyoufigureanythingoutabouttheirvaluesbasedonhowPresidentKennedyspeakstothemandwhathesays?
WeknowtheyvaluetheircommunitybecauseJFKmakesseveralreferencestothegoodthatthiseffortwilldothelocalssuchasmorejobsandabettereconomy.WeknowtheyvalueeducationandthefurtheringofsciencebecauseJFKdiscussesthebenefittothescientificcommunityaswellasthemedicalcommunity.WeknowtheyvaluetheideaofaGodandhisgoodwillsinceJFKmakesapointto“askGod’sblessing”onhismission.
4. Purpose:WhatisPresidentKennedy’sgoal?
JFKwantstogarnersupportandexcitementforthemissiontoputamanontheMoon.HehascometoHoustonspecificallytotrytogetthelocalsonboardsincetheywillbeincrediblyimportanttotheentireeffort.Evidenceforthisisrightinthefirstparagraph.
5. Subject:Whatisthemainideaofthespeech?
JFK’smainideaisthatputtingamanontheMoonwillnotonlybepositiveforthelocalcommunity,butalsosomethingAmericamustdobecauseAmericansdonotshyawayfromachallenge.
Appeals
1. AppealtoEmotion:WhatdoesPresidentKennedysaytoappealtohisaudience’semotions?
• JFKdiscusseshowspacesciencewillbecomeeithera“forceforgoodorill,”andtheoutcomedependsonhumanity.HementionstheneedforAmericato“occupyapositionofpre-eminence”sothatwecansteertheoutcome,directlyappealingtohisaudience’ssenseofresponsibilityandpatriotism.
• JFKrepeatedlydiscussesthat“wechoosetogotothemoon”notbecauseitiseasybutbecauseitishard.Hediscussesthatitwillbe“themosthazardousanddangerousandgreatestadventureonwhichmanhaseverembarked.”
• JFKuseswordslike“setsail”and“furthestoutpost”and“oldfrontieroftheWest.”Thesewouldappealtotheadventurousspirit.
• JFKtellshislistenersthatthereisknowledgetobegainedfor“allpeople,”andthatspaceis“hostiletousall.”Thatwouldeffectivelypullpeopletogetherandinspireunity.
• JFKdiscusses“Riceplay[ing]Texas”asanexampleofsomethingthatishard,butisdoneanyway.(HereheisreferringtotheirfootballteamscompetingsinceTexashistoricallyhasagoodfootballteamandRice,notsomuch.)Pride!Goteam!
• JFKasksfor“God’sblessingonthe…adventure.”Christianvalues.
2. AppealtoLogic:WhatdoesPresidentKennedysaytoappealtohisaudience’slogicandreason?
• Hemakesareferenceto“35yearsago,fly[ing]theAtlantic.”Thisshowstheaudiencethattherehavebeenthingsinthepastthatwefeltwereimpossibleanddangerousthatarenowcommonplacetous.FlyingacrosstheAtlanticOceanisalogicalcomparisontospacetravel.
• Hediscusseshow“scienceandeducationwillbeenrichedbynewknowledge”aswellasmanyotherreferencestothebenefitsofspacetravelandspacescienceincludingtoRiceUniversityspecifically.Byshowingthebenefitstothescientificcommunity,hegivespeopleanunderstandingthatthebenefitsareworththerisksandcosts.ItalsogivesthemapersonalstakeinthedecisionforanythatworkorattendRiceUniversityinthesciencefields.
• Hereassurestheaudiencethatwewillnot“gounprotected.”Thismakeshisaudiencefeelasifitisnotahastyandunreasonablyunsafedecision.Appealstothosethatmightbedubioustowardtheprospectofspaceexploration.
• Hementionshowmanyjobshavealreadybeencreatedandhowtheregionandthestatewillflourishas“theheartofalargescientificandengineeringcommunity.”Thelong-termbenefitstotheHoustonareaareclearlypositiveoutcomes.
ReadingandAnalysisDrillTheanswersbelowareonlypossibleanswers;theyarenottheonlycorrectones.
1. Thepresident’sappealstoemotionfillhislistenerswithasenseofparticipationinthe“adventure”thatisputtingamanontheMoon.Thelistenersarenotsimplylisteningtoagovernmentofficialexplainwhyhemadeadecision;theyaremadetofeelpride,unity,control,andpatriotism.Thepresident’swordsmakethelistenerfeelasifhe,asanAmerican,isbravefortakingthison.Thelistenerfeelslikeapioneerwhoisdoingwhathisancestorsbeforehimdid:exploringtheunknown.Thepresident’sappealstologicmotivatethelistenerstosupportthemissionbecauseofalltheprosperityitwillbringtheircommunity.First,thepresidenthelpsthemunderstandthatgoalsthathaveseemedasimpossibleinthepasthavebeenaccomplishedtoquellanydoubters.Then,hedetailsallofthewonderfulthingsthatwilltakeplaceinHoustonwhenthechangetakesplaceandformanyyearstocome.
2. HadthepresidentbeenspeakingtoaPortugueseaudience,itismuchlesslikelythattheywouldhavebeenexcitedaboutAmericanpatriotismorfeltanynostalgiafortheAmericanpioneeringheritage.Evenifthepresidenthadsimplybeeninanotherstate,allofthedetailsabouthowHoustonwillbenefitwouldnothavebeenaseffective.WhatdotheresidentsofCheyenne,Wyoming,careaboutjobsinHouston?
3. Thetoneofthispassageisinspiringanddetermined.Thepassagebeginswiththephrase“Wesetsailonthisnewsea,”whichconveystheideaofexplorationanddiscovery,connectingtheearliestexplorersandfoundersofAmerica.AlthoughKennedyacknowledgestheuncertaintysurroundingsuchaventure(exploringspace),histoneisconfidentandself-assured:“Idosaythatspacecanbeexploredandmastered”;“Wechoosetogotothemoon…anddootherthings,notbecausetheyareeasy,butbecausetheyarehard…”;“…weshallmakeupandmoveahead.”Finally,heendswithashortanecdoteabouttheBritishexplorerGeorgeMallory,whoexplainedhisreasonsforclimbingMountEverestassuch:“Becauseitisthere.”Kennedy’swordsareinfusedwithanadventurousspirit,aperseveranceinthefaceofchallenges,thatencapsulatesthephilosophicalunderpinningsoftheUnitedStates.
4. Whenthepresidentchosetousetheword“choose”inthefamousline“Wechoosetogotothemoon,”hewasmakingawisechoice.Orperhapsitwasthepresident’sspeechwriter—buteitherway,thiswordismorepowerfulthanhadhesaidsomethinglike“Weprobablyshouldgotothemoon”or“Wecantrytogotothemoon.”Thewordchooseputsthepowerofchoiceinthelistener.Whenpeoplebelievetheyarechoosingsomething(evenifaspeakertellsthemtheyarechoosingit),theyfeelempowered.Anotherexampleofdictionthatmadethespeechconvincingisthepresident’suseoftheword“adventure”inhisconcludingremarks.IndescribinghismissiontoputamanontheMoonasan“adventure”heavoidedthenegativedoubtsofsomelisteners.“Adventure”ispositiveandexciting.Hecouldhavesaid“weaskGod’sblessingonthe…mostexpensivedecisiononwhichmanhasembarked”or“onthe…overwhelmingtask,”bothofwhichwouldleavethelistenerwithasenseofcynicismoruncertainty.Therearelotsofgreatchoicesforconvincingdictioninthisspeech,soifyoufoundanotherexample,that’sgreat!
5. TheorderofKennedy’sspeechiscarefullyconstructedtoemotionallycaptivatethelistener.Thisisaskillthatpoliticalspeechwritersmusthave,ortheywillprobablynotkeeptheirjobsverylong.Kennedy’sopeningbringsthelistenersinbymakingthemfeelasifspaceexplorationistheirresponsibility(whichmakesthemcontinuetolistenearnestly).Themiddleofthespeechaddressesdoubtsandconcerns,whichreassurespeopleandmakesthemfeelasifKennedyisforthright.Theendingdiscussesthebenefitsthatthelistenerswillreapandwrapsupwithatieintoseveralpreviouslymentionedpoints,whichgivesthespeechaniceclosure.Inhislastsentence,KennedyentreatsGodforablessing,whichendsthespeechonahumblenote.Allofthesepiecesfittogetherinexactlythatordertoensurethatthelistenerwillfeelallofthosethings.IfKennedyhadbegunhumbleandendeddoubtful,thelistenerswouldgetthefeelingthathewasn’tveryconfident.
6. Thereisnocorrectresponsehereastherearemanypossibleanswers.Herearethreeoftheeffectivepartsofthespeechthatyoucouldwriteabout.However,ifyouwroteadifferentsetofthree,that’sfine.Youshouldpickwhicheverthreeseemedthemosteffectivetoyou.
1. Nostalgiaforthelistener’spioneeringheritage(AppealtoEmotion)
2. AddressingtheconcernthatAmericaisalreadybehindinthespacerace(AppealtoLogic)
3. Pointingoutthelocalbenefits(AppealtoLogic)
Summary◦ TheSATEssaymaybe“optional,”butyoushouldalwaysopttodoit—especiallyifyou’renotsure
whethertheschoolsyou’reapplyingtorequireit.It’sbettertobesafethansorry—andtositforanextra50minutesonceratherthanhavetositfortheentiretestasecondtimeafterfindingoutyouneedtheessaytoapplytoyourdreamschool!
◦ Theessayiscomprisedofthreeseparatetasksthatwillbescoredindividually:Reading,Analysis,andWriting.
◦ Theessaydoesnot requireyou toagreeordisagreewithapositionor towriteaboutapersonalexperience.Instead,youwillhavetoreadapassageandanalyzehowtheauthorbuildshisorherargument.
◦ ToscorewellontheReadingtask,youwillhavetobeabletoidentify(inyouressay)themainideaandsupportingdetailsofthetext.ThinkSOAPS:• Speaker• Occasion• Audience• Purpose• Subject
◦ To scorewellon theAnalysis task,youwill have tobe able to explain (inyour essay)how theauthorusesspecificstyleelementsandrhetoricaldevicestocreateaneffectiveargument.
◦ Whilereadingandanalyzingthepassage,youshouldalsothinkaboutwhethertheauthormakesanykindofappeal(tocredibility,emotion,orlogic)tohisorheraudience.
Chapter19WritingtheEssayAlright!You’veannotated,you’veSOAPS’ed,you’vemadeconnections,andnowyouactuallyhave towritetheessay!Inthischapter,we’llgothroughthebasicpartsofaneffectiveessayandprovideessaywritingtips,abunchofsampleessays,andsomefeedbackfromourSATexperts.
TASK3:WRITINGThepreviouschaptercoveredthefirsttwotasksrequiredtodevelopyouressay:ReadingandAnalysis.Nowweturntothethirdandfinaltask:writingtheessay.AccordingtoETSandtheCollegeBoard,yourWritingscorewillbebasedonwhetheryou
• makeuseofacentralclaim• useeffectiveorganizationandprogressionofideas• usevariedsentencestructures• employprecisewordchoice• maintainconsistent,appropriatestyleandtone• showcommandoftheconventionsofstandardwrittenEnglish
Thisisalsowhereyoushowyourgraderthatyouhaveread,understood,andanalyzedthetext.
SATESSAYTEMPLATE
IntroductionYourintroductionneedstodothreethings:
1. Describethetext.Thisiswhereyou’llbringintheSOAPSpoints.Thiscanbedoneinonesentence.
2. Paraphrasetheargument.Thisiswhereyou’llshowyourgraderthatyouunderstandthetextbyconciselysummingupthemainpointsandtheoverallmessageofthetext.TheReadingscorecomesfromyourdemonstrationofcomprehensionofthetext.
3. Introducetheexamplesyouwillbediscussinginthebodyparagraphs.Youwillestablishaframeworkinyourintroductionthatyoushouldthenfollowfortherestoftheessay.
BodyParagraphsThe body paragraphs will focus on different appeals or style elements the author uses to effectivelycommunicatetheargument.Eachbodyparagraphwillneedtodothefollowing:
1. Nameandexplaintherhetoricaldeviceorappeal.• Whereisitinthetext?
• Useshort,relevantquotestoshowyouunderstandthetextandtherhetoricaldevice,butdonotrelyonlongexcerptsfromthepassage.Inordertogetahighscore,youneedtouseyourwordstoexplainwhat’sgoingon.
2. Identifytheeffectsoftheauthor’srhetoricalchoices.• Explaintheconnectionbetweentherhetoricaldevice/appealandthetext,andyourargumentin
general.Donotsimplyquotechunksoftextandthenbrieflyparaphrase.Yourgoalistoanswerthequestion,“Howdoesthiscontributetotheauthor’sargument?”
• Forexample,donotsimplysay,“Thisisanexampleofimagery.”Explainwhytheimageryiseffective.Perhapstheauthor’sdescriptionsofthebeautifulsunseteffectivelydrawinthereader,creatinganemotionalconnectionbetweentheauthorandheraudience.Thisconnectionmaymaketheaudiencemoresympathetictotheauthor’ssubsequentpointsbecausethereisanemotionalconnectionnow.
• Explaininghowthedeviceorappealworksishowyoushowyourgraderyourabilitytoanalyzethetext.
Conclusion1. Restatethegoalofthetextandbrieflyparaphrasetheelementsyoudiscussedinyouressay.2. Beconciseandaccurate.
SATEssayWritingTips
• Maintainformalstyleandobjectivetone.Avoid“I”and“you.”Donotuseslang.• Usevariedsentencestructure.• Writeneatly.• Usecleartransitions.• Useshort,relevantquotesfromthetext.• Don’tworryaboutofficialtermsforthings.“Appealtoemotions”isfineinsteadof
specificallyreferencing“pathos,”and“comparisonoftwothings”canbeusedinsteadofreferringtoametaphor.Ifyoudoknowtheofficialterms,though,feelfreetousethem!
EssayWritingontheSAT
Employingthesetechniquesinyouressaywill
helpboostyourscore!
SAMPLEESSAYSLet’stakealookatafewfinalproductsforthepromptintroducedinthepreviouschapter.(Seethispage.)Besuretonoticewhatscorestheyreceivedandwhy.
Note:Youcanfindblankessayanswersheetsinyouron-linetoolsthataccompany
thisbook.Justregisteryourbook(see
“RegisterYourBookOnline!”)tounlockyourStudentTools,andthendownloadandprintthe
forms.(Forgoodmeasure,we’vealsoincludedextra
bubblesheets.)
SampleEssay1
InhiseloquentspeechatRiceStadium,former-PresidentKennedywieldsavastarrayoforatorytoolsandconstructsacaseforinvestmentinspaceexploration.Throughouthisaddress,Kennedymakesuseofevidence, reasoning,andstylisticelementsthattogetherformhisargumentforthedecisionthattheUnitedStatesshouldbecomeadominantforceinthenewfieldofspaceexploration,andattempttoreachthemoon.
Kennedybeginshisaddresswithananalogyofspaceexplorationasa“newsea,”whichheeffectivelycontinues by referring to the possible future of space as “whether this new ocean will be a sea ofpeace,”andrevisitsinhisfinalpleafordivineblessing“aswesetsail.”Theoceanisnottheonlynaturalanalogy utilized by Kennedy in his speech, for he also makes use of references to mountaineeringthroughthe rhetoricalquestion “whyclimbthehighestmountain,”aswellasquotingGeorgeMallory’sstatedreasonfortheexpeditionupMountEverest: “Because it is there,”andstatingthat “space isthere, and we’re going to climb it.” Beyond natural analogies, Kennedy paints with colorful language,suchasspeakingof“thefiresofwar,”“reaptheharvest,”the“infancy”ofspaceexploration,andoldHoustonas“thefurthestoutpostontheoldfrontier.”Kennedyalsoappealstothelocalityinwhichhespeaksbyasking“WhydoesRiceplayTexas?”andreferencing“yourCityofHouston.”
Kennedy’saddressmakesusenotonlyofcreativelanguage,butalsoofpiecesofevidence.Theprimaryevidencewithwhichheappealsisalistofbeneficialeconomicresultsofspaceexploration.HespecifiesthattheareaofHoustonwillsee“doublethenumberofscientistsandengineers,”bearanincreasein“salaries and expenses to $60 million a year,” receive investments of “some $200 million in plant andlaboratoryfacilities,”andbethesourceoffunds“fornewspaceefforts[of]over$1billion.”Inadditionto economic gains, Kennedy mentions a long list of educational boons such as “new knowledge of ouruniverseandenvironment,” “newtechniquesof learningandmappingandobservation,”and“newtoolsandcomputersforindustry,medicine,thehomeaswellastheschool.”
MixedamongtheevidentialandrhetoricalcomponentsofKennedy’saddressarethreadsofreasoning,whichdisplaythethoughtprocessbywhichKennedysupportshisappealfornationalmovementtowards
theexplorationofspace.Kennedyprovidesmanyreasonsforthedecision,includingtheuniversalappealof“newknowledgetobegained,andnewrightstobewon.”SomeoftheotherexplanationsKennedyprovides for the decision include that “space science…has no conscience of its own,” that the“opportunityforpeacefulcooperationmaynevercomeagain,”andthatspaceexplorationisworthdoing“because[itis]hard,”which—whileapparentlyparadoxical—Kennedyexplainsaswell-reasonedsince“that goal will serve to organize and measure the best of our energies and skills.” He incorporatesadditionalthoughtfulelementsashediscussesthatwhile“wearebehind,…wedonot intendtostaybehind,andinthisdecadeweshallmakeupandmoveahead.”
Through these variable forms of evocative language, supportive evidence, and sound logic, formerPresidentKennedyforgesanappealtohisaudiencethatiswell-roundedandsubtlysculptedintoanaddressthatexemplifiestheoratoryskillforwhichhewaswellknown.
ScoreReading:8Analysis:4Writing:8
SAT Experts Say: This essay contains a very impressive summary of the argument, but very littleanalysis.Itisclearthatthisstudentcanidentifythestylisticelements,butheorshedoesnotdiscusstheirimpactonthereaderorwhytheauthorusesthem.
APerfectScoreAsyoureadthissampleessay,takenoteofhowthestudentappliesthe
writingtipsfromthispage.
SampleEssay2
Thepowerful impactofPresidentKennedy’s speechatRiceStadiumonthecontroversialdecision todirectmoneyoftheUnitedStatestowardsbuildingapreeminentspaceprogramliesintheeloquenceand universality with which he weaves his appeal. Through analogies as well as acknowledging andaddressing the concerns of those dubious towards the idea of space exploration, Kennedy crafts apersuasiveargument,solidifiedbyreferencestopriorexplorationsanddetailsofeconomicincentives.
Perhaps the most necessary element which distinguishes a well-formulated argument from a mereexercise of rhetoric is the proper use of supportive evidence, of which President Kennedy’s addressincorporatesseveralexamples.Thefirstexampleheutilizes issubtle,butpowerful.TheUnitedStateshadinvestedsignificantlyinthedevelopmentofnucleartechnology,andpartoftheargumentforthat
investmenthadbeenthatnucleartechnologycouldbeusedbytheUnitedStatesforitsownbenefitandprotection,oragainsttheUnitedStatesbyforeignnationswhomayintendharm.ThatargumenttranslatesclearlytospaceaswellinKennedy’swordsthat“Whether[spacesciencebecomes]aforceforgoodorilldependsonman,andonlyiftheUnitedStatesoccupiesapositionofpre-eminencecanwehelpdecide[thefutureofspace].”AfurtherpieceofevidenceKennedyusestosupporthisargumentistheexampleofflightacrosstheAtlantic.PresidentKennedyremindshisaudienceofthiseventinordertoreferenceapreviousaccomplishmentthathadalsooncebeenseenasprohibitivelydifficult,muchaspracticalexplorationofspacewasseenbymanyin1962.Inhisaddress,Kennedyalsoutilizesanotherevidentiarycategory,fillingthesecondhalfofhisspeechwithalotofspecificeconomicbenefitsforthe area surrounding Houston from the newly bolstered space program as it develops, designed tooverwhelmthelistenerwiththispositivesideofinvestment.
Kennedy’smasteryofpersuasiverhetoricplaysoutnotonlyintheevidencetowhichherefers,butalsointheanalogieswoventhroughhisaddress,whichservetoevokeemotionalresponsesinhislisteners.Theinitial words of Kennedy’s address provide the first of these analogies. Rooted in the history ofexploration,Kennedystatesthat“Wesetsailonthisnewsea.”Aformofevidenceinitself,thisanalogyservestorecallthe listener’smindtoafrontierthatwasonceseenasunfathomablyexpansiveandbeyondhumanmastery.Kennedycontinuestheseaanalogybysayingthatspacemaybecome“aseaofpeaceoranewterrifyingtheaterofwar,”callingtothelistener’smindtheunpredictablenatureoftheseaitselftobecalmorhorrifyinglyvolatile,ashesuggeststhatthepositionoftheUnitedStatesinspaceexplorationmaydecidethenatureofthisnewfrontier.Kennedyalsoreachesfurtherbackintothehistoricalcommonality ofhis listenersasheanalogouslydescribesHoustonas “oncethefurthestoutpostontheoldfrontieroftheWest”inordertocallthelistener’smindtothenatureofchangeovertime.TheHoustoninwhichKennedygavethisspeechlookedessentiallynothingliketheHoustonoftheoldWest,andthisanalogyprovokesthelistener’simaginationtoprojectthepossibilitiesforanewHouston,builtonastrongspaceprogram.AthirdanalogywithwhichKennedyappealstohislisteners’emotionsisthereferencetotheirlocalsportsteam.AsKennedyasks“WhydoesRiceplayTexas?”heseekstoraisethe ubiquitous sense of pride many feel for their sports teams of preference, which he hopes maytranslatetoasenseofnationalprideforthespaceprogram.
Asmostanywell-craftedargumentwilldo,Kennedyalsoacknowledgestheargumentsofthosewhomayholdacounter perspective.Byasking “Butwhy, some say, themoon?”Kennedy introducesa potentialcounterargumentthatthegoalofreachingthemoonmaybearbitrarilylofty.Ratherthandismissingthispointasirrelevant,Kennedyseekstodisarmitbyembracingtheloftynatureofreachingthemoonandcallingattentiontootherloftygoalsdeemedworthwhile,suchasto“climbthehighestmountain”and “fly the Atlantic.” He continues to acknowledge the nature of this potential objection by sayingthat the goal has been chosen “because [it is] hard,” and therefore will “serve to organize andmeasurethebestofourenergiesandskills.”AnotherpossiblecounterargumentKennedyaddresses isthat “we are behind…in manned flight.” Again, Kennedy could have easily attempted to dismiss thisargumentby protestingthatthegap is small,buthe insteadchoseagaintoaffirmtheobjectionbystating “we…will be behind for some time.” Having fully acknowledged the strength of this potentialproblem,KennedythenproceedstodescribetheprecisemeansbywhichtheUnitedStates“shallmakeup and move ahead” through “new knowledge,” “new techniques,” and “new tools,” which Kennedyseamlesslyseguesintoeconomicbenefits,asdescribedabove.
ThedifficultyofdissectinganaddresslikethatofPresidentKennedyatRiceStadiumisitselfafinalexampleofthepersuasivenessofKennedy’srhetoric.ThepowerofKennedy’saddresscanbeseenmostclearlyintheinterwovennatureofallitselements.Throughthemarriageofthesedifferentelements,Kennedy’sspeechencourages,calms,andinspires.
ScoreReading:8Analysis:8Writing:8
SATExpertsSay:Thisstudentshowsaclearunderstandingofthetextandwritesasolidpieceanalyzingtheauthor’sargument.HeorsheindicateswhatKennedydoes(ex:“fill[s]thesecondhalfofhisspeechwith a lot of specific economic benefits”) and then tells us why Kennedy did it (“to overwhelm thelistenerwiththispositivesideofinvestment.”)ThisistheanalysisthatwaslackinginSampleEssay1which,combinedwithgoodcomprehensionandsolidwritingskills,earnedthisessayaperfectscore.
SampleEssay3
Kenedygaveaspeechaboutgoingtothemoon.It’sgotalotofstylisticelementsinit.Hiswholespeechisabouthowdangerousitisandhowweshoulddoitbecauseit’sdangerous.Hesaysit’slikeEverestandthat’shardanditkilledaguywhotriedtodoitbutweoughtadoitanyway.Atthebeginninghesaiditwaslikegoingtoseaanditwouldbedangerousbecauseofhostilepiratesorsomething.Andthatit’slike Rice playing Texas. So maybe he could of meant we should do hard stuff even though you’llprobablyloseordie.Alsohesaidit’sliketheOldWest.Ithinkmaybewelikepeopletryingdothingsthataredangerous,somaybethat’swhypeoplelikethisspeechsomuch.
ScoreReading:2Analysis:4Writing:2
SATExpertsSay: This student demonstrates practically no comprehension of the passage.The essaydoesnotpresentanargument,but rathermakesgeneral statementsabout theessay thatdonothaveanyrelevance to the prompt. In addition, the essay is sloppily written, including several spelling andgrammaticalerrors—“Kenedy,”“oughta,”“couldof,”andsoon.The tone is too informal (“becauseofhostile pirates or something,” “we oughta do it anyway”), and thewriting is disorganized; there is nologicalprogressionofideas.Thisessaywouldreceivealowscore.
SampleEssay4
In1962,PresidentJohnF.Kennedydeliveredastirring,poeticspeechatRiceStadium.Hestructuredhisaddressusingcomplexrhetoricaldevicesthatmakeitanexemplarfortheages.Inparticular,hespoke
inadirect,simplemannerthatwasveryaccessibletohisaudience,butlayeredthatsimplespeechwithcomplexrhetoricalflourishessuchasalliteration,anaphora,andepistrophethroughout.Asaresult,theaddresscreatedapleasingauditoryeffectthatkepttheaudienceengagedthroughoutthespeech.
Beginning with his first words, and continuing throughout the address, President Kennedy usedalliteration to capture the attention and the mood of his audience. In the first paragraph alone,Kennedyreferencessettingsailonthenewsea,feedingthefiresofwar,andthemistakesthatmanhas made. Like a newspaper headline or song lyric, these phrases have a rhythm that make themcatchy and memorable and demands the attention of the audience. At key lines the speech evensettlesintoaniambicrhythmbeforereturningtoablankprosestyle.
ThepleasingrhythmofKennedy’saddress isalsosignificantlyenhancedbyhisuseofanaphoraandepistrophe (also referred to as anadiplosis). Kennedy frequently employs anaphora—the repetition ofbeginning words in parallel phrases—at key points throughout his speech, and practically in everyparagraph. In the first paragraph he repeats the phrase “I do”; in the second, rhetorical questionsbeginningwitharepeated“why”;inthethird,“wechoose”repeated,followedby“because”repeated,followed by “one” repeated; and so on. And as he closes the speech, Kennedy uses epistrophe, thecomplementarydeviceinwhichawordorphraseisrepeatedattheendofsuccessiveparallelclauses,noting that various things “are there.” This repetition of phrases has a very powerful effect on thelistener,becausethephrasesaresomemorablewhenrepeated,subconsciously leadingthelistenertoconcludethatthepointbeingarguedmustbeveryimportant.
Through his use of evocative language, President Kennedy devised a speech that has a powerfuleffectonhisaudience.Thecombinationofplainlanguagewithrhythm,repetition,andrhetoricevincesKennedy’smasteryoforatoryandmakeshisaddressliveonthroughtheages.
ScoreReading:2Analysis:6Writing:6
SATExpertsSay:Themainproblemwiththisessay,asreflectedinthescoresabove,isthatthestudentfails to showwhether he or she actually understood the speech and its central ideas. The essay lacksinterpretation of the content of the speech itself, focusing only on its rhetorical devices. Although theessaydoesagood jobof identifying thesedevices, thediscussiondoesnotpoint to thepurposeof theessay; in otherwords, the student does not sufficiently explain how those devices are used to supportKennedy’s specific claims. However, the essay demonstrates solid writing skills and offers a decentanalysisofthestylisticdevicesandothertechnicalelements.
SampleEssay5
In1962,JohnF.Kennedygavean inspiringspeechatRiceStadiumdesignedtoconvincehisaudiencethat space exploration was worth the risk, expense, and commitment that would be required. Heemployedavarietyofrhetoricaldevicesincomposingacomplexandpowerfulmessage.
OneprominentfeatureofPresidentKennedy’sspeechwas itsuseofsimileandmetaphor. Inthefirstparagraph,Kennedybeginsbycomparingthemissiontothemoontoanoceanvoyage,implicitlycomparingspaceexplorationtothediscoveryofAmerica.Hebeginsbystatingthatwe“setsailonthisnewsea,”andelaboratesbyemphasizingthattheUnitedStatescanuse its powertohelpdeterminewhetherthat “new ocean” will be a “sea of peace” or rather a dangerous mistake. He continues to makemetaphoricalcomparisonsbyposingrhetoricalquestionsaboutclimbingamountainandmakingatrans-Atlanticflight—pastexamplesofonce-impossibletasksthatwereunder-takenandachievedthroughhardworkandperseverance.
AnotherimportantfeatureofKennedy’sspeechishisuseoffactsandsupportingevidencetobolsterhisargument.Kennedyacknowledgesthatwe“willbebehindforsometime inmannedflight,”butaversthat we “shall make up and move ahead.” He follows this claim with specific supporting evidence. Hebeginsbydiscussing scientificadvancements inknowledgeandtechnologythathebelieveswillallowtheUnitedStatestoachievethisgoal.Hethengoes intodetailaboutthepositiveeconomiceffectsthatwillbebroughtaboutbytheinvestmentinthespaceprogram,andtiesthesefactstotheoverallthemeoftheessaybyanalogizingspaceexplorationtothesettlementofthewesternUnitedStates:hedescribesHoustonas“oncethefurthestoutpostontheoldfrontieroftheWest”andimaginesitastheheartofanewtechnologicalcenter.
AthirddeviceusedbyKennedyisreferencetolocalevents,history,andprideashespeaksinHouston.By asking “Why does Rice play Texas?”, Kennedy humorously plays on the long-time football rivalrybetweenthefootballteamsbyputtingitinthesamecategoryasthefirsttrans-Atlanticflight.Later,hespecificallydescribesplanstoinvestinadvancedtechnologyatRice,aswellasthecityofHouston(“yourCityofHouston”),theregion,andthestateofTexasasawhole.
By using these techniques of analogy, supporting evidence, and reference to local facts and history,Kennedy created a very complex and interesting speech. While many of his other speeches may bebetterknown,thisspeechisanexcellentexampleofthedepthofhisrhetoricalskill.
ScoreReading:6Analysis:4Writing:6
SATExpertsSay: This is a solid essay that demonstrates sufficient comprehension of the speech, itscentral ideas,and importantdetails, and thatusesevidence from thespeech to support itsargument. Inaddition,theessayfollowsaclear, logicalprogressionofideasandshowseffectiveuseoflanguageinwriting.Thereisalsoaclearintroductionandconclusion.However,thisessaywouldlosepointsintheAnalysis category, as the student doesn’t go far enough in explaining the importance of the speech’sfeatures.
SampleEssay6
Thisspeechisabouthowweshouldgotothemoon.Hestartsbytalkingabouthowit’slikeanoceanand
itcouldbeahostiletheaterofwar,soweshouldprotectourselveswhenwesetsailinspace.
InthenextparagraphhesaysthatspaceislikeclimbingamountainorlikeRiceplayingTexas.Iguesshe’stryingtomakeajokewiththeaudience,becauseRicealwayslosestoTexas,butthat’snotaverysmartthingtocomparegoingtospaceto.
Nexthe’salllikeitwillbesoharditwillbetogotospace.Andwe’llbebehindforalongtimeandthenahead.Mr.Negative,right?Thatdoesn’tmakemewanttodoit.
Thenspendsalotoftimetalkingaboutbusinessindustriesandmoneystuff.Boring.
Finally,hesaysweshouldgotothemoonbecauseit’sliketryingclimbamountain.Thismakesnosensebecausehesaidearlieritwaslikesailing,andalsobecausewhywouldwewanttobeliketheguywhodiedtryingtoclimbamountain?Iguessit’sacoolideathoughsoweshouldtrytodoit,butheshouldhavejustsaidthatinstead.
ScoreReading:4Analysis:2Writing:4
SATExpertsSay:Thisisveryweakessay.Thoughtheessayshowsaverybasicunderstandingofthespeech,itdoesnotpresentacase,containanalysis,orrespondtothepromptinanyway.Whilethetoneisveryinformalandevenflippant,thewriting(technicallyspeaking)ismostlyerror-free,whichmightearntheessayafewWritingpoints.Overall,though,theessayissloppy,lacksfocus,anddoesnotmakeanypoint.
Summary◦ Writing, the third and final task of the SAT Essay, is about putting all your ideas together in a
coherent,well-writtenessay.
◦ The essaywill not require you towrite about a personal experience or give your opinion on acertain topic. This essay is a technical analysis of an argument, not your opinion about thatargument.
◦ InordertogetagoodscorefortheWritingtask,youshouldmakeaclaimandbeabletosupportitwith evidence from the passage. You should also organize your thoughts in a coherent, logicalmanner,andshowcommandofstandardwrittenEnglishbyvaryingyourwordchoiceandsentencestructure.
◦ Besurethatyouressayhasthethreekeyparts:introduction,bodyparagraphs,andconclusion.Yourintroductionshoulddescribethetextandparaphrasetheargumentbeingmade,aswellasintroducethespecificelementsofthepassageandargumentthatyouwilldiscussintheessay.Yourconclusionshouldrestatethegoalofthepassage/argumentandsumupthepointsyoumade.
◦ Keepanalysisinmindasyouwriteyouressay.Youshouldnotmerelydescribeatext,butexplainhowthattextiswrittenandstructuredtoaccomplishacertaingoal.Andremember,citeevidence!
THESATISAWEEKAWAY—WHATSHOULDYOUDO?Firstofall,youshouldpracticethetechniqueswe’vetaughtyouonlotsofpracticetests.Ifyouhaven’tdone so already, take and score the practice tests in this book and online. You can also download apracticetestfromtheCollegeBoard’swebsite,www.collegeboard.org.
Ifyouwantmorepractice,pickupacopyofourveryown9PracticeTests for theSAT atyour localbookstoreorthroughourwebsite,atPrincetonReview.com/bookstore.
PerfectYourSkillsInadditiontotakingthe
practicetestsinthisbook,youshouldregisteryour
book(See“RegisterYourBookOnline!”)togainaccessto
evenmorepractice,aswellasotherfantasticresourcestoenhance
yourprep.
GettingPsychedTheSATisabigdeal,butdon’tletitscareyou.Sometimesstudentsgetsonervousaboutdoingwellthattheyfreezeuponthetestandruintheirscores.ThebestthingtodoistothinkoftheSATasagame.It’sagameyoucangetbetterat,andbeatingthetestcanbefun.Whenyougointothetestcenter,justthinkaboutallthosepoorstudentswhodon’tknowhowtoPlugInwhentheyseevariablesintheanswerchoices.
The best way to keep from getting nervous is to build confidence in yourself and in your ability torememberanduseourtechniques.Whenyoutakepracticetests,timeyourselfexactlyasyouwillbetimedontherealSAT.Developasenseofhowlong35minutesis,forexample,andhowmuchtimeyoucanaffordtospendoncrackingdifficultproblems.Ifyouknowaheadoftimewhattoexpect,youwon’tbeasnervous.
Of course, taking a real SAT ismuchmore nerve-racking than taking a practice test. Prepare yourselfaheadoftimeforthefactthat35minuteswillseemtogobyalotfasteronarealSATthanitdidonyourpracticetests.
It’sallrighttobenervous;thepointofbeingpreparedistokeepfrompanicking.
VegOutAlthoughpreparationiskeytodoingwellonthe
test,youshouldn’texhaustyourselftryingtocraminformationintoyour
head.Takesomebreaksbetweenstudysessionsto
relax,unwind,andrestyourmind.
ShouldYouSleepfor36Hours?SomeguidancecounselorstelltheirstudentstogetalotofsleepthenightbeforetheSAT.Thisprobablyisn’tagoodidea.Ifyouaren’tusedtosleeping12hoursanight,doingsowilljustmakeyougroggyforthetest.Thesamegoesforgoingoutallnight:Tiredpeoplearenotgoodtesttakers.
A much better idea is to get up early each morning for the entire week before the test and do yourhomeworkbeforeschool.Thiswillgetyourbrainaccustomedtofunctioningatthathourofthemorning.Youwanttobesharpattesttime.
Beforedinnerthenightbeforethetest,spendanhourorsoreviewingordoingafewpracticeproblems.Thegoalhereistobrushuponthematerial,nottoexhaustyourselfbyover-cramming.
Furthermore…Hereareafewpointersfortestdayandbeyond:
1. Eatagoodbreakfastbeforethetest—yourbrainneedsenergy.2. WorkoutafewSATproblemsonthemorningofthetesttohelpdustoffanycobwebsinyour
headandgetyoustartedthinkinganalytically.3. Arriveatthetestcenterearly.Everyoneisheadedtothesameplaceatthesametime.4. Youmusttakeacceptableidentificationtothetestcenteronthedayofthetest.Acceptable
identificationmustincludearecognizablephotographandyourname.AcceptableformsofIDincludeyourdriver’slicense,aschoolIDwithaphoto,oravalidpassport.Ifyoudon’thaveanofficialpieceofIDwithyoursignatureandyourphoto,youcanhaveyourschoolmakeanIDforyouusingaStudentIDformprovidedbytheCollegeBoard.CompleteinstructionsformakingsuchanIDarefoundontheCollegeBoard’swebsiteandintheStudentRegistrationBookletfortheSATandSATSubjectTests.AccordingtoETSandtheCollegeBoard,thefollowingformsofIDareunacceptable:abirthcertificate,acreditcard,oraSocialSecuritycard.MakesureyoureadalloftherulesintheStudentRegistrationBooklet,becauseconflictswithETSarejustnotworththeheadache.YouronlyconcernonthedayofthetestshouldbebeatingtheSAT.Toavoidhasslesandunnecessarystress,makeabsolutelycertainthatyoutakeyouradmissionsticketandyourIDwithyouonthedayofthetest.
#1:EatBreakfastYou’llworkbetterona
satisfiedstomach.
#2:TrySomeProblemsGetyourmindmoving.
#3:ShowUpEarlyLeavetimefortraffic.
#4:TakeIDAdriver’slicense,apassport,ora
schoolphotoIDwilldo.
5. TheonlyoutsidematerialsyouareallowedtouseonthetestareNo.2pencils,awristwatch(anabsolutenecessity—remember,nocellphonesallowed!),andacalculator.Thelatestruleisthatmechanicalpencilsarenotallowed.We’renotsurewhy,butyoushouldtakelotsofsharpenedwoodenNo.2pencilsjusttobesafe.Digitalwatchesarebest,butifithasabeeper,makesureyouturnitoff.Proctorswillconfiscatepocketdictionaries,wordlists,portablecomputers,andthelike.Proctorshaveoccasionallyalsoconfiscatedstopwatchesandtravelclocks.Technically,youshouldbepermittedtousethese,butyoucannevertellwithsomeproctors.Takeawatchandavoidthehassles.
#5:TakeEquipmentAfewsharpened
No.2pencils,awatch,andacalculator.
6. Someproctorsallowstudentstobringfoodintothetestroom;othersdon’t.Bringasnacklikeabanana,whichissuretogiveyouanenergyboost.Saveituntilyourbreakandeatoutsidethetestroom.
#6:TakeFruitorOtherEnergyFood
Grapesororangescangiveyouanenergyboost
ifyouneedit.
7. Youaregoingtobesittinginthesameplaceformorethanthreehours,somakesureyourdeskisn’tbrokenorunusuallyuncomfortable.Ifyouareleft-handed,askforaleft-handeddesk.(Thecentermaynothaveone,butitwon’thurttoask.)Ifthesunisinyoureyes,asktomove.Iftheroomistoodark,asksomeonetoturnonthelights.Don’thesitatetospeakup.
#7:YourDesk…shouldbecomfortable
andsuitedtoyourneeds.
8. Makesureyourbookletisprintedlegibly.Bookletssometimescontainprintingerrorsthatmakesomepagesimpossibletoread.Oneyearmorethan10,000studentshadtoretaketheSATbecauseofaprintingerrorintheirbooklets.Also,checkyouranswersheettomakesureitisn’tflawed.
#8:YourTest…shouldbeprinted
legiblyinyourbooklet.
9. Makesureyoudarkenallyourresponsesbeforethetestisover.Atthesametime,eraseanyextraneousmarksontheanswersheet.Astraymarkinthemarginofyouranswersheetcanresultincorrectresponsesbeingmarkedaswrong.
#9:BubblewithCareAstraymark
canhurtyourscore.
10. YoudeservetotakeyourSATundergoodconditions.Ifyoufeelthatyourtestwasnotadministeredproperly(thehighschoolbandwaspracticingoutsidethewindow,oryourproctorhoveredoveryourshoulderduringthetest),don’thesitatetospeakup.
#10:We’reHereforYouThePrincetonReviewisproudtoadvisestudentswhofeeltheirexamwas
notadministeredproperly.
ReadingTest65MINUTES,52QUESTIONS
TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassageorpairofpassagesbelowisfollowedbyanumberofquestions.Afterreadingeachpassageorpair,choosethebestanswertoeachquestionbasedonwhatisstatedorimpliedinthepassageorpassagesandinanyaccompanyinggraphics(suchasatableorgraph).
Questions1–10arebasedonthefollowingpassage.
ThepassageisadaptedfromKirstinValdezQuade,“Jubilee.”Originallypublishedin2013.
1. ThemainpurposeofthefirstparagraphistoA) describeAndrea’slifestyle.B) explainthesourceofAndrea’sembarrassment.C) characterizethefarmworkers’vehicles.D) contrastAndrea’sstatuswiththatoftheotherguests.
2. InthecontextoftheconversationbetweenAndreaandMatty,Andrea’scommentsinlines12–16(“Itold…too”)mainlyservetoA) suggestthatthesourceoftheLowells’wealthshouldoffendMatty.B) emphasizetoMattythesizeoftheLowells’property.C) showMattythequalityoftheLowells’produce.D) informMattythatAndreaplanstoworkfortheLowells.
3. Asusedinline19,“adopters”mostnearlymeansA) embracers.B) parents.C) devices.D) admirers.
4. Theauthorusestheimageofsilkskirtsandsandals(lines25–26)mostlikelytoA) arguethattheguestswereimpracticalintheirchoiceofattire.B) reinforcetheideathattheguestsworefancierclothingthanmostpeople.C) highlightthedifferencesbetweentheguestsandtheusualworkers.D) provethatthegueststhoughttheywereofahigherclassthanthefieldworkers.
5. ItcanreasonablybeinferredfromthepassagethattheLowellsdidnotexpectAndreabecauseA) theLowellshadnotexplicitlyinvitedAndrea.B) Andreaneededanicercartoattend.C) theLowellsrequiredthateveryguestbeacompanyemployee.D) Andreawassupposedtobeawayatcollege.
6. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines31–33(“Butwhatever…thought”)B) Line35(“Rather,her…invited”)C) Lines35–37(“Butshe…come”)
D) Lines37–38(“Afterall…before”)
7. Thenarratorusestheword“exuberance”(line53)mainlytoemphasizeAndrea’sfather’sA) humility.B) courage.C) optimism.D) poverty.
8. WhichchoicebestsupportstheclaimthattheElPrimotacotruckwasnotassuccessfulasplanned?A) Lines7–10(“UsuallyAndrea…vindication”)B) Lines28–29(“You’dhave…him”)C) Lines46–48(“Andthere…yellow”)D) Lines60–63(“Herfather…hoped”)
9. ThepassagestatesthatAndrea’sparentsreactedtoreceivingtheLowells’invitationwithA) silence.B) delight.C) hurt.D) confusion.
10. Accordingtothepassage,whatdoesAndreahopetoachievebyattendingtheparty?A) Shehopestoassimilatetoherhosts’culture.B) Shewantstosupportherfather’sposition.C) Sheexpectstounsettletheotherguests.D) Sheplanstoshametheparty’shostsinfrontoftheirchildren.
Questions11–20arebasedonthefollowingpassages.
Passage1isadaptedfromMartinLutherKing,Jr.,“BirthofaNewNation.”Originallydeliveredin1957.Passage2isadaptedfromFrantzFanon,“TheWretchedoftheEarth.”Originallypublishedin1961.
D) alienate.
12. Thesentenceinlines28–29(“Andit’s…it”)primarilyserveswhichfunctioninPassage1?A) Itacknowledgesandcelebratesanalternativeplanofaction.B) ItcondescendstoandbelittlesacontemporaryofKing’s.C) Itdistractsandredirectstheaudiencetoanotherperspective.D) ItintroducesandqualifiesthecentralargumentofKing’sspeech.
13. Asusedinline30,“free”mostnearlymeansA) complimentary.B) liberated.C) exempt.D) able.
14. InPassage1,Kingcontendsthatnonviolentprotestleadstowhichresult?A) Itcausesdivisionsbetweencountries.B) Itcreatesfeelingsofemptinessandbitterness.C) Itmaintainsrelationshipsthroughtransitions.D) Itfailstoachievefreedomfromcolonialism.
15. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines4–7(“Ifthere…slavery”)B) Lines22–24(“hecould…revolt”)C) Lines44–45(“Theaftermath…bitterness”)D) Lines49–53(“Letus…sisters”)
16. InPassage2,FanonindicatesthatdecolonizationisaprocessthatisA) turbulentandcapableofchangingeverything.B) nonviolentandalwayssuccessful.C) primitiveandsomethingtobeavoided.D) naturalandabletobecontrolled.
17. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines60–61(“Theextraordinary…demanded”)B) Lines62–64(“Decolonization,which…disorder”)
C) Lines64–66(“Butit…understanding”)D) Lines71–72(“Thatis…successful”)
18. TheprimarypurposeofeachpassageistoA) presentahistoricaloverviewofrecentdemocraticrevolutions.B) provideasetofspecificguidelinestoincitearevolt.C) criticizetheactionsofthosewhoworkagainstthegoalsofthepeople.D) describeaneffectivewayforasocietytoworktowardsignificantchange.
19. Basedonthepassages,KingwouldmostlikelydescribethebehaviorthatFanonrecommendsinlines88–90(“Frombirth…violence”)asA) anacceptablealternativetopositiveaction.B) amisunderstoodculturaltemptation.C) anunnecessarymethodforachievingagoal.D) abravesteptakenbyanoppressedgroup.
20. Basedonthepassages,onecommonalityinthestancesKingandFanontaketowardrevolutionanddecolonizationisthatA) bothauthorsbelievetheprocesswillresultinradicalsocietalchange.B) bothauthorsrelyheavilyontheguidanceofearlierleaders.C) neitherauthoradvocatestheuseofviolence.D) neitherauthorsupportspeaceasameanstochangesociety.
Questions21–31arebasedonthefollowingpassage.
ThepassageisadaptedfromElsaYoungsteadt,“FreeUpgrades,Unfortunately.”©2006byAmericanScientist.
21. TheprimarypurposeofthepassageistoA) supportthefindingsofclassiclaboratoryexperimentation.B) assertthatcontroversialfindingsshouldcausealarm.C) presentconcernsraisedbytheresultsofastudy.D) criticizethemethodologyofanexistingstudy.
22. WhatdidthescientistsintheStanfordUniversitystudydiscoverabouttuberculosisbacteriathat“underminedthiscomfortingconventionalwisdom”(lines16–17)?A) Bacteriahaveshowntheabilitytoresistantibioticsthroughmutationwithoutlosing
strength.B) MycobacteriumtuberculosishasbecometheleadingcauseofdeathintheUnited
States.C) RNAandDNAinterchangeabilityintuberculosishasledtostrongerantibiotics.D) Rifampincannolongerbeusedtotreatdiseaseduetoproliferationofpolymerase
molecules.
23. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines35–36(“WithoutRNA…survive”)
B) Lines49–53(“TheStanford…infections”)C) Lines58–61(“Contraryto…ancestor”)D) Lines64–66(“Somechanges…occurs”)
24. Asusedinline26,“hardy”mostnearlymeansA) difficult.B) strong.C) terrible.D) thick.
25. Whichstatementaboutrifampincanbemostreasonablyinferredfromthepassage?A) ItstoppedtuberculosisfrombeingtheleadingcauseofdeathintheUnitedStates.B) Ithassuccessfullyinhibitedproteinproductioninbacteria.C) ItmakesRNAfortuberculosisbacteriacompatiblewithotherDNA.D) Itisthemosteffectiveknowntreatmentfortuberculosis.
26. Aspresentedinthepassage,theStanfordUniversitystudyreliedonwhichtypeofevidence?A) AnecdotalopinionB) SecondhandobservationC) AnimalstudiesD) Clinicaltesting
27. TheauthorindicatesthatpriortotheStanfordUniversitystudythescientistsgenerallybelievedthatantibiotic-resistantstrainsoftuberculosisA) hadabetterchanceofsurvivalthantheirantibiotic-susceptibleancestors.B) wouldonceagainbecomethemostdeadlyofdiseases.C) resultedinloweredamountsofsputuminthosetheyinfect.D) didnothaveasurvivalrateequaltothatofnon-resistantstrains.
28. Accordingtothepassage,SebastienGagneuxplanstoconductfurtherstudiestoanswerwhichofthefollowingquestions?A) Aremorevirulentstrainsoftuberculosislikelytocauseapanic?B) Dodrug-resistantbacteriacostmoretotreat?C) Howdoantibiotic-resistantbacteriacompensatefordeficienciescausedby
mutation?
D) Whyaresomestrainsofbacteriamorelikelytoresistantibioticsthanothers?
29. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines71–74(“Gagneuxis…mutations”)B) Lines79–81(“thespread…antibiotics”)C) Lines85–87(“Drug-resistantbacteria…now”)D) Lines88–89(“Thedrug-resistant…over”)
30. Theauthormentionsan“alarmistpanic”(line76)mostlikelyinordertoA) bringattentiontothethreatposedbyantibiotic-resistantbacteria.B) statethat19thcenturypublic-healthpracticeswereunabletohaltthespreadof
tuberculosis.C) identifytheinevitableresultoframpantsocietalantibioticabuse.D) drawacontrastbetweenanundesirableoutcomeandareasonableresponse.
31. Theprimaryfunctionofthefinalparagraph(lines84–91)istoA) reevaluatethehypothesisoftheStanfordUniversitystudy.B) provideawarningsupportedbyresultsoftheStanfordUniversitystudy.C) credittheStanfordUniversitystudywithchangingsociety.D) explainthemethodologyoftheStanfordUniversitystudy.
Questions32–42arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromTimCushing,“EncyclopaediaBritannica:CivilityintheFaceofAdversity.”©2012byInnovation.
32. ThemainpurposeofthepassageistoA) reviewattitudesinresponsetothechangingroleofanestablishedbrand.B) demonstratehowevolvingwithasenseofclassalteredtheencyclopediamarket.C) confrontthemisplacednotionthatdigitalencyclopediascausedmassiveupheaval.D) examinetheevolvingmechanismsbywhichencyclopediacompaniesadaptedto
includeDVDsandonlinematerials.
33. Asusedinline31,“doors”mostnearlymeansA) openings.B) operations.C) entrances.D) lights.
34. Accordingtothepassage,whichactionshouldlegacycompaniestakeinanunviablemarket?A) Theyshouldfocusonprovidingthebestpossibleproduct.B) Theyshouldgracefullyacceptthattheirproductsarenolongerrelevant.C) Theyshouldendeavortointegratenewbusinesspractices.D) Theyshouldeliminateobsoletemethodsandsystems.
35. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines8–12(“While…didn’tdo”)B) Lines34–36(“Britannicarealized…game”)C) Lines42–44(“Greensteinexplains…story”)D) Lines48–50(“Itstill…peak”)
36. Theextendedquotationinlines45–64ismostlikelyincludedtoA) illustrateanunusualresponse.B) condemncommonactivities.C) discusssuccessfultechniques.D) showfutileactions.
37. Accordingtothepassage,acompanyinachangingmarketshouldavoidA) changinganewproductintoanantiquatedform.B) reworkingitsproductsforalternativesocialclasses.C) maintainingflexibilityandunderstandingofnewtechnologies.D) attemptingtoclingtooutdatedsuccess.
38. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines18–19(“Itsold…salesmen”)B) Lines28–30(“ThenWikipedia…books”)
C) Lines65–68(“This‘evolving…fields”)D) Lines80–82(“It’sone…upheaval”)
39. Asusedinline83,“noises”mostnearlymeansA) sounds.B) screams.C) apologies.D) complaints.
40. Basedonthetable,itisverylikelythatwhatpercentofstudentswilluseanonlineencyclopediaasaresource?A) 2%B) 4%C) 19%D) 75%
41. Whichstatementisbestsupportedbythedatainthetable?A) ComparingprintedbooksandSweetSearch,teachersfeelthatstudentsaretwiceas
likelytoutilizeprintedbooks.B) ComparingonlinedatabasessuchasEBSCOandaresearchlibrarian,teachersfeel
thatsimilarpercentagesofstudentsareverylikelytousethoseresources.C) ComparingSparkNotesandonlinedatabases,teachersfeelthatmorestudentsare
verylikelytouseSparkNotes,andfeweraresomewhatlikelytouseSparkNotes.D) ComparingGoogleandtextbooks,Googleisafarsuperiorresearchtool.
42. ThedatainthetablemoststronglysupportstheclaimthatA) “[t]hiswasanexpensivewaytodistributeaproduct”(lines19–20).B) “Wikipediacamealongandateeveryone’slunchinthereferencesection”(lines28–
29).C) “whatBritannicadidn’tdoisperhapsthemostastonishingaspect”(lines43–44).D) “[t]heonceleadingfirmchangeditsorganizationalform”(lines46–47).
Questions43–52arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromJoeTurner,“FillUpYourGasTankwithBamboo?”©2015byScience.
43. ThepassageiswrittenfromtheperspectiveofanA) advocatearguingformoreprojectfunding.B) educatorexplainingtextbookchemistryconcepts.C) expertlaudingthesuccessesofanindustry.D) objectiveobserverevaluatingnewresearch.
44. Thelastsentenceofthefirstparagraphprimarilyservesto
A) assessrecentcommercialaccomplishments.B) explainwhyonefuelismoreexpensivethananother.C) proposeapotentialsolutiontoaknownproblem.D) restatetheresultsofabanneryear.
45. Accordingtothepassage,nonfoodcropsproducefewerindirectlanduseemissionsbyA) occupyinglandthatwouldotherwiseproducecorn.B) curtailingsuddenincreasesinfoodprices.C) limitingthefertilizerrequiredtoproducebiofuels.D) stoppingtheproliferationoffossilfueluse.
46. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines35–37(“Thesecrops…land”)B) Lines37–40(“Inan…straw”)C) Lines41–44(“Theenzymes…expensive”)D) Lines47–49(“Itis…year”)
47. Asusedinline37,“idealworld”mostnearlymeansA) best-casescenario.B) dreamsequence.C) perfectmodel.D) utopiansociety.
48. ItcanmostreasonablybeinferredfromtheresultsoftheIndianaUniversitystudyinvolvingZymomonasmobilisthatA) allbacteriacanfermentcornandtreesintofuel.B) totalgreenhousegasemissionswillremainunchanged.C) researcherswouldpreferbiofuelstobeusedasafoodsource.D) biofuelplantmaterialsarelessexpensivethannitrogenfertilizer.
49. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines59–63(“thebacterium…costs”)B) Lines64–66(“Theprocess…fertilizer”)C) Lines68–71(“Whereasusing…problems”)D) Lines73–75(“Evenif…crops”)
50. Asusedinline73,“slim”mostnearlymeansA) brittle.B) negligible.C) skinny.D) useless.
51. AccordingtoFigure1,inwhatyearistherequiredstatutoryvolumeofconventionalethanolclosesttothatofanotherfueltype?A) 2010B) 2012C) 2018D) 2022
52. AccordingtoFigure2,whichofthefollowingfuelsisleastlikelytomeetthevolumerequirementsshowninFigure1?A) Biomass-baseddieselB) CellulosicethanolC) ConventionalethanolD) Otheradvancedrenewablefuels
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
WritingandLanguageTest35MINUTES,44QUESTIONS
TurntoSection2ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassagebelowisaccompaniedbyanumberofquestions.Forsomequestions,youwillconsiderhowthepassagemightberevisedtoimprovetheexpressionofideas.Forotherquestions,youwillconsiderhowthepassagemightbeeditedtocorrecterrorsinsentencestructure,usage,orpunctuation.Apassageoraquestionmaybeaccompaniedbyoneormoregraphics(suchasatableorgraph)thatyouwillconsiderasyoumakerevisingandeditingdecisions.
Somequestionswilldirectyoutoanunderlinedportionofapassage.Otherquestionswilldirectyoutoalocationinapassageoraskyoutothinkaboutthepassageasawhole.
Afterreadingeachpassage,choosetheanswertoeachquestionthatmosteffectivelyimprovesthequalityofwritinginthepassageorthatmakesthepassageconformtotheconventionsofstandardwrittenEnglish.Manyquestionsincludea“NOCHANGE”option.Choosethatoptionifyouthinkthebestchoiceistoleavetherelevantportionofthepassageasitis.
Questions1–11arebasedonthefollowingpassage.
TheBaseBordenAquifer
Locatedabout60kilometersnorthwestofToronto,theaquiferattheBordenexperimentalsitehasbeenrepeatedlyexposedtoavarietyof 1 pollutants—since1978,researchershavebeenrunningcontrolledexperimentsinwhichtheyreleasepotentiallyhazardouschemicalsintothegroundwater.Oftenthesechemicalsintheaquifer 2 isexcavatedbeforeconcentrationscanreachdangerouslevels,butsomepollutantsareallowedfreemovementiftheresearchersdeterminethattheconcentrationswillultimatelydropbackintoanenvironmentallyacceptablerange.
1.A) NOCHANGEB) pollutants,since1978,C) pollutants:since1978—D) pollutants.Since1978:
2.A) NOCHANGEB) areexcavatedC) excavateD) wasexcavated
3 Thisprocessmayseemobjectionable,buttheexperimentsprovidevaluableinsightsintothebehaviorofsomeofthemostdangerousandprevalentgroundwaterpollutants.Chlorinatedsolvents,suchasTCEandPCE,arethemostcommonlytestedsourcesofgroundwaterpollutionatthesite.Thesesolvents,usedindry-cleaningandotherindustries,areresponsibleforasignificantportionofthegroundwatercontaminationinNorthAmerica. 4 Whenthesolventsareimproperlydisposedof,theycanseepintothegroundwater.Contaminatedgroundwatercausesavarietyofhealthproblems,includingnervoussystemdamage,liverdamage,andcancer.
3. Whichchoiceprovidesthebesttransitionfromthepreviousparagraphtothisone?A) NOCHANGEB) GroundwaterintheUnitedStatesispollutedwithavarietyofharmfulchemicals.C) Despitetheconstantinfluxofpollution,thewaterintheaquiferremainsremarkably
clean.D) SinceitisonaCanadianForcesbase,veryfewciviliansareexposedtothe
contaminatedwaterinthisaquifer.
4. Whichchoicemosteffectivelycombinestheunderlinedsentences?
A) Whenthesolventsareimproperlydisposedof,theycanseepintothegroundwater;thegroundwaterpollutioncausedbythisreleaseofsolventsisharmfultohumanhealthandleadstonervoussystemdamage,liverdamage,andcancer.
B) Whenthesolventsareimproperlydisposedof,theycanseepintothegroundwater,andgroundwatercontaminatedwiththesesolventscausesavarietyofhealthproblems,includingnervoussystemdamage,liverdamage,andcancer.
C) Whenthesolventsareimproperlydisposedof,theycanseepintothegroundwater,causingavarietyofhealthproblems,includingnervoussystemdamage,liverdamage,andcancer.
D) Whenthesolventsareimproperlydisposedof,theycanseepintothegroundwater—theresultofthegroundwaterbeingcontaminatedwiththesesolventsisavarietyofhealthproblems,includingnervoussystemdamage,liverdamage,andcancer.
Traditionallaboratoryexperimentscannotreplicatethevariationingeologicfeaturesthatexistsinnature. 5 Forinstance,researcherscannotaccuratelymodelthebehaviorofthesecontaminantsbasedonlaboratorystudies.ThedatagatheredattheBordenexperimentalsiteallowresearcherstomakeimprovementstotheirmodelsandbetterpredictthemovementandconcentrationsofthesehazardouschemicals. 6 However,somepeoplearestillskepticalofthevalueoftheseexperiments.
5.A) NOCHANGEB) Asaresult,C) Although,D) Next,
6. WhichchoiceprovidesthemosteffectiveresponsetoapossiblerelevantcounterclaimoftheargumentinsupportofthecontrolledstudiesattheBordenexperimentalsite?A) NOCHANGEB) Hazardouschemicalsshouldbebetterregulatedtopreventgroundwater
contamination.C) Traditionallaboratoryexperimentsstillprovideplentyofusefulinformation.D) Theresearchersremainawarethatfieldstudiescarrygreaterriskthanlaboratory
studies,sotherisksofeachstudyarecarefullyexaminedbeforeanystudyproceeds.
ResearchersattheUniversityofWaterlooconductedtheinitialexperimentatthesitein 7 1978,theyselectedthelocationtoperformasalttracerexperiment.Theresearchersinjectedchlorideionsintotheaquifer 8 plusthenallowedtheionstomigratenaturallyformonths.Theresultsshowedthatthedispersaloftheionswasless 9 uniformand,predictable,thanhadpreviouslybeenassumed.
7.
A) NOCHANGEB) 1978.WhentheyselectedC) 1978,selectingD) 1978.Selecting
8.A) NOCHANGEB) whilealsoallowingC) plusalsoallowedD) andallowed
9.A) NOCHANGEB) lessuniformandpredictablethanC) lessuniform,andpredictablethanD) lessuniformandpredictablethan,
Theunexpectedresultswere 10 respectedforabreakthroughthatdemonstratedthevalueofconductingexperimentsinthefield,andthesitewasconvertedintoalong-termresearchfacility.
10.A) NOCHANGEB) worshippedasC) recognizedasbeingD) hailedas
Forthefirstdecade,thesitewasusedmainlytogainunderstandingofthetransportofthecontaminantsinanefforttoimprovemathematicalmodelsofdispersion.However,inmorerecentyears,thesitehasbeenusedtotestnewtechnologiesaimedatcontainingorremovingcontaminantsingroundwater. 11 Theresearchconductedatthesitehasdirectlyledtosomeofthemostadvancedmethodsofremovinggroundwaterpollutantsinusetoday.Soeventhoughpollutinganaquiferdoesnotsoundveryenvironmentallyconscious,bypollutingthisparticularaquiferundercontrolledconditions,scientistshavebeenabletocomeupwithmoreeffectivemethodsofremovingpollutantsfromtheaquifersthatmillionsofpeoplerelyonforsafedrinkingwatereveryday.
11. Atthispoint,theauthorwantstoaddanexampleofoneofthetechnologiestestedattheBordensite.Whichchoicebestaccomplishesthisgoal?A) TheWaterloobarrier,averticaltreatmentwallthatcanbeinsertedintothegroundto
disrupttheflowofpollutantsandallowcontaminantstoberemoved,isonesuch
innovationthathasshownpromisehere.B) ManyoftheproceduresusedtocontainchemicalsattheBordensitearenowinuse
inindustrialsitesaroundtheworld.C) EdwardSudicky,aprofessorattheUniversityofWaterloo,publishedapaper
detailingtheresultsofdecadesworthofexperimentsconductedbyacademicsfromacrosstheglobe.
D) In1988,agroupofuniversitiesinCanadaandtheUnitedStatesestablishedaUniversityConsortiumSolvents-in-GroundwaterResearchProgramtorunthesestudies.
Questions12–22arebasedonthefollowingpassage.
Yes,WeCanal
12 Becausewemaytakeitforgrantednowthatvariousmodesoftransportationcanmakeitoverorthroughjustaboutanynaturalobstacle,the 13 easetomoveisinfactrelativelynew.AftertheLouisianaPurchaseof1803,theUnitedStatesapproximatelydoubledinsize,addingwhatisnowaboutthemiddlethirdofU.S.territory. 14 Therewasjustoneproblem—journeysovertheAppalachianMountainsintheNorthcouldmaketraveltothefertileWestmoretroublethanitwasworth.
12.A) NOCHANGEB) AfterC) WhileD) For
13.A) NOCHANGEB) easymovingC) easeofmovementD) easetomovement
14. Atthispoint,thewriterisconsideringaddingthefollowingsentence.
Additionally,thenewterritoriesprovidedgreatresourcesforthenation,includingfertilefarmlandsandtheseeminglyendlessMississippiRiver.
Shouldthewritermakethisadditionhere?A) Yes,becauseitlistssomeoftheWest’spositiveattributeswithwhichthenext
sentencewillcontrast.B) Yes,becauseitrestatesthefirstsentence’scentralargumentinamoreconciseway.C) No,becauseitrepeatsinformationthatisgiventhroughouttheparagraph.D) No,becauseitisnotrelevanttotheparagraph’smaindiscussionoftheUnited
States.
Atthetime,thedevelopedstateswereprimarilyalongtheAtlanticcoast.Bythe 15 1840sthepopulation,hadexpanded,agreatdealintothenewterritoriesofIllinois,Tennessee,andespeciallyOhio.Whatmadeitpossible?Withsuchavastmovementofpeople,theanswershouldbehugelycomplex,butthistimeitcanbesummedupinjustthreewords:theErieCanal.
15.
A) NOCHANGEB) 1840s:thepopulationhadexpandedC) 1840s,thepopulationhadexpandedD) 1840s,thepopulationhad,expanded
Horsesandwagonswereeffectivemeansoftransportinggoodsacrossshortdistances,but 16 thesebecameunreliablewhenfacedwithmountainsandinhospitableconditions.Themostefficientmethodoftravel,especiallyforlargequantitiesofgoods,waswater.Afterall,thenewAmericanshadbeentradingwith 17 thereEnglishcounterpart’sacrosstheoceanforcenturiesalready.
16. Whichchoicebestsupportsthemainpointoftheparagraph?A) NOCHANGEB) noteveryonecouldaffordtokeepahorseorawagon.C) manyAmericansduringthistimewerenotevenawarethatthereweresuchvast
territoriestotheWest.D) therewerefewplacestosleepandwaterone’shorsesonthejourney.
17.A) NOCHANGEB) theirEnglishcounterpartsC) they’reEnglishcounterpartsD) they’reEnglishcounterpart’s
[1]LinkingNorthAmericaandEuropewassimpleenoughduetomodernsailingtechnologies,andriversandstreamshadbeenwellchartedthroughoutthethirteenoriginalcolonies.[2]Thelakeswouldallowboatstoavoidthemost 18 treacherouspartsofthemountainrange,andonelakeinparticular,LakeErie,providedaccesstoavarietyofpointstotheWest,includingmodern-dayBuffalo,Cleveland,andDetroit.[3]Anyshipthatcouldaccesstheseplaces 19 bygettingtherefromthegreatshippingportsintheEastcouldeasilycreatemanynewmarketsforgoods.[4]TheErieCanalwouldallowforthataccess.[5]Themissinglinkcamefromwhat 20 amannamedGeorgeWashingtoncalled“America’sMediterranean,”theGreatLakes. 21
Afternearlyadecadeofwork,theErieCanalwascompletedin1825.ThecanalranfromAlbanytoBuffaloinNewYorkState.Thismanmade 22 waterway,havingdugbyworkersandhorseswithoutthebenefitofelectricityorcombustibleengines,stretchedapproximately363miles.Afterthecanalwasbuilt,boatscouldpasseasilybetweentheHudsonRiver,thegatewaytoNewYorkandtheAtlantic,andLakeErie,thegatewaytothenewWest.
18.A) NOCHANGE
B) hasslingC) prevaricatingD) annoying
19.A) NOCHANGEB) bywayofgettingtoitC) —intheprocessofgettingthere—D) DELETEtheunderlinedportion.
20.A) NOCHANGEB) theoneknownasC) theworld-renownedmanD) DELETEtheunderlinedportion.
21. Tomakethisparagraphmostlogical,sentence5shouldbeA) placedbeforesentence1.B) placedbeforesentence2.C) placedbeforesentence3.D) DELETEDfromtheparagraph.
22.A) NOCHANGEB) waterway;diggingC) waterway,itwasD) waterway,dug
Questions23–33arebasedonthefollowingpassageandsupplementarymaterial.
MinimumWage,MaximumDebate
23 TheAmericanworkforceexperiencesrisesandfallsinemployment.Theymightbeflippingburgers,tearingmovie 24 tickets,or,operatingamusement-parkrides.Thesejobsdon’tpaywell,butthey’renotquitemeantto—theyarejustwaysforkidswhoareoutofschoolforthesummertomakealittleextraspendingcash.Buthowcouldaminimum-wage 25 jobeffectsomeonewhosefamilydependsonit?Couldminimumwagesupportafamilywithchildrenandmortgageorrentpayments?
Thesequestionsarepartofalargerdiscussionaboutwaystocombatpovertyinthemodernworld.Peoplewhoworkatjobsthatpaypoverty 26 wages,yearlyearningsbelow$24,300forafamilyoffourin2016needtobeabletolive,andoftentheyareunabletodosobecausetheirwagesaresolowthatnoteven80hoursofworkcouldcoveralloftheirexpenses.Anobvioussolutiontothisproblemwouldbetoraisetheminimumwage,soeventhoseatthebottomofthepayscalecanaffordlife’snecessities.
23. Whichchoiceisthebestintroductiontotheparagraph?A) NOCHANGEB) Thenumberofjobsthathavebeenoutsourcedtoothercountrieshasrisensteadily.C) Gettingajobisanexcitingprospectandoftenanunpredictableone.D) Manyteenshavegruelingsummerjobsatwhichtheymakeminimumwage.
24.A) NOCHANGEB) tickets,orC) tickets:orD) tickets;or
25.A) NOCHANGEB) jobaffectsomeonewho’sC) jobaffectsomeonewhoseD) jobaffectsomeone,whose
26.A) NOCHANGEB) wages:yearlyearningsbelow$24,300forafamilyoffourin2016,C) wagesyearlyearningsbelow$24,300forafamilyoffourin2016,D) wages(yearlyearningsbelow$24,300forafamilyoffourin2016)
27 Somesmall-businessowners,forinstance,arguethatahigherminimumwagewouldcutsomuchintotheirprofitthattheywouldbeforcedtohirefewerworkers. 28 However,ahigherminimumwagewouldactuallydestroyjobsratherthancreatethem,leadingtohigherunemploymentandslowereconomicgrowth.Bossesatlargerbusinesses,too,particularlyfast-foodchainsandbig-boxstores,arguethat 29they’repricescanonlybesolowbecausetheyareabletopaylowwages.Thesebusinessleadersarguethattheycannotcontinuetooffersuchbargainprices,atleastcomparedto 30 what’snexttotheircompetitors,iftheypaytheirworkersmore.
27. Atthispoint,thewriterisconsideringaddingthefollowingsentence.
Eventhoughpayincreaseproposalshavebeenofferedtoaddresstheearningsgap,theissueremainscontroversial.
Shouldthewritermakethisadditionhere?A) Yes,becauseitintroducesthesubjectmatterofthisparagraphinageneralway.B) Yes,becauseitinsertstheauthor’sopinionasaturningpointintheessay.C) No,becauseitdoesnotadequatelycitetherangeofissuesinthepoliticalsphere.D) No,becauseitdoesnotgiveaspecificvaluefortheminimumwage.
28.A) NOCHANGEB) Nevertheless,C) Subsequently,D) Conversely,
29.A) NOCHANGEB) theirC) thereD) one’s
30.A) NOCHANGEB) thoseofC) thatofD) DELETEtheunderlinedportion.
Evenonwhatmayseemlikearelatively 31 hotbuttonissue,thedebatesurroundinghowtoeasepovertyiscomplicated.Inaway,theissueisasoldasthenationitself.Howcananationguaranteeallof
itscitizensachancetoenjoythebenefitsofcitizenship?Wagesshouldadjustwiththeinflationofcurrency,buthowisitpossibletoknowwhenwe’vesetthemattherightlevelstosucceed?Somesayourcurrentminimumishighenough. 32
Adaptedfrom“MinimumRelativetoAverageWagesofFullTimeWorkers,”atwww.OECD.org,bytheOrganisationforEconomicCo-operationandDevelopment.
Inrecentyears,asthedebatesurroundingtheminimumwage 33 firesup,anewidea,theguaranteedminimumincome,hasbeguntogainsometraction.Withthisproposal,allcitizenswouldbegivenaminimumlivingsalarybythegovernment,thusguaranteeingthat,evenintimesofhighunemployment,everyonecanlivewithacertainamountofdignity.Whiletheremayneverbeananswerthateveryonecanagreeon,thegoalofeliminatingpovertyremainsagoodone,particularlyasitbenefitsrichandpooralike.
31.A) NOCHANGEB) hottopicC) honestD) straightforward
32. Atthispoint,thewriterisconsideringaddingthefollowingsentence.
Indeed,theUnitedStateshasaminimumwagetomedianincomeratiothatisoneofthetop10suchratiosworldwide.
Shouldthewritermakethisadditionhere?A) Yes,becauseitprovidesaconclusivebitofevidenceamidthevaguenessofthe
questionsaskedinthisparagraph.
B) Yes,becauseitprovidessupportfortheargumentsmadebythesmallandlargebusinessesmentionedinthisessay.
C) No,becauseitrepeatsinformationthatisgivenelsewhereinthisparagraph.D) No,becauseitdoesnotaccuratelyreflectdatafromthegraphgiveninthepassage.
33.A) NOCHANGEB) blazesatrail,C) rageson,D) burnsitdown,
Questions34–44arebasedonthefollowingpassage.
Truth,Fiction,andReality
34 Viewers’expectationsofwhat“reality”meanstendtoshiftastheywatchmoredocumentaryfilms.Documentaryfilmshavebecomenormalfeaturesofmanypeople’sviewingregimens.Documentariestypicallypresentthemselvesaslong-formjournalism,usingthemediumoffeature-lengthfilmtoexploreastoryoraconcept.Thesefilmsuse“real”peopleandexpertsratherthanactors.Therefore,aspeoplewatchmoredocumentaries,theirexpectationschangeforwhat“realistic” 35films,evenfictionfilms—shouldlooklike.
34. Whichchoicemosteffectivelycombinestheunderlinedsentences?A) Asdocumentaryfilmsshifttheviewers’expectationsofwhat“reality”meansafter
watchingsomanyofthem,documentarieshavebecomenormalfeaturesofmanyviewingregimens.
B) Manypeople’sviewingregimensincludemanydocumentaryfilmsandshifttheexpectationsofwhat“reality”meanswhendocumentariesbecomepartofhowtheywatchfilms,includingfictionalones.
C) Viewersexpect“reality”toshiftwhenwatchingfictionfilms,andthishaschangedtheirexpectationsofwhat“reality”meanswhenpeople’sviewingregimensbeginfeaturingmanydocumentaryfilms.
D) Asdocumentaryfilmsincreasinglybecomenormalfeaturesofmanypeople’sviewingregimens,thoseviewers’expectationsofwhat“reality”meanstendtoshift.
35.A) NOCHANGEB) films—C) films:D) films;
ArecentJapanesefilmtakesthesenotionsofrealitytoaparticularextreme.DirectorRyusukeHamaguchi 36 releasedafilm,in2015calledHappyHour.Thefilmcanbedifficulttofindandwatchintheatersbecauseofitsfive-and-a-half-hourlength,butthisispartiallythepoint.HappyHourisconcernedwithrepresentingafictionalversionoflifeasitisactuallylivedbyacertaincross-sectionofwomeninJapan.Fourwomen,eachintheir30s,liveouttheconsequencesoftheirlongfriendshipsandmarriagesasundetectableshiftsalterthemslowly.Therearenoneoftherapid-fireedits,glamoroussuperstaractors,or 37 longticketholderlinesthatcharacterizespeedierfilms.Indeed,thelengthofthefilmandthequietnessofthedirection,asinallof 38 Hamaguchiswork’s,makeusfeelthatweareexperiencingsomethingotherthanamovie—theseaspectscanalmostmakeitfeelthatweareexperiencinglifeitself.
36.
A) NOCHANGEB) releasedafilmC) released:afilmD) released,afilm
37. Whichchoiceismostconsistentwiththepreviousexamplesinthesentence?A) NOCHANGEB) superimposedEnglishsubtitlesC) explosivespecialeffectsD) professionaladvertisingcampaigns
38.A) NOCHANGEB) Hamaguchi’swork,C) Hamaguchi’swork’s,D) Hamaguchis’work’s,
Infact,HappyHouris 39 sorealisticthatviewerscanwonderwhetherthisfictionalfilmisitselfakindofauthenticreality.However,thatideahasbeenonethatartistshaveusedtheirworksto 40researchallalong.Isn’titpossiblethatallofourexperiencesareinasenseconstructedandthatfilmisjustanotherlensthroughwhichweviewourownexperiencesaswell?Watchingafilmfromthe1940s,wemayconsidertheactingawkwardandstilted.Thefilmstodayseemmuchmorerealistic.Ifaudiences70yearsfromnowwatchourfilmswithasimilarsenseofsuperiority, 41 therefore,whatwouldthatmeanforourownsenseofreality?
39. ThewriterwantsaconclusiontothesentenceandintroductiontotheparagraphthatlogicallycompletesthediscussionofHappyHourandprovidesaneffectivetransitionintothisparagraph’sdiscussion.Whichchoicebestaccomplishesthesegoals?A) NOCHANGEB) afilmthatistoolongtobeshownintraditionaltheatersbecauseitcanonlybe
shownonceaday.C) atypicalofthekindofmoviescomingoutofJapan,whichareverysimilarto
Hollywoodfilms.D) theworkofanaccomplisheddirectorthatisnotlikelypossibleforayounger
director.
40.A) NOCHANGE
B) huntC) scoutD) explore
41.A) NOCHANGEB) moreover,C) however,D) so,
Theconvergenceofdocumentaryandfictionfilmmakingisoneofthemostinterestingculturaldevelopmentsofourtime.Ithasgreatconsequencesforthemediumitselfand 42 incorporatesinnovationsnotyetseeninHollywoodfilms.Weall 43 werecreatingonlinepersonalitiesforourselves,butperhapsourin-the-worldpersonalitiesarejustasfabricatedas 44 thoseofouronlineavatars.Bothconstructedidentitiesareultimatelyreflectionsoftheinformationwedigest,andwhetherthatcontentiscalleda“documentary,”“journalism,”or“fiction”isinconsequentialthemomentweallowourselvestobeinfluenced.
42. Whichchoicemosteffectivelysetsupthemainideaoftheremainderoftheparagraph?A) NOCHANGEB) couldimpacthowpeoplegenerallyinteractwiththeworld.C) hassignificantlychangedthewaypeoplewatchmoviestoday.D) requiresapatienceonthepartoftheaudiencethatisrare.
43.A) NOCHANGEB) wouldcreateC) havecreatedD) wouldhavecreated
44.A) NOCHANGEB) themC) thatD) DELETEtheunderlinedportion.
STOP
Ifyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.Donotturntoanyothersectioninthetest.
MathTest–NoCalculator25MINUTES,20QUESTIONS
TurntoSection3ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–15,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions16–20,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion16onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorisnotpermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Whatisthesumofthecomplexnumbers6+2iand3+5i,wherei= ?
A) 9+7iB) 18+10iC) 16D) 16i
2. Maryhasdecidedtoearnextramoneybylandscapingyards.Inadditiontoherhourlyrate,shechargeseachcustomeraflatfeefortravelandsupplies.TheequationC=9h+14representsthetotalcostC,indollars,Marywillchargeforhhoursofwork.Whatdoes14representintheequation?A) Thetotalcost,indollars,MarychargesacustomerforonehourofworkB) Thetotalcost,indollars,MarychargesacustomerforanyamountofworkC) Theamountoftheflatfee,indollarsD) Thehourlyrate,indollars
3. Jeffhastwodifferentbrandsoftrailmix.TrailMixXcontains30%peanutsbyvolumeandTrailMixYcontains70%peanutsbyvolume.Combined,thetwotrailmixesJeffpurchasedcontainatotalof12cupsofpeanuts.Whichequationmodelsthisrelationship,whereaisthenumberofcupsofTrailMixXandbisthenumberofcupsofTrailMixY?A) 12=0.3a+0.7bB) 12=0.7a+0.3bC) 12=30a+70bD) 12=70a+30b
4. Ifp= qandq=12,whatisthevalueof3p–4?
A) 8B) 9C) 17D) 23
5. Whichofthefollowingisthegraphoftheequationy=–3x+6inthexy-plane?
D)
6.
9y2–16=(zy+r)(zy–r)
Intheequationabove,zandrareconstants.Whichofthefollowingcouldbethevalueofz?A) 16B) 9C) 4D) 3
7.
Thetableaboveshowssomevaluesofthefunctionsfandg.Forwhichvalueofxisf(x)–g(x)=x?A) 2B) 1C) 0D) –1
8. If + = ,whatisthevalueoft?
A) 32
B) 16C) 4D)
9. AphysicsstudentusestheformulaE=10mhtoestimatethepotentialenergy,E,ofaballthathasamassofmkilogramsandisataheightofhmetersabovetheground.Whichofthefollowingcorrectlyexpressesm,intermsofEandh?
A) m=
B) m=
C) m=
D) m=
10. Whichofthefollowingisequivalentto ?
A) b−
B) b
C) b+1−
D) b+3
11. Tayloristrainingforagymnasticscompetition.Hergoalistopracticeanaverageofatleast45hourspermonthfor5months.Shepracticedfor39hoursthefirstmonth,48hoursthesecondmonth,46hoursthethirdmonth,and49hoursthefourthmonth.Whichinequalitycanbeusedtorepresentthenumberofhours,h,Taylorcouldpracticeinthe5thmonthtomeethergoal?
A) 39+46+48+49+h≥5(45)
B) +h≥5(45)
C) 39+46+48+49≥h(45)
D) +h≥45
12. Thevertexoftheparabolainthexy-planebelowis(0,n).Whichofthefollowingistrue
abouttheparabolawiththeequationy=a(x+m)2+n?
A) Thevertexis(–m,n)andthegraphopensdownward.B) Thevertexis(m,n)andthegraphopensdownward.C) Thevertexis(–m,n)andthegraphopensupward.D) Thevertexis(m,n)andthegraphopensupward.
13. Arestaurantownerisbuyingpotatoesandcarrotsfromhervegetablesupplier.Thesupplierwilldelivernomorethan$500worthofproductineachdelivery.Eachpoundofpotatoescosts$3.25andeachpoundofcarrotscosts$2.47.Theownerneedstobuyatleastthreetimesasmanypoundsofpotatoesaspoundsofcarrots.Letprepresentthenumberofpoundsofpotatoesandletcrepresentthenumberofpoundsofcarrots,wherepandcarenonnegativeintegers.Whichofthefollowingsystemsofinequalitiesbestrepresentsthissituation?A) 3.25p+2.47c≤500
3p≥cB) 3.25p+2.47c≤500
p≥3cC) 9.75p+2.47c≤500
p≥3cD) 9.75p+2.47c≤500
3p≥c
14. Whichofthefollowingisequivalentto ?
A)
B)
C)
D)
15.
3x2+6x=d
Intheequationabove,disaconstant.Iftheequationhasnorealsolutions,whichofthefollowingcouldbethevalueofd?A) 4B) 2C) –2D) –4
DIRECTIONS
Forquestions16–20,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpretedas
,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
16.
= n
Whatvalueofnisthesolutionoftheequationabove?
17. Howmanypintsofa30%sugarsolutionmustbeaddedto5pintsofa5%sugarsolutiontoobtaina20%sugarsolution?
18. Ifx =81forpositiveintegersxandy,whatisonepossiblevalueofy?
19. PointsRandSlieoncircleOwithradius2,andtheareaofsectorROSis .What
fractionoftheareaofthecircleistheareaofsectorROS?
20.
Inthefigureabove,GIisparalleltoFJ.WhatisthelengthofHJ?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–Calculator55MINUTES,38QUESTIONS
TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–30,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions31–38,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion31onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorispermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1.
RebeccaandNataliebeginbicyclingfromtheirhomesatthesametimetoadestinationthatis2,400yardsfromNatalie’shouse.ThegraphshowsthedistancethatRebeccaandNataliearefromNatalie’shousealongtheroute.NatalieandRebeccaeachbicycleataconstantrateandRebecca’shouseisonthewayfromNatalie’shousetothedestination.Nataliereachedthedestinationin8minutesandRebeccareachedthedestinationin12minutes.Accordingtothegraph,Rebecca’stripishowmanyyardsshorterthanNatalie’s?A) 2,400B) 900C) 600D) 300
2. Alejandrobegandrivingtoworkandthenstoppedinastoreforsometime.Oncehebeganagain,hecontinuedtoworkataslowerspeed.WhichofthefollowinggraphscouldmodelthetotaldistancetraveledbyAlejandroversustime?A)
B)
C)
D)
3. Whichexpressionisequivalentto(4y2–5)–(−6y2+3y–11)?A) −2y2+3y–16B) −2y2–3y–16C) 10y2+3y–6D) 10y2–3y+6
4.
12a+9b<36
Whichofthefollowinginequalitiesisequaltotheinequalityshownabove?A) a+b<3B) 3a+4b<12C) 4a+3b<12D) 4a+3b<3
5.
WhatistheMostImportantIssueintheElection?
Issue PercentofThoseSurveyed
Economy 54%
Crime 15%
Environment 12%
HealthCare 7%
Education 3%
Other 9%
Thetableaboveshowsasummaryof1,800responsestoasurveyquestion.Basedontheinformationinthetable,howmanyofthosesurveyedbelievethatthemostimportantissueintheelectionistheeconomyorcrime?A) 1,242B) 1,296C) 1,328D) 1,384
6. Acablecompanychargescustomersaone-timeinstallationfeeof$150plusxdollarsforeachmonth.Ifacustomerpaid$960forthefirst18months,includingtheinstallationfee,whatisthevalueofx?A) 45B) 55C) 65D) 75
7.
Thetableaboveshowsthecoffeeselectionsofthepeopleatanoffice.Ofpeoplewhoselectmilk,whatfractionalsoselectsugar?
A)
B)
C)
D)
8. Theadministrativestaffofahighschoolwantedtogaugethepreferenceofitsentirestudentbodyforincreasingfundingtotheathleticdepartment.Thestaffsurveyed200studentswhoplayasport.Thesurveyshowedthatthemajorityofthosesurveyedwereinfavorofincreasingfundingtotheathleticdepartment.Whichofthefollowingistrueabouttheadministrativestaff’ssurvey?A) Thesurveyshouldhaveincludedmorestudentswhoplayasport.B) Thesurveysampleisbiasedbecauseitisnotrepresentativeoftheentirestudent
body.C) Itshowsthatamajorityofstudentsfavoredincreasedfundingtotheathletic
department.D) Thesurveysampleshouldhaveonlyincludedstudentswhodidnotplayasport.
9. Between1839and1860,theUnitedKingdomandChinaengagedinthetwowarsknownastheOpiumWars.ThelengthoftheFirstOpiumWarwas218daysshorterthantheSecond,andthetwowarstogetherlastedatotalof2,738days.HowmanydaysdidtheFirstOpiumWarlast?A) 1,140B) 1,180C) 1,260D) 1,480
10. In2011,Torontohadapopulationof2.615millionpeople,whichwasanincreaseof0.134millionpeoplefromthepopulationin2001.In2001,therewere43hospitalslocatedwithinToronto.WhichofthefollowingistheapproximatenumberofresidentsservedperhospitalinTorontoin2001?A) 320B) 3,100C) 57,700D) 60,800
Questions11–13refertothefollowinginformation.
Ateamofresearchobstetriciansconductedastudytodeterminethegrowthrateofafetus.Thegraphandtableabovemodeltheweight,w,inounces,ofafetustweeksafterconception.
11. Overwhichtimeperiodistheaveragegrowthofafetusthegreatest?A) Week0toWeek12B) Week12toWeek24C) Week30toWeek39D) Week39toWeek42
12. ThegrowthrateofafetusfromWeek33toWeek39isnearlyconstant.Onthisinterval,whichofthefollowingbestmodelstheweight,w,inounces,ofafetustweeksafterconception?A) w=2.5t–220B) w=5.8t–180C) w=8.1t–200D) w=12.4t–150
13. Thefunctionw,definedbyw(t)=ct+d,wherecanddareconstants,modelstheweight,inounces,ofafetusaftertweeksofgrowthduringatimeperiodinwhichthegrowthisapproximatelylinear.Whatdoescrepresent?A) Thepredictedtotalincreaseinweight,inounces,ofafetusduringtheperiod
B) ThepredictednumberofouncesofgrowthperweekduringtheperiodC) Thepredictedweight,inounces,ofafetusatthebeginningoftheperiodD) Thepredictedweight,inounces,ofafetusattheendoftheperiod
14.
6x+5y=9
5x−5y=2
Forthesolution(x,y)tothesystemofequationsabove,whatisthevalueofx−y?
A) −
B)
C)
D)
15.
TrianglesPQRandXYZareshownabove.Whichofthefollowingisequaltotheratio
?
A)
B)
Questions17–19refertothefollowinginformation.
In a certain board game, playersmine for gold and silver at the beginning of each round. Players arerestricted in the amount of gold and silver they canmine using the equation 3g+ s= 38,whereg isamountofgold,inounces,theplayerminesandsistheamountofsilver,inounces,theplayermines.Aplayercanchoose theamountofgoldandsilver tomineat thebeginningof the first roundandwillreceivethesameamountofeachineachsucceedinground.
17. Julietwantstouseastrategyinwhichsheminesatleast4ouncesofgoldandatleast14ouncesofsilveratthebeginningofeachround.Accordingtothegame’sequation,whichofthefollowinginequalitiesrepresentsthesetofallpossibleamountsofgoldthatshecanminetomeetthisstrategy?A) 8≤g≤14B) 4≤g≤8C) g≥4D) 0≤g≤4
18. Johnnywantstocreateastrategydesignedtomine6poundsofgold,takingbetween10and15ouncesperroundforagameinwhichthereisanevennumberofrounds.WithinJohnny’sstrategy,whichofthefollowingmustbetheamountofsilver,inounces,Johnnymines?(16ounces=1pound)A) 2B) 8C) 9.6D) 12
19. Whichofthefollowingexpressestheamountofgoldminedeachroundintermsofthe
amountofsilverminedinthatround?
A) g=– (38+s)
B) g=– (38–s)
C) g= (38+s)
D) g= (38–s)
20. Astudywasconductedontheheightsoffourth-gradersinaparticularcounty.Arandomsampleofgirlswastakenwitheachgirl’sheightmeasuredandrecorded.Thesamplecontained250girls,and20%ofthegirlsweremorethan57inchestall.Whichofthefollowingconclusionsisbestsupportedbythesampledata?A) Approximately20%ofallfourth-gradegirlsinthecountyweretallerthan57inches.B) Approximately20%ofallfourth-gradersinthecountyweretallerthan57inches.C) Theaverageheightofallfourth-gradersinthecountywas57inches.D) Themajorityofallfourth-gradersinthecountyareshorterthan57inches.
21. Whatisthesumofthesolutionsto(x+5)(x−0.4)=0?A) −5.4B) −4.6C) 4.6D) 5.4
22. Duringhispreviousvisit,acustomer’sbillatarestaurantwas$91.94.Athiscurrentvisit,thebillis$86.53.Tothenearesttenthofapercent,bywhatpercentdidthecustomer’sbilldecrease?A) 5.4%B) 5.9%C) 6.2%D) 6.3%
23.
EntryYearintotheEuropeanUnion
Year NumberofCountries
1957 6
1973 3
1981 1
1986 2
1995 3
2004 10
2007 2
In2012,therewere27nationsintheEuropeanUnion,asshowninthetableabove.Basedonthetable,whatisthemedianentryyearforthe27countries?A) 1981B) 1986C) 1995D) 2004
24.
Apendulumwasreleased5centimeterstotherightofitsequilibriumpointandallowedtoswinguntilitcametoarest.Thegraphaboverepresentstherelationshipbetweentimeelapsedafterthependulumwasreleasedandthedistancefromtheequilibriumpointwithnegativedistancesrepresentingdistancestotheleftoftheequilibriumpointandpositivedistancesrepresentingdistancestotherightoftheequilibriumpoint.Afteritwasreleased,howmanytimeswasthependulum1centimetertotheleftoftheequilibriumpoint?A) OneB) TwoC) ThreeD) Four
25. Inthexy-plane,thegraphof2x2+2x+2y2−10y=85isacircle.Whatistheradiusofthecircle?
A)B) 9.5
C)D) 7
26.
x g(x)
0 −3
3 3
9 15
Someofthevaluesofthelinearfunctiongareshowninthetableabove.Whatisthevalueofg(4)?A) 5B) 6C) 7D) 8
27. Ataconstanttemperature,iftheratioofthevolumesoftwocontainersfilledwithequalamountsofgasisp:q,thentheratioofthepressuresinthecontainersisq:p.Inthediagrambelow,ContainerXisfilledwithgasandthepressureinContainerXismeasured.ThenallthegasispumpedintoContainerY.OncethepressureinContainerYismeasured,thegasisfinallypumpedintoContainerZ,andthepressureinContainerZismeasured.
IfthepressureinContainerXis300torr,whatisthepressure,intorr,inContainerZafterthegashasbeenpumpedintoit?A) 100
B) 330C) 900D) 9,000
28. Themeandistance,d,inmicrometers,glucosetravelsinfreesolutionintsecondscanbedeterminedusingtheformulad=10 .Whichofthefollowinggivestheaveragespeedoftheglucose,inmicrometerspersecond,overthefirsttsecondsafteritbeginstomove?A) 10t
B)
C)
D)
29. Thescatterplotbelowshowsspending,inbillionsofdollars,onDVDrentalsandsalesintheUnitedStatesovera10-yearperiod.
Ofthefollowingequations,whichbestmodelsthescatterplot?A) y=−0.4339x2+5.6673x+0.7685B) y=0.4339x2+5.6673x+0.7685C) y=−0.4339x2−5.6673x−0.7685D) y=0.4339x2+5.6673x−0.7685
30. Twodistinctpointsonthenumberlineareatadistanceof2unitsfromthepointwithcoordinate−5.Thesolutiontowhichofthefollowingequationsgivesthecoordinatesofbothpoints?A) |x–2|=5B) |x+2|=5C) |x–5|=2
DIRECTIONS
Forquestions31–38,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpretedas
,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
31. Ahomeownerischoosingbetweendifferentsizesofcylindricalswimmingpools.Ifshewantsapoolwitharadiusof3feetandaheightbetween5.75feetand6feet,whatisonepossiblevolume,roundedtothenearestcubicfoot,ofapoolthehomeownercouldselect?
32. Agroupofroommatesequallysharedthe$6,000rentforanapartment.Whenfouroftheroommatesmovedout,thoseroommatesremainingstillsharedthe$6,000rentequally,buteachroommate’sshareoftherentincreasedby$250.Howmanyroommateswerethereoriginally?
33.
5(3y–12)–(23+11y)=13
Whatvalueofysatisfiestheequationabove?
34. Thelinewiththeequation x+ y=1isgraphedonthexy-plane.Whatisthey-
coordinateofthey-interceptoftheline?
35.
JenniferandMichaelhaveeachspentsixsemestersincollege,andtheirGPAsduringthesesixsemestersareshowninthetableabove.ThemeanoftheGPAsforMichael’ssixsemestersis0.2lessthanthemeanoftheGPAsforJennifer’ssixsemesters.Whatisthe
valueofy?
36. Inthexy-plane,thegraphofy=2x2+13xintersectsthegraphofy=−xatthepoints(0,0)and(–k,k).Whatisthevalueofk?
37. Alocalhomeownerassociationhasvotedtoaltercurrentfinesfornoiseviolations.Ofthememberswhovoted,35%votedtoraisefines,10%votedtokeepthefinesthesame,30%votedtolowerthefines,andtheremaining15votedtoeliminatethefinescompletely.Howmanymoremembersvotedtoraisethefinesthantolowerthefines?
38. ThenumberofpeopleinOxfordCountywhosupportaproposedhighwaysystemwasppeopleonJanuary1,2006.Thenumberofpeoplewhosupportthehighwaysystemtripleseveryyearuntilthereare675whosupporttheproposalonJanuary1,2009.Whatisthevalueofp?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
SATEssay
ESSAYBOOK
DIRECTIONS
Theessaygivesyouanopportunitytoshowhoweffectivelyyoucanreadandcomprehendapassageandwriteanessayanalyzingthepassage.Inyouressayyoushoulddemonstratethatyouhavereadthepassagecarefully,presentaclearandlogicalanalysis,anduselanguageprecisely.
Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteorprintsothatwhatyouarewritingislegibletothosereaders.
Youhave50minutestoreadthepassageandwriteanessayinresponsetothepromptprovidedinsidethisbooklet.
REMINDER
— Donotwriteyouressayinthisbooklet.Onlywhatyouwriteonthelinedpagesofyouranswerbookletwillbeevaluated.
— Anoff-topicessaywillnotbeevaluated.
Asyoureadthepassagebelow,considerhowRobertSterlingYarduses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
AdaptedfromRobertSterlingYard,“MakingaBusinessofScenery.”©June1916byTheNation’sBusiness.
1 Castingaboutforthecauseofabusinesslovingnation’simpressiveapathytowarditsnationalparks,Ifindthatitliesinanentirefailuretoperceivethehard-fistedreasonsfortheirexistence.Untilrecently—itisamatterofalmostmonths—theincomparablesceneryofthislandhasbeencommonlyregardedasanaestheticluxury.
2 Thatscenery,handledinabusinessway,hascommercialvalueis,ofcourse,arecognizedfact;butthatournationalparkssohandled,onanationalscale,canbequicklyturnedintoaneconomicassetofincalculablevaluetothisnationisanewideatothepublic,althoughbynomeansnewtothegroupofearnestmenbehindthepresentadministrationofthesegreatproperties.Thepropositionisneithernewnoruntried.Itssuccessisincontestablyproved.Switzerlandlivesonherscenery.
3 TheSwissareabusinesspeople.Theyperceivedthatsnow-coveredpeakswereasgoodasgoldmines;thatglaciersandprecipicespaidlikefactories;thatlakeshoreswereasprofitableasoceanfronts.Sotheydevelopedtheirproperties.TheStatebuiltfineroadsandthepeopleputtheirprofitsintohotelsandchalets.Whentheyover-developedtheirmarkettheStatesoughtincreasedcustomabroad.ItestablishedtouristagenciesinFranceandGermanyandRussiaandEngland;later,andextensively,inAmerica.Itspentgoodmoneyinever-increasingsumsinadvertising,testingeachventurewithitsresultingincreaseofgrossincome,untilSwitzerland’sscenerybusinessbecame,previoustothepresentwar,agreatnationalbusiness…
4 TherearefewAmericanstodaywhoknow,orhearingit,actuallyrealizethatAmericansceneryinquality,variety,andquantityoutclassesSwitzerland’sdecisively.Butrecentlyanotherpeopleinthishemisphererealizedit.AfewyearsagoCanadaobserved,heededandacted.Canadahasenteredthescenerybusinessenergeticallyandthoroughly.ShestudiedSwissmethodsandimproveduponthem.Sheputbusinessmeninchargeandgavethempower.Havingrailroadprosperityandlocalbusinessforherobject,sheplannedcarefullyandexecutedboldly.PickingouttheLakeLouiseregionasherpointoffirstconcentration,shesetabouttheestablishmentofitstrademark.Shebegantoadvertiseextensivelyandwell.
5 Andtheresults?
6 Thesecountries,SwitzerlandandCanada,todaysharethescenicreputationoftheworld.IthasbeenestimatedthatinnormaltimestheAlpsdrawahundredmillionAmericandollarsayear.Abroad,theCanadianRockiesaresupposedtobetheonlysceneryinNorthAmericaworthlookingat,andbeforelastsummer(andperhapstoday),itwasthefixedbeliefofmostAmericansthattheyexcelledanythingintheUnitedStates…
7 Butherearethefacts:
8 TheSwissAlpsmaybeoffsetbyourGlacierNationalParkalone.Gloryforglory,beautyforbeauty,Glacierwillmatchpointsandusuallyscore.ButwhoeverheardoftheGlacierNationalPark?And,besides,wehavethespectacularglaciersofMountRainierNationalPark,andthemarvelousmountainsceneryofourSierraparks,tosaynothingofthenewRockyMountainNationalPark,lessthanfiftymilesfromDenver,whoseaveragetimberlineisloftierthanmostofSwitzerland’ssummits,andwhoserockypeakschallengetheworldforsheerbeautyandaccessibility.SomuchfortheAlps…
9 TheclosingofEuropeturnedtheeyesofthispeopleuponitsownland.Thepacificexpositionsdrewattentionwestward.Thecryof“SeeAmericaFirst”focusedthenationalgaze.Americanscenerywasdiscovered.
10 SincethenthedoctrinehasspreadwithAmericanrapidity.Whatthispeoplewants,itsCongressgrants;andwewantournationalparksdeveloped.WewantroadsandtrailslikeSwitzerland’s.Wewanthotelsofallpricesfromlowesttohighest…Wewantadequatefacilitiesandsuppliesforcampingoutatlowestprices.Wewantgoodfishing.Wewantourwildanimallifeconservedanddeveloped.Wewantspecialfacilitiesfornaturestudy.
11 Allthesethingsthispeoplewantsandmusthave,butitdoesnotwantthemattheexpenseoftheUnitedStatesTreasure.Thisisabusinesspropositionandmustbebuiltupsoundly.Wehavethebiggestandfineststockofsceneryintheworldandthereisanenormousmarketforit.Wecansellitataprofit,andtheprofitwillbuyourdevelopment.Thebiggerthebusinessgrowsthegreaterthereductionofcostsandthelowerthecharges.WhenwearedoinganationalbusinessonSwitzerland’sscale,wecanmatchSwitzerland’slowprices.
12 Thereisthestoryinaparagraph.Itisabusinessproposition.
WriteanessayinwhichyouexplainhowRobertYardbuildsanargumenttopersuadehisaudiencethatthenationalparksshouldberunlikeaprivatebusiness.Inyouressay,analyzehowYardusesoneormoreofthefeatureslistedintheboxabove (or featuresofyourownchoice) tostrengthen the logicandpersuasivenessofhisargument.Besure thatyouranalysisfocusesonthemostrelevantaspectsofthepassage.
YouressayshouldnotexplainwhetheryouagreewithYard’sclaims,butratherexplainhowYardbuildsanargumenttopersuadehisaudience.
ENDOFTEST
PRACTICETEST1ANSWERKEY
Section1:Reading
1. D2. B3. A4. C5. A6. B7. C8. D9. B10. C11. A12. A13. B14. C15. D16. A17. B18. D19. C20. A21. C22. A23. C24. B25. B26. D27. D28. C29. A30. D31. B32. A33. B
34. C35. B36. A37. D38. C39. D40. D41. B42. B43. D44. C45. C46. A47. A48. D49. A50. B51. D52. B
Section2:Writing&Language
1. A2. B3. A4. C5. B6. D7. C8. D9. B10. D11. A12. C13. C14. A15. C16. A17. B
18. A19. D20. D21. B22. D23. D24. B25. C26. D27. A28. C29. B30. B31. D32. D33. C34. D35. B36. B37. C38. B39. A40. D41. C42. B43. C44. A
Section3:Math(NoCalculator)
1. A2. C3. A4. D5. B6. D7. D8. B9. B
10. C11. A12. C13. B14. B15. D
16. or5.25
17. 7.518. 1,2,3,4,6,or12
19. or.125
20. 24
Section4:Math(Calculator)
1. B2. C3. D4. C5. A6. A7. B8. B9. C10. C11. C12. C13. B14. C15. D16. C17. B18. A19. D20. A21. B22. B23. C
24. D25. D26. A27. A28. C29. A30. D31. 163,164,165,166,167,168,169,or17032. 1233. 24
34. or3.5
35. 3.236. 737. 338. 25
PRACTICETEST1EXPLANATIONS
Section1:Reading1. D This question asks about the main purpose of the first paragraph. The first paragraph
describesAndrea’sarrivalatthefarm.Inthisparagraph,theauthorstatesthatluxurycarsare linedupwhere the farmworkersnormallyparked theirbeat-upsedansandrustingpickups.ThepassagegoesontosaythatusuallyAndreawasembarrassedbyhermother’soldChryslerwithitswoodpanel,butonthisdayshewasn’t.ThepassagetherebysetsupacontrastbetweenthecarAndrea’sfamilyownsandthecarsthattheotherpartyguestsown.Look forananswer thatmatches thisprediction.Choice (A)mentionsAndrea’s lifestyle.TheonlythingthefirstparagraphstatesaboutAndreaisthatherfamilydrivesanoldcarandthatsheisnotembarrassedtoparkitalongsidetheluxuryvehicles.Andrea’slifestyleisnot described, so eliminate (A). Choice (B) reverses information from the passage. Thefirst paragraph states that while usually Andrea was embarrassed by her mother’s oldChrysler with its wood panel…today she parked it among the luxury vehicles with asenseofvindication.Inotherwords,onthisdayshewasnotembarrassed.Choice(C)maybetemptingbecausethefarmworkers’beat-upsedansandrustingpickupsaredescribedinthepassage.However,thosevehiclesthemselvesarenotthemainfocusoftheparagraph.Eliminate (C).Choice (D)matches theprediction. Incontrasting the luxuryvehicleswiththevehiclethatAndreaisdriving,thefirstparagraphcontrastsAndrea’sstatuswiththatoftheotherguests.
2. B ThisquestionasksaboutthefunctionofAndrea’scommentsinlines12–16.Intheselines,AndreaisspeakingtoMatty.ShetellsMattythattheLowellsownthewholewideworld…Likethreehundredacres.Practicallythisentiresideoftheriver.Applesandpearsandblueberries, too. The purpose of these lines is to emphasize the scope of the Lowells’property. Find an answer thatmatches this prediction. There is nothing in these lines toshowthatAndreathinksMattyshouldbeoffendedbytheLowells’wealth,soeliminate(A).Choice (B) is a clear paraphrase of the prediction, so keep it.Andrea doesmention theapples,pears,andblueberriesinthelines,butshedoesnotcommentonthequalityofthefruit. Eliminate (C).Choice (D) can be eliminated because it has nothing to dowith theprediction.Thecorrectansweris(B).
3. A Thisquestionaskswhatthewordadoptersmostnearlymeans,asusedinline19.Readthewindow, cross out the word adopters, and replace it with another word or phrase thatmakes sense based on the context of the passage. Then, eliminate anything that does notmatchtheprediction.Intheparagraphpriortowherethewordadoptersappears,Andreastates that the Lowells grow blueberries. In the paragraph in which the word adoptersappears,thepassagestatesthattheblueberryindustryinCaliforniahadbeenexpanding.TheLowellswerepartofthisexpandingblueberryindustry.Lookforananswerthatmeanssomethinglike“peoplewhojoinin.”Theonlychoicethatmatchesthispredictionis(A),embracers.Choice (B),parents,may seem tempting, but this is a different definition ofadoptersfromtheoneusedinthecontextofthispassage.Choice(C),devices,couldmatch
thewordadapters,butnotthewordadopters.Choice(D),admirers,hasnothingtodowithjoininganexpandingblueberryindustry.Thecorrectansweris(A).
4. C Thisquestionaskswhytheauthorusestheimageofsilkskirtsandsandals inlines24–26.TheparagraphstatesthatAndreasnorts,picturingtheLowells’friendsintheirBrooksBrotherschinosandsilk skirtsandstrappyheeledsandalsmaking theirwaydown therows.Theimagereinforcesthenotionthattheguests’attirewouldbeimpracticalforthejobthat theworkers do every day. Find an answer thatmatches this prediction. Choice (A)mightinitiallylookattractivebecausetheirattireisinappropriateforpickingblueberries,but they were invited to a party, not a workday. Eliminate (A). Choice (B) may seemtempting, since theguestsarewearing fancierclothing than the fieldworkers.However,theinclusionofthewordmostmakesthisanswerchoicetoogeneral.Thereisnoindicationthat the guests’ clotheswere fancier than clothesworn bymostpeople. Choice (C) is agoodparaphraseoftheprediction,sokeepit.Choice(D)canbeeliminatedbecausethereisnoindicationaboutwhattheguestsactuallythink.Andreasayswhatshethinkstheguestsbelieve, but there is nothing in thewindow about their actual thoughts.Additionally, thewordprovemakes thewordingof this answer stronger than thewordingof the text.Thecorrectansweris(C).
5. A ThisquestionaskswhytheLowellsdidnotexpectAndrea.Notethatthefollowingquestionis a best evidencequestion, so this question andquestion6 canbe answered in tandem.Since the answer to this question may be difficult to find in the text, look at the “bestevidence”answerchoicesforquestion6first.Thelinesfor(6A)statethatAndreadidn’tactuallycarewhat theLowells thought.Thisanswerdoesnotprovidea reasonforwhytheLowellsdidnotexpectAndrea.Eliminate(6A).Thelinesfor(6B)statethatAndrea’sparentshadbeeninvited.Thismatches(5A).TheLowellsdidnotexpectAndreabecausetheyhadinvitedherparentsratherthanAndrea.Connect(6B)with(5A).Thelinesfor(6C)state thatAndreawascertain theLowellsdidn’tactuallyexpect [herparents] tocome.This information does not explainwhy the Lowellswould not have expectedAndrea tocome.Eliminate(6C).Thelinesfor(6D)statethatAndrea’sparentshadneverbeeninvitedbefore. This information does not explain why the Lowells would not have expectedAndrea.Eliminate(6D).Thecorrectanswersare(5A)and(6B).
6. B Seetheexplanationforquestion5.
7. C ThisquestionaskswhatqualityofAndrea’sfatherthewordexuberanceemphasizes.Inthepassage,thewordexuberanceisusedtodescribehowAndrea’sfatherfeelsaboutthetacotruck. According to her father, the truck would pay for itself and would give himsomethingtodo.Inotherwords,Andrea’sfatherhasapositivefeelingaboutthetruckanditspossibilities.Lookattheanswerchoicestofindananswerthatmatchesthisprediction.Neither (A) nor (D) match the prediction, as both of these answers have a negativeconnotation.Choice(B),courage,doesn’tmatch theprediction.There isno indication inthe passage that buying the truck made Andrea’s father feel courageous. Choice (C),optimism,isthebestmatchfortheprediction.
8. D ThisquestionaskswhichoftheanswerssupporttheclaimthattheElPrimotacotruckwas
notassuccessfulasplanned.Usethelinereferencesgivenintheanswers.Thelinesfor(A)discusshowAndreawasusuallyembarrassedbyhermother’scar,buttodayshedidn’tfeelthesameembarrassment.Theselinesareunrelatedtothetacotruck.Eliminate(A).Thelinesfor (B)arepartofadiscussion thatAndreahaswithMattyabouthis lackofa job.Thisdiscussionisunrelatedtothetacotruck.Eliminate(B).Thelinesfor(C)describethetruckashavingafestivelittlelinedrawingdebossedinredandyellow.Theselinesdonotdiscusswhether the taco truckwas successfulornot.The lines for (D) state thatAndreasuspectedfromhermother’sstrainedsilenceonthesubjectthatthetacotruckwasn’taslucrative as he’d hoped. In other words, the truck didn’t bring in as much money asAndrea’sfatherhadhoped,whichisdirectevidenceforthequestionthatthetacotruckwasnotassuccessfulasplanned.Thecorrectansweris(D).
9. B This question is asking about how Andrea’s parents reacted to receiving the Lowells’invitation.Usechronologyandthe leadword invitation to find thewindowtoread.TheLowell’s invitation ismentionedon line71.According to lines70–73,Herparents hadbeendelightedtoseethetacotruckfeaturedontheLowells’invitation,andhadgushedabouthowtouchedtheyweretohavereceivedit.Findananswerchoicethatmatchesthisprediction. Choices (A), (C), and (D) suggest that Andrea’s parents had a negative orpossiblyneutral reaction toreceiving the invitation,whichdoesnotmatch theprediction.Eliminatetheseanswerchoices.Delight isconsistentwithherparentsgushingandbeingtouchedtoreceive[theinvitation].Thecorrectansweris(B).
10. C ThisquestionaskswhatAndreahopestoachievebyattendingtheparty.Thereisnoclearleadwordinthequestion,sousechronologytofindtheanswer.Theanswerforquestion9wasinline71.Therefore,startreadingafterline71.Accordingtothelastparagraphofthepassage,Andreafelt fullof thebrazencourageshewouldneedtocrashthisparty.Shewouldshowupfullofbreezy,sparklingconfidencethatwouldstartlethesepeople.Lookforananswerchoice thatsuggestsAndreawished tostartle theotherguests.Neither (A)nor(B)haveanyrelationtohowAndrea’spresencemightimpacttheguests.WhileitmightmakesensethatAndreawishestoshamethehosts,thereisnoactualmentionofthatinthepassage.Additionally,thereisnothinginthetextaboutthechildrenofthehosts.Eliminate(D).Thecorrectansweris(C).
11. A Thisquestionaskswhat thewordbreakmostnearlymeans,asused in line17.Read thewindow,crossoutthewordbreak,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction.Thefirstparagraphstatesthatfreedomisnevergivenout,butitcomesthroughthepersistentandthecontinualagitationandrevoltonthepartofthosewhoarecaughtin thesystem.Therefore, the statement thatanationorapeople canbreakaloose fromoppression isrelatedtothisideaofanationorpeoplefreeingitself.Lookforananswerthatmatchesthisprediction.Choice(A)matchestheprediction.Thewordseparatecanbeused todescribeanationorpeople freeing itself fromoppression.Choices (B),rupture,and (C), damage, may seem tempting because they both relate to a definition of break.However,thesedefinitionsofthewordbreakarenothowthewordisusedinthispassage.Eliminateboth(B)and(C).Choice(D),alienate,meanstocausesomeonetofeelisolated
orestranged.Thisdoesnotmatchtheprediction.Eliminate(D).Thecorrectansweris(A).
12. A ThisquestionasksaboutthefunctionofthequestionAndit’sabeautifulthing,isn’tit? inPassage1.Accordingtothepassage,initiallyNkrumahcouldnotseehowtheycouldevergetaloosefromcolonialismwithoutarmedrevolt.ButafterstudyingGandhihecame toseethattheonlywaywasthroughnonviolentpositiveaction.Itisthispositiveactionofnonviolencethatthequestiondescribesasabeautifulthing.Findananswerthatmatchesthisprediction.Thepositiveactionispresentedasanalternativetoarmedrevolt,anditisdescribedasabeautifulthing,sokeep(A).Choice(B)canbeeliminatedbecausethereisnoindicationinthepassagethatanyoneisbeingcondescendedtoorbelittled.Choice(C)canbeeliminatedbecausethereisnodistractionorredirection.Thequestioncontinuesapreviouspoint;itdoesn’tqualifyit.Eliminate(D).Thecorrectansweris(A).
13. B This question askswhat theword freemost nearlymeans, as used in line 30. Read thewindow,crossout theword free, and replace itwithanotherwordorphrase thatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction. A nation that is now free refers to Ghana, which has gotten aloose fromcolonialism through positive action rather than armed revolt. Eliminate anything that isinconsistentwith“nolongerbeingundercolonialrule.”Theonlyanswerthatmatchesthismeaningis(B),liberated.Notethat(A)and(C)maybetemptinganswers,astheseanswersrelatetootherdefinitionsoffree,buttheydonotmatchthecontextandcanbeeliminated.
14. C This question asks what result nonviolent protest leads to, according to Passage 1.Becausethisisapairedquestionwithnolinereferenceorgoodleadword,thisquestioncanbedone in tandemwithquestion15.Lookat the“bestevidence”answerchoices forquestion 15 first. The lines for (15A) state that If there had not been abolitionists inAmerica,wemightstillhaveslavery.Theselinesareunrelatedtotheresultofnonviolentprotests,anddonotmatchanyoftheanswerstoQ14.Eliminate(15A).Thelinesfor(15B)relatetoNkrumah’scommentthatin thebeginninghecouldnotseehow[Ghana]couldevergetaloosefromcolonialismwithoutarmedrevolt.Theselinescouldsupport(14D),but thatanswerpairdoesnotaddress thequestion.Eliminate (15B).The lines for (15C)state that the aftermath of violence are emptiness and bitterness. It may be tempting toconnect(15C)with(14B).However,rememberthatthequestionisaskingabouttheresultsofnonviolentprotest,andtheselinesrelatetotheresultofviolentprotest.Eliminate(15C).The lines for (15D) state that the result of nonviolent protest is that once thewalls ofsegregation have completely crumbled…we will be able to live with people as theirbrothersandsisters.Thismatchesanswer(14C).Connectanswer(15D)with(14C).Thecorrectanswersare(14C)and(15D).
15. D Seetheexplanationforquestion14.
16. A ThisquestionaskshowFanondescribes theprocessofdecolonization.Because this isapaired questionwith no line reference or good leadword, this question can be done intandemwithquestion17.Lookatthe“bestevidence”answerchoicesforquestion17first.The lines for (17A)state that it is important that thechange in social structure is willed,calledfor,demanded.Thismatchesnoneoftheanswersinquestion16.Eliminate(17A).
Thelinesfor(17B)statethatdecolonizationsetsouttochangetheorderoftheworldandisaprogramofcompletedisorder.Thismatches(16A),asturbulentmeanscharacterizedbydisorderandchangingtheorderoftheworldwoulddefinitelybechangingeverything.Connect(17B)with(16A).Thelinesfor(17C)statethatdecolonizationcannotcomeasaresultofmagicalpractices,norofanaturalshock,norofafriendlyunderstanding.Thissupportsnoneoftheanswersinquestion16.Eliminate(17C).Thelinesfor(17D)statethatifwetrytodescribeit,alldecolonizationissuccessful.Itmaybetemptingtoconnectthisanswerwith(16B).However,thefirstparagraphofPassage2statesthatdecolonizationisalwaysviolent.Forthisreason,eliminateboth(17D)and(16B).Thecorrectanswersare(16A)and(17B).
17. B Seetheexplanationforquestion16.
18. D Thisquestionasksaboutthepurposeofbothpassages.Becausethisisaquestionaboutbothpassages, itshouldbedoneafterallof thequestionsforeachindividualpassage.Choice(A) can be eliminated because neither passage provides a historical overviewof recentdemocraticrevolutions.Choice (B) can be eliminated because neither passage providesspecific guidelines for anything.Neither passage criticizes those who work against thegoals of the people, so eliminate (C). Choice (D) looks good: Passage 1 describesnonviolence as an effectivemeans to create societal change, while Passage 2 describesviolenceasaneffectivemeanstocreatesocietalchange.
19. C This question asks how King would most likely describe the behavior that Fanonrecommends in lines 88-90. Because this question asks about both passages, do thisquestionaftercompletingallthequestionsthataskabouteachindividualpassage.Inlines88–90, Fanon states that it is clear to the native that theworld can only be called intoquestionbyabsoluteviolence,butinPassage1,Kingarguesthatnonviolencecanalsobesuccessful. Therefore, King would disagree with the statement given. Find an answerchoicethatmatchesthisprediction.Choice(A)isareversal.Kingisinfavorofnonviolentprotest, and thereforedoesnot believe that violencepresentsan acceptable alternative.Eliminate(A).Choice(B)canbeeliminatedbecausethereisnoindicationthatKingviewsviolence as a misunderstood cultural temptation. Choice (C) matches the prediction.SinceKingcitesNkrumahsayingthatnonviolenceistheonlyway,hewoulddisagreewithFanonthattheworldcanonlybechangedthroughviolence.ForKing,violenceisthereforeanunnecessarymethod for changing the world. Choice (D) can be eliminated becausethere isno indication that theauthorofPassage1considersviolence tobeabravestep.Thecorrectansweris(C).
20. A Thisquestionaskswhat the stancesof theauthorsofPassages1and2have incommon.Becausethisquestionasksaboutbothpassages,dothisquestionaftercompletingallofthequestions that ask about each individual passage. The key difference between the twopassages is that the author of Passage 1 advocates for nonviolence as ameans to enactsocietalchange,whereastheauthorofPassage2advocatesforviolenceasameanstoenactsocietalchange.Bothauthors,however,want socialchange.Choices (C)and (D)canbeeliminatedbecause,whiletheauthorsbothagreesocietalchangeisnecessary,theydisagreeaboutthemeanstoaffectthechange.WhiletheauthorofPassage1mentionsGandhi,there
isno indication thathe reliesheavilyonGandhi’sguidance, and theauthorofPassage2mentionsnoearlierleaders.Onthisbasis,eliminate(B).Thecorrectansweris(A).
21. C This question asks about the primary purpose of the passage. Because this is a generalquestion, it shouldbedone after all of the specificquestions.Thepassagedescribes theresults of a Stanford University study that showed that antibiotic-resistant strains oftuberculosisevolveoverthecourseoftreatmentandremainvirulent.Thepassagegoesonto discuss the concerns raised by the study. The passage concludes by stating that drug-resistantbacteriaareheretostay.Findananswerthatmatchesthisprediction.Choice(A)can be eliminated because, while the passage does mention classic laboratoryexperiments,itdoesnotsupportthosefindings.Choice(B)canbeeliminatedbecauseitisthe opposite ofwhat the passage says.Thepassagedoes review theStanfordUniversitystudyanddiscussestheconcernsraisedbythestudy.Keep(C).Eliminate(D)becausethepassagedoesnotcriticizethemethodologyofanystudy.Thecorrectansweris(C).
22. A ThisquestionaskswhatthescientistsintheStanfordUniversitystudydiscoveredabouttuberculosis bacteria that “undermined this comforting conventional wisdom.” Noticethatthisisapairedquestionwithbestevidenceanswersthatcoveralargepartofthetext.Therefore,questions22and23canbedoneintandem.Lookatthe“bestevidence”answerchoices forquestion23 first.The lines for (23A) state thatWithoutRNA, bacteria can’tmake the proteins they need to survive. This does not support any of the answers inquestion 22. Eliminate (23A). The lines in (23B) provide information about when theStanfordgroupcollected tuberculosisbacteria from thesputumofpatients.Thisdoesnotsupportanyof theanswers inquestion22.Eliminate (23B).The lines in (23C)state thatfiveofthetenresistantstrainsheldtheirowninthesetests,andoneactuallydominateditsantibiotic-susceptibleancestor.Thissupportstheideain(22A)thatbacteriacanresistantibioticswithoutlosingstrength.Connectanswer(23C)with(22A).Thelinesfor(23D)statethatSomechangessimplyhavealowcosttobeginwith,and,thestudyalsofound,thecostdependsonthestraininwhichthemutationoccurs.Thisdoesnotsupportanyoftheanswersinquestion22.Thecorrectanswersare(22A)and(23C).
23. C Seetheexplanationforquestion22.
24. B Thisquestionaskswhat thewordhardymostnearlymeans,asused in line26.Read thewindow,crossoutthewordhardy,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction.Inthepassage,thewordhardyisusedinconnectionwithdrug-resistantstrainsthatremainvirulent.Inotherwords,thesearepotentstrainsthatkeeptheirstrength.Lookfor aword thatmeans “strong” or “tough.”The only answer choice thatmatches is (B).While (C) may be tempting since a virulent strain would be terrible, no such valuejudgmentaboutthedrug-resistantstrainsismadeinthepassage.
25. B Thisquestionaskswhatstatementaboutrifampincanbemostreasonablyinferredfromthepassage.Usetheleadwordrifampinandchronologytofindthewindow.Theanswertoquestion24wasinline26.Therefore,startlookingforrifampinafterline26.Thefirstmention of rifampin is in line 30.According to the passage, rifampin…disables the so-
calledpolymerasemoleculeandprevents the crucial flowof information fromDNA toRNA.WithoutRNA,bacteriacan’tmaketheproteinstheyneedtosurvive.Findananswerthatmatchesthisprediction.Choice(A)maybetemptingatfirstbecausethepassagestatesthat rifampin is one of the preferred first-line treatments for the disease. However, thepassagedoesnotsaythatthisdrugstoppedtuberculosisfrombeingtheleadingcauseofdeath in the United States. Eliminate (A). Choice (B) is a good paraphrase of theprediction,sokeepit.Choice(C)canbeeliminatedbecausethereisnosuggestioninthepassage that rifampinmakesRNA compatiblewithDNA.Choice (D) can be eliminatedbecause there isnomention in thepassageas towhether rifampin ismoreeffective thanotherdrugs.Thecorrectansweris(B).
26. D This question asks which type of evidence the Stanford University study relied on. UseStanford as the lead word and chronology to find the window to read. The answer toquestion25was in line35, so theanswer to thisquestion shouldcomesomewhereafterline35.Line49containsthewordStanford.Accordingtothepassage,theStanfordgroupcollectedtuberculosisbacteriafromthesputumofpatients,firstatthebeginningoftheirinfections,andasecondtimeaftersomeof thosepatientsdevelopedrifampin-resistantinfections.Lookforananswerthatmatchesthisprediction.GiventhattheStanfordgroupdidresearchusingpatients,theonlyanswerthatmatchesis(D),clinicaltesting.
27. D This question asks about what scientists believed about antibiotic-resistant strains oftuberculosispriortotheStanfordstudy.Remembertouseanswerstoquestionsfromearlierinthepassageif theyarerelevant.Question22askedaboutconventionalwisdom,whichthoughtantibiotic-resistantbacteriawereweakerthantheirnon-resistantcounterparts.Findananswerthatmatchesthisprediction.Choice(A)canbeeliminatedbecausepriortothestudy,thescientistsbelievedtheantibiotic-resistantstrainshadaworsechanceofsurvival.Eliminate (B) because prior to the study, the scientists expected the antibiotic-resistantstrainstobelesslikelytosurvive.Therefore,itisunlikelythattheyexpectedtheantibiotic-resistant strain to become the most deadly of diseases. Choice (C) can be eliminatedbecause,whilesputumwasmentionedearlierinthepassage,itwasmentionedinrelationtohowthescientistscollectedthestudysamples,notinrelationtothescientists’expectationsof the study outcomes. Choice (D) matches the prediction. Given that the scientistsdiscoveredtheresistantbacteriawerenotweakerthantheircounterpartsandtheresultsofthe studywere contrary to expectations, it can be concluded that prior to the study, thescientistsexpectedtheantibiotic-resistantstrainsnottosurvive.
28. C This question asks what question Sebastien Gagneux plans to answer through furtherstudies. Because this is the first question in a paired set, this question can be done intandemwithquestion29.Lookatthe“bestevidence”answerchoicesforquestion29first.The lines for (29A)state thatGagneux isplanning future studies to find theseputativecompensatory mutations and learn how they restore the performance of strains thatacquire antibiotic-resistant mutations. This supports the question in (28C). Connectanswers (29A) and (28C). The lines in (29B) quote Levin as saying that the spread oftuberculosisdoesnotdependsolelyontheefficacyorlackofefficacyofantibiotics.ThisinformationisunrelatedtoGagneux’sfutureresearchplans.Eliminate(29B).Thelinesfor
(29C)statethatdrug-resistantbacteriaareheretostay.This informationisunrelatedtoGagneux’sfutureresearchplansanddoesnotsupportanyof theanswersforquestion28.Eliminate (29C). The lines for (29D) quote Levin as saying that the drug-resistantmutationsthataren’tcostlyaretheonesthatwilltakeover.Itmaybetemptingtoconnect(29D)with (28B) since (28B) includes theword cost. However, the information in thelines for (29D) is unrelated to Gagneux’s future research plans. Eliminate (29D). Thecorrectanswersare(28C)and(29A).
29. A Seetheexplanationforquestion28.
30. D Thisquestionaskswhytheauthormentionsthealarmistpanicinline76.Accordingtothepassage,theauthorsdon’twanttheirstudytofuelanalarmistpanic…thedatadon’tcallforit.ThepassagegoesontoquoteLevinassaying“thespreadoftuberculosisdoesnotdependsolelyontheefficacyorlackofefficacyofantibiotics.”Therefore,thealarmistpanic is related to thepublic’s reaction to thestudyresults.Findananswer thatmatchesthisprediction.Choice(A)canbeeliminatedbecausethepassagestatesthatthedatadoesnotcallforanalarmistpanic.Therefore,theauthorisnotusingthetermtobringattentionto a threat. Eliminate (B) because there is no mention of 19th century public-healthpracticesinthewindow.Theauthorisnotidentifyinganinevitableresultofantibioticuse,so eliminate (C). Choice (D) matches the prediction. The author is drawing a contrastbetweenthestudydata(anundesirableoutcome)andareasonableresponse,whichisnotalarmistpanic,asthedatadon’tcallforit.
31. B Thisquestionasksabout theprimary functionof the finalparagraph.The finalparagraphbroadlysummarizesthestudyfindingsandmakesageneralpredictionaboutfuturebacteriamutations. Find an answer that matches this prediction. Choice (A) can be eliminatedbecause there is nomention to reevaluate the StanfordUniversity study. Choice (B) isconsistentwiththeprediction,sokeepit.Choice(C)canbeeliminatedbecausethereisnoindication that the author believes that the Stanford University study changed society.Eliminate(D)becausethelastparagraphdoesnotexplainthemethodologyoftheStanfordUniversitystudy.Thecorrectansweris(B).
32. A This question asks about the main purpose of the passage. Because this is a generalquestion,itshouldbedoneafterallofthespecificquestions.ThefirstparagraphstatesthatEB announced it would cease its printing operations. The second, third, and fourthparagraphsdiscusshowEBevolvedasanorganization.TheauthorandthewriterquotedbothpraiseEB for being forward thinking and civil.The last paragraph focuses onhowEB’s fans are reacting to the organization’s change. Choice (A) is consistent with thisstructure. The passage does review attitudes in response to the changing role of EB,which is an established brand. EB’s attitude was to adapt and stay civil. The biggestreaction of EB fans was to complain about the changes. Choice (B) can be eliminatedbecause the passage is not focused on how class altered the encyclopedia market.According to the passage, the advent of digital encyclopedias did cause a massiveupheaval,sothisnotionisnotmisplaced,eliminate(C).Thepassagedoesnotfocusontheevolvingmechanisms that encyclopedia companies have adapted, so eliminate (D). Thecorrectansweris(A).
33. B Thisquestionaskswhat theworddoorsmostnearlymeans,asused in line31.Read thewindow,crossouttheworddoors,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction.TheworddoorsisusedinthesentenceEncartahadtocloseitsdoorsacoupleof years ago. The next sentence goes on to explain that because Encartawasn’tgettingenoughsales,therewasnowaytokeepitgoing.Lookforananswerthatisconsistentwith“goingoutofbusiness.”Only(B),closeitsoperations,hasthesamemeaningascloseitsdoors.Choices(A),openings,and(C),entrances,maybetemptingbecauseonedefinitionofadoorisanopeningoranentrance.However,theworddoorisnotusedinthatcontextinthepassage.Thecorrectansweris(B).
34. C This question asks what action legacy companies should take in an unviable market.Becausethisisthefirstquestioninapairedset,itcanbeansweredintandemwithquestion35.Lookatthe“bestevidence”answerchoicesforquestion35first.Thelinesfor(35A)statethatveryfewwordshavebeenwrittendetailingEB’sadjustmenttothedigitalage,which isasmuchabout the things itdiddoas it isabout the things itdidn’tdo. Thisinformation suggests EB’s actions and non-actions were significant, but does not givedetails. These lines also do not support any of the answer choices for question 34.Eliminate (35A). The lines for (35B) state thatBritannica realized quicker than manylegacyentitiesthatthemarketitworkedinwasnolongerviableandchangeditsfocusearlyinthegame.Thisinformationsupports(34C).Connect(35B)with(34C).Thelinesfor(35C)notethatwhatBritannicadidn’tdoisperhapsthemostastonishingaspectofthisstory.The information in these lines does not answer the question ofwhat action legacycompanies should take inanunviablemarket.Eliminate (35C).The lines for (35D) statethatEBstill survives today…albeit,atamuchsmallerscale thanduring itspeak.Thisdoes not support any of the answers in question 34.The correct answers are (34C) and(35B).
35. B Seetheexplanationforquestion34.
36. A Thisquestionasksaboutthepurposeofthesecondlongquotation.Thequoteenumeratestheactivities thatEBdidnot engage in.For example,EBdidnotwhineor fussas somanyfirmshavedone.And,EBdidnotsueanyoneforpatentinfringementasseemssocommontoday inhigh tech.Thequoteconcludes thatEBevolvedwithasenseofclass.And theauthor notes that this “evolving with a sense of class” has escaped many legacyindustries.Findananswerthatmatchesthisprediction.Choice(A)isconsistentwiththeprediction:EB’s response to themarket changing is unlikewhatmany firms have done,making it unusual. Choice (B) can be eliminated because the author is praising EB, notcondemning their activities. Eliminate (C) because there are no specific successfultechniquesdescribedinthequote.Choice(D)canbeeliminatedbecausetheauthorpraisesEB,whichmeansthathedoesnotbelieveEB’sactionstobefutile.Further,althoughheiscriticizingtheothercompanies,thereisnomentionoftheoutcomeoftheactions,sothere’snoevidencethattheactionsarefutile.Thecorrectansweris(A).
37. D Thisquestionaskswhatacompanyinachangingmarketshouldavoid.Becausethisisthe
firstquestioninapairedset, itcanbeansweredin tandemwithquestion38.Lookat the“bestevidence”answerchoicesforquestion38first.Thelinesfor(38A)statethatEBsoldbookswithdoortodoorsalesmen.Thisdoesnotsupportanyof theanswers inquestion37. Eliminate (38A). The lines for (38B) state that Wikipedia came along and ateeveryone’slunchinthereferencesection.Thisdoesnotprovideananswertothequestionofwhatacompanyinachangingmarketshouldavoid.Eliminate(38B).Thelinesfor(38C)state that many legacy industries have made serious efforts to stop the clock, if notactually turn the clock back to when they had control of their respective fields. Thismatches(37D).Connect(38C)with(37D).Thelinesfor(38D)statethatIt’sonethingforanindustrytomakesomeatrociousnoiseswhenconfrontedwithmassiveupheaval.Thispart of the passage has nothing to dowithwhat a company in a changingmarket shouldavoid.Eliminate(38D).Thecorrectanswersare(37D)and(38C).
38. C Seetheexplanationforquestion37.
39. D Thisquestionaskswhatthewordnoisesmostnearlymeans,asusedinline83.Readthewindow,crossoutthewordnoises,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction.Thewordnoises isrelatedtowhatEB’sbiggestfansaredoing.Accordingtothepassage, the fansofEBhaveofferedbizarrely-wordedattacks onWikipedia as theymournthechangestoEB.Therefore,thenoisesmadebythefanscanbestbedescribedascomplaints about the changes.Look for an answer thatmatches thisprediction.Only (D)matchestheprediction.Choices(A)and(B)mayseemtempting,sincesoundsandscreamsarebothnoises.However, thefansarenot literallymakingsoundsorscreaming; theyarecomplainingaboutEB’schanges.
40. D Thisquestionaskswhatpercentofstudentswill[verylikely]useanonlineencyclopediaas a resource. Look at the table. The second row provides data onWikipedia or otheronline encyclopedias. The table shows that 75% of students are very likely to useWikipedia or other online encyclopedias as a resource.Therefore, the correct answer is(D).
41. B Thisquestionaskswhichoftheanswerchoicesisbestsupportedbythedatainthetable.Compareeachanswerchoicetotheinformationpresentedinthetable.For(A),lookatthePrintedbooks rowand theStudent-oriented search engines suchas Sweet Search row.Accordingtothetable,12%ofstudentsareverylikelytouseprintedbooks,and10%ofstudentsareverylikelytousestudent-orientedsearchenginessuchasSweetSearch.ThenumberofstudentswhoareSomewhatLikelytouseprintedbooksversusstudent-orientedsearch engines is also similar. Therefore, (A) is not true. For (B), look at theOnlinedatabasessuchasEBSCO,JSTOR,orGrolierrowandtheResearchlibrarianataschoolor library row.According to the data, 17%of students are very likely to use the onlinedatabasesand16%ofstudentsareverylikelytousearesearchlibrarian.Giventhatthesepercentagesareveryclose,keep(B).For(C),lookattheSparkNotes,CliffNotesorotherstudy guides row, and theOnline databases such as EBSCO, JSTOR, or Grolier row.Accordingtothedata,41%ofstudentsareverylikelytousearesourcesuchasSparkNotesand 17% of students are very likely to use an online database. Therefore, teachers do
believethatstudentsaremorelikelytouseSparkNotes.However,34%ofteachersbelievethatstudentsaresomewhatlikelytouseSparkNotes,whereas29%ofteachersbelievethatstudents are somewhat likely to use online databases. Eliminate (C), which says thereshould be fewer students somewhat likely to use SparkNotes than an online database.Choice (D)discusses the superiorityofone search tooloveranother.The tabledoesnotpresent any data concerning superiority.The table only looks at teachers’ perceptions ofwhichresearchtoolstudentsaremost likely touse.Eliminate(D).Thecorrectanswer is(B).
42. B Thisquestionaskswhichanswerchoiceismoststronglysupportedbythetable.Thelinesin (A) discuss the expense of distributing a product. The table does not provide anyinformationondistributionexpenses.Thelinesin(B)statethatWikipediacamealongandateeveryone’slunchinthereferencesection.Thephraseateeveryone’slunchmeansthatWikipediawasoneoftheprimaryreferencesused.Accordingtothetable,75%ofstudentswere very likely to useWikipedia. This percentage is lower only to Google and otheronlinesearchengines,sokeep(B).Thelinesin(C)discusswhatBritannicadidn’tdo.Thisinformation is not captured in the table. The lines in (D) discuss changes in the firm’sorganizationalform.Thisdataisnotcapturedinthetable.Therefore,thecorrectansweris(B).
43. D Thisquestionasksabouttheperspectivefromwhichthepassageiswritten.Becausethisisageneralquestion,itshouldbedoneafterallofthespecificquestions.Overall,thepassagediscusses new research findings in biofuel production. Find an answer thatmatches thisprediction.Choice(A)canbeeliminatedbecausewhilethepassageconcludesthatfurtherstudieswouldbeneeded todetermine theenvironmental impactsofbiofuels, there is norequestforprojectfunding.Eliminate(B)becausetheentirepassageisaboutresearchinbiofuelproduction,notchemistryconcepts.Choice(C)canbeeliminatedbecauselaudingmeans“praising,”and,whiletheresearchdiscussedinthepassageyieldedsomepromisingresults,accordingtothelastparagraph,furtherstudieswouldbeneeded todeterminetheenvironmental impacts of biofuel. Therefore, the entire passage is not lauding thesuccessesofanindustry.Eliminate(C).Choice(D)isconsistentwiththepredictionandisthecorrectanswer.
44. C Thisquestionasksaboutthefunctionofthelastsentenceofthefirstparagraph.Usethefirstparagraph as the window. According to the first paragraph, producing ethanol remainsconsiderablymoreexpensivethangasoline.Soresearchersarealwaysonthelookoutfornewwaystotrimcosts.Accordingtothelastsentenceof thefirstparagraph,researchershaveanewlead,amicrobethatcanuseabundantnitrogengasasthefertilizeritneedstoproduceethanolfromplants.Inotherwords,themicrobemaysolvetheproductioncostproblem. Find an answer that matches this prediction. Choice (A) may seem temptingbecause the last sentence describes a recent discovery—the microbe. However, themicrobeisnotacommercialaccomplishment.For thisreason,eliminate(A).Choice(B)mayseemtemptingbecausetheparagraphdiscussestherelativeproductioncostsofethanolandgasoline.However,thelastsentenceofthefirstparagraphdoesnotprovideareasonastowhyone fuel ismoreexpensive thananother.Eliminate (B).Choice(C) isconsistent
withtheprediction.Thelastsentenceofthefirstparagraphproposesthatthemicrobemaybeapotentialsolutionfortheproblemofthehighcostofproducingethanol.Eliminate(D)because the final sentenceof theparagraphdoesnot restate theresults of that year.Thecorrectansweris(C).
45. C This question asks how nonfood crops produce fewer indirect land use emissions.Becausethisisthisfirstquestioninapairedset,thisquestioncanbedoneintandemwithquestion46.Lookatthe“bestevidence”answerchoicesforquestion46first.Thelinesfor(46A) state that nonfood crops such as trees and bamboo need less fertilizer thantraditional biofuel crops. This matches (45C). Connect answers (46A) and (45C). Thelines in (46B)state that inan idealworld,biofuelswouldbeproducedonly fromplantmaterials that cannot be eaten. This information does not explain how nonfood cropsproducefewerindirectlanduseemissions.Eliminate(46B).Thelinesfor(46C)statethatthe enzymes needed to break down plants’ primary structural components…areexpensive. Itmay be tempting to connect this answerwith (45B), since (45B) discussesprices.However,thisanswerdoesnotexplainhownonfoodcropsproducefewerindirectland use emissions. Eliminate (46C). The lines in (46D) explain that an ethanolproduction plantmay be spendingmore than $1million on fertilizer a year. Itmay betempting toconnect thisanswerwith (45B), since (45B)discussesprices.However, thisinformation does not explain how nonfood crops produce fewer indirect land useemissions.Eliminate(46D).Thecorrectanswersare(45C)and(46A).
46. A Seetheexplanationforquestion45.
47. A Thisquestionaskswhatthephraseidealworldmostnearlymeans,asusedinline37.Readthewindow,crossoutthephraseidealworld,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction.Thepassagestatesthatresearchershaveturnedtononfoodcrops…forbiofuelproductionbecausethesecropsneedlessfertilizerandtheyoftenhavea lessdetrimentalimpactontheland.Thephraseanidealworldisusedtointroducetheideathatbiofuelswouldbeproducedonlyfromplantmaterialsthatcannotbeeaten.Incontext,thephraseanidealworldmeanssomethingalongthe linesof“in thebestsituation.”Findananswer thatmatches thisprediction.Choice (A)matches thisprediction.Choice (C)mayseem tempting, but biofuels are not a model for anything. Choice (D) may also seemtempting,sinceautopiansocietyisonethatpossesseshighlydesirableorperfectqualities.However,thedefinitionofautopiansocietyhastodowithasocietyhavinganidealsocial,political,andmoralclimate.Thecorrectansweris(A).
48. D ThisquestionaskswhatcanbeinferredfromtheresultsoftheIndianaUniversitystudyinvolving Zymomonas mobilis. Because this is this first question in a paired set, thisquestion can be done in tandem with question 49. Look at the “best evidence” answerchoices forquestion49 first.The lines for (49A) state that the research showed that thebacterium…usesmoreoftheplantmaterialwhenitusesnitrogengasthanwhenitisfednitrogen in fertilizer. If the same holds true in a production plant, this could reducebiofuelproductioncosts.Thissupportsanswer(48D).Connectanswers(49A)and(48D).Thelinesfor(49B)statethattheprocessisalsomoreenvironmentallyfriendly…because
therearegreenhousegasemissionsassociatedwithproducingnitrogenfertilizer.Itmaybe tempting to connect this answerwith (48B), since (48B)mentions greenhouse gases.However, (48B) isareversal.According to the lines in(49B), theamountofgreenhousegases would change. Eliminate both (49B) and (48B). The lines for (49C) state thatwhereas using Z. mobilis might make it cheaper for producers to use inexpensive,nonfoodcrops,therecouldalsobeaddedcostsandproblems.Thisinformationdoesnotmatchanyof thepossibleanswers forquestion48.Eliminate (49C).The lines for (49D)statethatevenifnitrogenfertilizersarenotusedinthefermentationprocess,theymightstillbeneededtogrowthecrops.Thisinformationmatchesnoneoftheanswersinquestion48.Eliminate(49D).Thecorrectanswersare(48D)and(49A).
49. A Seetheexplanationforquestion48.
50. B This question askswhat theword slimmost nearlymeans, as used in line 73.Read thewindow,crossouttheworldslim,andreplaceitwithanotherwordorphrasethatmakessensebasedonthecontextofthepassage.Then,eliminateanythingthatdoesnotmatchtheprediction. The passage states that questions remain about using Z. mobilis, that therecouldalsobeaddedcostsandproblems,andthatoverallbenefitstotheenvironmentmayalsobeslim.Incontext,thewordslimmeanssomethingalongthelinesof“small”or“lowinnumber.”Findananswerthatmatchesthisprediction.Choices(A),(C),and(D)donotmatchthisprediction.Choice(C)mayseemtempting,butthismeaningofslimdoesnotfitthecontext.Thecorrectansweris(B).
51. D Thisquestionasksinwhatyearistherequiredstatutoryvolumeofconventionalethanolclosesttothatofanotherfueltype,accordingtoFigure1.LookatFigure1.Thestatutoryrenewable fuel volume for conventional ethanol holds steady at approximately 12–15billion gallons for each of the years shown. The only fuel that matches that volume isCellulosicethanolintheyear2022.Therefore,thecorrectansweris(D).
52. B Thisquestion askswhich fuel is least likely tomeet the volume requirements shown inFigure 1, according to Figure 2. Look at Figure 2. Cellulosic ethanol is not visible inFigure2.However, thestatutory requirementsdepicted inFigure1showthe requirementforalargevolumeofcellulosicethanolbytheyear2022.Therefore,thecorrectansweris(B).
Section2:WritingandLanguage
TheBaseBordenAquifer1. A Thepunctuationischangingintheanswerchoices,sothequestionistestingSTOPandGO
punctuation.UsetheVerticalLineTest,andidentifytheideasascompleteor incomplete.Draw the vertical line between the words pollutants and since. The phrase before theverticallineisacompleteidea,andthephraseaftertheverticallineisacompleteidea.Toconnectacompleteideatoacompleteidea,STOPorHALF-STOPpunctuationisneeded.ThecommaisGOpunctuation,soeliminate(B).Thepunctuationischangingagain,souse
the Vertical Line Test again. Draw the vertical line between the words 1978 andresearchers.Thephrasebeforetheverticallineisanincompleteidea,andthephraseaftertheverticallineisacompleteidea,soGOpunctuationisneeded.ThedashandthecolonareHALF-STOPs,soeliminate(C)and(D).Thecorrectansweris(A).
2. B Verbsarechangingintheanswerchoices,sothequestionistestingconsistencyofverbs.Averb must be consistent with its subject and with the other verbs in the sentence. Thesubjectoftheverbischemicals,whichisplural.Tobeconsistent,theverbintheanswerchoicesmustalsobeplural.Theverbsisandwasaresingular,soeliminate(A)and(D).Theotherverb in the sentence isareallowed, so the correct answermust be consistent.Choice (C) changes the meaning of the sentence, so eliminate (C). Choice (B), areexcavated,isconsistentwithareallowed.Thecorrectansweris(B).
3. A Notethequestion!Thequestionasksforthebesttransitionfromthepreviousparagraph,so it’s testing consistency of ideas. The first paragraph discusses experiments in whichpollutants are allowed freemovement in groundwater. The second paragraph discusseswhichchemicalsaretestedandwhy.Thecorrectanswershouldbeconsistentwithbothoftheseideas.Statingthattheprocessmayseemobjectionable,buttheexperimentsprovidevaluableinsightsconnectstheseemingdangeroftheexperimentswiththereasonwhytheyareconducted,sokeep(A).Choice(B)doesn’tmentiontheexperiments,soeliminate(B).Choice(C)doesnotexplainwhytheexperimentsareconducted,soeliminate(C).Choice(D)mentionscivilians,whichisnotconsistentwitheitherparagraph,soeliminate(D).Thecorrectansweris(A).
4. C Note the question! The question asks for the choice that combines the underlinedsentences, so it’s testingprecisionandconcision.Choices (A), (B), and (D) repetitivelymentionthesolventsandthegroundwater,soeliminate(A),(B),and(D).Choice(C)isthemostconciseanswer.
5. B The transition words are changing in the answer choices, so the question is testingconsistency of ideas. The previous sentence states that laboratory experiments cannotreplicate the variation and the next sentence states that researchers cannot accuratelymodel thebehavior…basedon laboratory studies.The sentences state similar ideas, soeliminate(C),whichindicatesoppositeideas.Thesecondsentenceistheconsequenceofthefirst.It’snotanexample,soeliminate(A).Theresultisconsistentwithconsequence,sokeep(B).It’snotthenextstep,soeliminate(D).Thecorrectansweris(B).
6. D Notethequestion!ThequestionasksforaresponsetoapossiblerelevantcounterclaimoftheargumentinsupportofthecontrolledstudiesattheBordenexperimentalsite,soit’stesting consistency of ideas. The correct answer will state a negative aspect of theexperimentsbutthensupporttheexperimentswhiledismissingadanger.Choice(A)statesthe counterclaim but not the response that supports the experiments, so eliminate (A).Choice (B) provides a general regulation for groundwater but doesn’t address theexperiments, so eliminate (B). Choice (C) states a positive aspect of the traditionallaboratory experiments, not the Borden experiments, so eliminate (C). Choice (D)mentionsboththeriskoftheexperimentsandthattheexperimentersareawareoftherisk
andstudyitcarefullybeforeanystudyproceeds,sokeep(D).Thecorrectansweris(D).
7. C Thepunctuationischangingintheanswerchoices,sothequestionistestingSTOPandGOpunctuation.Use theVerticalLineTest,and identify the ideasascompleteor incomplete.Draw thevertical linebetween thewords1978and they.Thephrasebefore theverticallineisacompleteidea,andthephraseaftertheverticallineisacompleteidea.Toconnecta complete idea to a complete idea, STOP or HALF-STOP punctuation is needed. ThecommaisGOpunctuation,soeliminate(A).Thewordsafterthepunctuationarechanging,sousetheVerticalLineTestoneachoneseparately.In(B),thephrasebeforetheverticallineisacompleteidea,andthephraseaftertheverticallineisanincompleteidea,soGOpunctuationisneeded.TheperiodisSTOPpunctuation,soeliminate(B).Forboth(C)and(D),thephrasebeforetheverticallineisacompleteidea,andthephraseaftertheverticallineisanincompleteidea,soGOpunctuationisneeded.TheperiodisSTOPpunctuation,soeliminate(D).Thecorrectansweris(C).
8. D The transitions are changing in the choices, so the question is testing consistency andprecision.Inthesentence,theresearchersdidtwothings:theyinjectedchlorideionsandthey allowed the ions to migrate. The correct answer will be a transition indicating ajoiningoftwosimilarthings.Thewordplusindicatesaddition,soeliminate(A)and(C).Thephrasewhilealsoindicatesacontrast,soeliminate(B).Thecorrectansweris(D).
9. B Commasarechangingintheanswerchoices,sothequestionistestingthefourwaystousea comma. Check for unnecessary information. The word predictable is needed in thesentence, so it should not be set apart by commas; eliminate (A).The sentence does notcontain a list, so there’s no need to use a comma. Eliminate (C) and (D). The correctansweris(B).
10. D Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Look for awordwhosedefinition is consistentwith theother ideas in the sentence.Thesentence discusses how the results were a breakthrough that resulted in a long-termresearch facility, so the definition shouldmean “praised as.”Respectedmeans “held inhigh esteem,” so it’s close. However, stating that the results were respected for abreakthroughisnotthecorrectphrase.Eliminate(A).Worshipdoesmean“praise,”but itusuallyhasareligiousconnotation.Eliminate(B).Recognizedasbeingmeans“identifiedas,”whichisclose,sokeep(C).Hailedmeans“enthusiasticallyacclaimed”or“praised,”sokeep(D).Choice(C)isbothlongerandhasaneutraltone,soeliminate(C).Thecorrectansweris(D).
11. A Notethequestion!Thequestionasksforanexampleofoneof thetechnologiestestedatthe Borden site, so it’s testing consistency of ideas. The correct answer will state atechnologyusedatthesite.Theverticaltreatmentwallisatechnologythatcouldbeatthesite, so keep (A). Choice (B)mentionsmany of the procedures but does notmention aspecific technology,soeliminate(B).Choice(C)doesnotmentionaspecific technology,soeliminate(C).Choice(D)doesnotmentionaspecifictechnology,soeliminate(D).Thecorrectansweris(A).
Yes,WeCanal12. C Introductory transitions are changing in the answer choices, so thequestion is testing the
consistency of that introduction. The sentence after the introduction states that thoughwemay take it forgrantednow that variousmodesof transportationcanmake it overorthroughjustaboutanynaturalobstacle,theeasetomoveisinfactrelativelynew.Thefactthatmodesoftransportationcanmakeitoverorthroughanynaturalobstaclestandsin contrast to the truth that the ease to move is in fact relatively new, so the propertransition will address this contrast. Because, after, and for are each same directiontransitions, soeliminate (A), (B),and (D).While is theonlyword that can functionas achangeofdirectionsinceitcanworkbothways,dependingoncontext.Thecorrectansweris(C).
13. C Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Lookforaphrasewhosedefinitionisconsistentwiththeotherideasinthesentence.Thesentencestatesthatwemaytakeitforgrantedthatvariousmodesoftransportationcanmake itoveror through justaboutanynaturalobstacle,but that thisphenomenon is infactrelativelynew.Therefore,thecorrectphrasingwillaccuratelysummarizehowmodesoftransportationcanmakeitoverorthroughjustaboutanynaturalobstaclewithanounsuchas“movement.”Easetomoveandeasymovingarebothverbs,soeliminate(A)and(B).Easeofmovementaccuratelyrestatestheconceptbeforethecomma,sokeep(C).Easetomovementwould indicate that themodesof transportation themselvescause theirownmovement,soeliminate(D).Thecorrectansweris(C).
14. A Notethequestion!Thequestionaskswhetherthesentenceshouldbeadded,soitistestingconsistency.Ifthecontentofthenewsentenceisconsistentwiththetopicspresentedinthepassage, then it should be added. The previous sentence discusses the LouisianaPurchase…adding…about themiddle thirdofU.S. territory, and the followingsentencementionsoneproblem[that] couldmake travel to the fertileWestmore trouble than itwasworth.Theproposedsentencewouldaddinformationstatingthat thenewterritoriesprovidedgreat resources for the nation, including fertile farmlands and the seeminglyendlessMississippiRiver,whichbuildsonthecontentoftheparagraphregardingtraveltothe new Louisiana Territories, so eliminate (C) and (D). The sentence does not simplyrestate the first sentence’s central argument, so eliminate (B). The additional sentencedoes list some of theWest’s positive attributes in contrast with the next sentence. Thecorrectansweris(A).
15. C Commasarechangingintheanswerchoices,sothequestionistestingthefourwaystousea comma. The phrase had expanded and the population had each contain necessaryinformation that shouldnotbe surroundedbycommas, soeliminate (A)and (D).Use theVerticalLineTesttoevaluatetheremainingchoices,drawingtheverticallinebetweenthewords1840sandthe.Thephrasebythe1840s isan incomplete idea,and thephrase thepopulationhadexpandedagreatdealintothenewterritoriesofIllinois,Tennessee,andespeciallyOhioisacompleteidea.Toconnectacompleteideatoanincompleteidea,GOpunctuationisneeded,soeliminate(B).Thecorrectansweris(C).
16. A Note the question!The question askswhich choice best supports themain point of theparagraph,soitistestingconsistency.Accordingtothebeginningofthesentence,horsesandwagonswereeffectivemeansof transportinggoodsacrossshortdistances,and thetransitionbut leads into theunderlinedportion that states these became unreliablewhenfaced with mountains and inhospitable conditions. Because of the transition but, theunderlinedportionshouldstand incontrastwith therestof theparagraph,which isabouthow the most efficient method of travel…was water; keep (A). The affordability of ahorseorawagon,howmanyAmericanswereawareofsuchvastterritoriestotheWest,andplacestosleepandwaterone’shorsesarenotideasthatcontrasttheideathatthemostefficientmethodoftravel…waswater;eliminate(B),(C),and(D).Thecorrectansweris(A).
17. B Apostrophes are changing in the answer choices, so the question is testing apostropheusage. From the meaning of the sentence, it can be predicted that the counterpartsthemselves donot possess the ocean for centuries already, so no apostrophe should beadded to counterparts; eliminate (A) and (D). It can also be predicted that theEnglishcounterpartsbelongtothepluralsubjectthenewAmericans.Usedintheword“they’re,”an apostrophe indicates the contraction “they are.” Eliminate (C). Their is the pluralpossessivepronoun.Thecorrectansweris(B).
18. A Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Lookforawordconsistentwiththeotherideasinthesentence.Inthepreviousparagraph,mountainsarementionedintandemwith inhospitableconditions, so theunderlinedwordshould mean something like “inhospitable” or “dangerous.” Treacherous means“dangerous,” so keep (A).Hassling and annoying are synonyms, but the mountains are“dangerous,”not justannoying;eliminate (B)and (D).Prevaricatingmeans “deceiving,”butthemountainsaredangerousnotdeceptive,soeliminate(C).Thecorrectansweris(A).
19. D Thewords are changing in the answer choices,with the option to delete the underlinedportion in (D). This question is testing precision and concision. Consider the option todeletecarefully,asitisoftencorrect.Sincethesentenceindicatesthatanyshipthatcouldaccesstheseplacesfromthegreatshippingportsintheeast,itisunnecessarytorestatetheships’accessasecondtimewiththephrasebygettingthere,bywayofgettingtoit,orintheprocessofgettingthere;eliminate(A),(B),and(C).Thebestoptionistodeletetheunderlinedportionbecauseitisthemostconciseanswer.Thecorrectansweris(D).
20. D Thewords are changing in the answer choices,with the option to delete the underlinedportion in (D). This question is testing precision and concision. Consider the option todeletecarefully,asitisoftencorrect.GeorgeWashingtonisalreadyaman’sname,sothephrasesamannamed,theoneknownas,andtheworld-renownedmanareeachredundant;eliminate(A),(B),and(C).Thebestoptionistodeletetheunderlinedportionbecauseitisthemostconciseanswer.Thecorrectansweris(D).
21. B Note the question! The question askswhere sentence 5 should be placed, so it’s testingconsistency.Determinethesubjectmatterofthesentence,andfindtheothersentencesthatalsodiscussthatinformation.Sentence5introducesthemissinglinktotheWest,America’s
Mediterranean, theGreatLakes. Therefore, this sentence should come before any othermentionof theGreatLakes.Sentence2statesthat the lakes…andone lake inparticular,LakeErie,providedaccesstoavarietyofpointstotheWest,sosentence5shouldcomebeforesentence2.Thecorrectansweris(B).
22. D Verbs are changing in the answer choices, so the question is testing the consistency ofverbs.Averbmustbeconsistentwithitssubjectandwiththeotherverbsinthesentence.Theverbinthiscaseishavingdugandaswrittenreferstothismanmadewaterway—theErieCanal.Itcanbepredictedthattheintendedmeaningofthesentenceisnotthatthecanalitselfwasdugbyworkersandhorses,butratherthattheworkersandhorsesdugthecanal;eliminate(A).Thecanalwasneitherdiggingnorwasbyworkersandhorses,soeliminate(B)and (C).Thismanmadewaterwaywasdugbyworkersmatches the prediction. Thecorrectansweris(D).
MinimumWage,MaximumDebate23. D Note the question! The question asks which sentence is the best introduction to the
paragraph,soitistestingconsistency.Ifthecontentofananswerchoiceismoreconsistentwith the ideassurrounding it, then it shouldbeadded;otherwise, it shouldnotbeadded,because leaving thesentenceas iswillbe themostconsistentoption.The introduction tothesecondsentenceofthepassagesaysthattheymightbeflippingburgers,sothecorrectanswer choice will correctly identify who might be flipping burgers. The Americanworkforce is a collective noun thatwould notmatch they, so eliminate (A).Neither thenumber of jobs norgetting a jobmight be flipping burgers, so eliminate (B) and (C).Manyteensisasubjectthatmightbeflippingburgers.Thecorrectansweris(D).
24. B Commasarechangingintheanswerchoices,sothequestionistestingthefourwaystouseacomma.Thesentencecontainsalistofthreethingsthattheymightbedoing:1)flippingburgers,2)tearingmovietickets,or3)operatingamusement-parkrides.Orshouldnotbesurroundedbycommaswhenusedinalist,soeliminate(A).Thereshouldalsobeacommaafter each item in the list.Choices (C) and (D)use a colon and semicolon, so eliminatethem.Choice(B)hasacommaaftereachiteminthelist,soitisthecorrectanswer.
25. C Vocabularyandpronounsarechanginginthechoices,sothequestionistestingwordchoiceandconsistencyofpronouns.First,lookforaphrasewithadefinitionthatisconsistentwiththeotherideasinthesentence.Thesentenceaskshowcouldaminimum-wage jobeffectsomeonewhose familydependson it?Note that thewordeffectchanges toaffect in theanswerchoices.Effectasaverbmeans“tobringabout”andaminimum-wagejobdoesnot“bring about” someone whose family depends on it, so eliminate (A).Affect, however,means“acton”andmatchestheintendedmeaningofthesentence.Thepronounwho’sisthecontractionfor“whois,”soeliminate(B).Theintendedsubjectofthesentenceissomeonewhose family depends on it and should not be split by a comma, so eliminate (D). Thecorrectansweris(C).
26. D Commasarechangingintheanswerchoices,sothequestionistestingthefourwaystouseacomma.Thepartofthesentenceyearlyearningsbelow$24,300forafamilyoffourin
2016 need to be able to live is necessary information, so as written it should not besurrounded by commas; eliminate (A). However, yearly earnings below $24,300 for afamily of four in 2016 by itself is unnecessary information that could be bracketed bycommas.Choices(B)and(C)donotproperlybrackettheinformation,soeliminatethem.Bracketingtheinformationwithparenthesesisanacceptablealternativetobracketingwithcommas.Thecorrectansweris(D).
27. A Notethequestion!Thequestionaskswhetherthesentenceshouldbeadded,soitistestingconsistency.Ifthecontentofthenewsentenceisconsistentwiththetopicspresentedinthepassage,thenitshouldbeadded.Thelastsentenceofthepreviousparagraphstatesthatanobvioussolutionwouldbetoraisetheminimumwage,soeventhoseatthebottomofthepayscalecanaffordlife’snecessities.However,thecurrentfirstsentenceofthisparagraphsaysthatsomesmall-businessowners…arguethatahigherminimumwagewouldcutsomuch into their profit that theywould be forced to hire fewerworkers, which directlyopposes theobvioussolution.Theproposedsentencewouldadd information,stating thateventhoughpayincreaseproposalshavebeenofferedtoaddresstheearningsgap, theissueremainscontroversial,whichprovidesatransitionfromtheobvioussolution to theobjection to the solution from the small-business owners; eliminate (C) and (D). Thesentencedoesnot insert theauthor’sopinion, so eliminate (B).The additional sentencedoes introduce the subject matter of this paragraph, which is that the issue remainscontroversial.Thecorrectansweris(A).
28. C Introductory transitions are changing in the answer choices, so thequestion is testing theconsistency of that introduction. The sentence after the introduction states that a higherminimumwagewouldactuallydestroy jobs rather than create them, leading tohigherunemploymentandslowereconomicgrowth.Thisisconsistentwiththeinformationinthepriorsentence,whichstatesthatsomesmallerbusinessowners,forinstance,arguethatahigherminimumwagewouldcutsomuchinto theirprofit that theywouldbeforcedtohirefewerworkers.Therefore,itcanbepredictedthatthecorrectanswerwillbeasamedirection transition. However, nevertheless, and conversely are change-directiontransitions,soeliminate(A),(B),and(D).Subsequentlyisasame-directiontransitionthatbuildsuponthepriorsentence.Thecorrectansweris(C).
29. B Pronouns are changing in the answer choices, so the question is testing consistency ofpronouns.Thepronounreferstothepricespossessedbythebossesat largerbusinesses,particularlyfast-foodchainsandbigboxstores,sothecorrectanswermustbebothpluraland possessive. They’re is a contraction meaning “they are” and not possessive, soeliminate(A).Theirisapluralpossessivepronoun,sokeep(B).Therereferstoplace,soeliminate(C).One’sissingular,soeliminate(D).Thecorrectansweris(B).
30. B Thewords are changing in the answer choices,with the option to delete the underlinedportion in (D). This question is testing precision and concision. Consider the option todeletecarefully,asitisoftencorrect,thoughthistimeitleavesoutakeywordtomakeacomparison valid. The sentence introduces the comparison of bargain prices that thesebusiness leadersargue theycannotcontinue tooffer,andbargainprices thatcannotbecomparedwithwhat’snexttotheircompetitors,northeircompetitorsalone;eliminate(A)
and (D). Choice (B) correctly uses those to refer to the bargain prices of theircompetitors,sokeep(B).Bargainpricesareplural,soeliminate(C).Thecorrectansweris(B).
31. D Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Look for a word or phrase whose definition is consistent with the other ideas in thesentence.From the introductoryphraseevenon, it can be determined that the underlinedwordwillcontrastwiththesecondpartofthesentencestatingthatthedebatesurroundinghow to ease poverty is complicated. From this information, it can be predicted that thecorrectanswershouldbesomethinglike“notcomplicated.”Hotbuttonandhot topicareslangphrasesthatmean“controversial”anddonotmatchtheprediction,soeliminate(A)and (B).Honest does not match “not complicated,” so eliminate (C). Straightforwardmatches“notcomplicated.”Thecorrectansweris(D).
32. D Notethequestion!Thequestionaskswhetherthesentenceshouldbeadded,soitistestingconsistency.Ifthecontentofthenewsentenceisconsistentwiththetopicspresentedinthepassage,thenitshouldbeadded.ThesentencestatesthattheUnitedStateshasaminimumwagetomedianincomeratiothatisoneofthetop10suchratiosworldwide.First,checkthegraphtoseethat,accordingtothedata,theUnitedStatesisbehind16othernationsintermsofminimumwagetomedianincomeratio;eliminate(A)and(B).Theinformationinthe sentence is not given elsewhere in this paragraph, so eliminate (C). Indeed, theinformationdoesnotaccuratelyreflectdatafromthegraph.Thecorrectansweris(D).
33. C Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Lookforaphrasewhosedefinitionisconsistentwiththeotherideasinthesentence.Thesentencearoundtheunderlinedphrasestatesthatasthedebatesurroundingtheminimumwage does something,anew idea, theguaranteedminimum income,hasbegun togainsome traction. Since there are no change-direction transitions in the sentence, it can bepredicted that the correct answer choicewill be something also like “gains traction” or“maintainsandbuildsmomentum.”Firesupisaslangphrasethatmeans“tostartorbegin,”andalthoughthedebateisbuildingmomentumortraction,thereisnoindicationthatitisanewdebate;eliminate(A).Blazesatrailisaslangphrasethatmeans“createanewmethodorway,”whichdoesnotmatch theprediction;eliminate (B).Rageson is a slangphrasethatmeans“maintainsandbuildsongoingmomentum,”sokeep(C).Burns itdown is theoppositeoftheprediction,soeliminate(D).Thecorrectansweris(C).
Truth,Fiction,andReality34. D Notethequestion!Thequestionaskswhichoptionbestcombinesthetwosentences,soit’s
testing precision and concision. Look for the answer that combines the sentences whilemaintaining the meaning of the originals. The two sentences both use the phrasedocumentary films, so the correct answer will eliminate this redundancy withoutintroducing another. Choices (A) and (B) maintain the redundancy, so eliminate them.Accordingtotheoriginalpairofsentences,viewers’expectationsofwhat“reality”meanstendtoshift,whichhasasignificantlydifferentmeaningthanviewersexpect“reality”toshift;eliminate(C).Thecorrectansweris(D).
35. B Thepunctuationischangingintheanswerchoices,sothequestionistestingSTOPandGOpunctuation.UsetheVerticalLineTest,andidentifytheideasascompleteor incomplete.Drawtheverticallinebetweenthewordsfilmsandeven.Thephrasetherefore,aspeoplewatchmore documentaries, their expectations change for what “realistic” films is anincompleteidea,andthephraseevenfictionfilms—shouldlooklikeisalsoanincompleteidea.Toconnecttwoincompleteideas,GOpunctuationisneeded;eliminate(C)and(D).Thephraseevenfictionfilmsisunnecessaryinformationinthecontextofthefullsentenceandshouldbebracketedbycommas.Since there is adashafter fiction films in thenon-underlinedportionofthesentence,acommaisnotanacceptableoption;eliminate(A).Thecorrectansweris(B).
36. B Thepunctuationischangingintheanswerchoices,sothequestionistestingSTOPandGOpunctuation.Use theVerticalLineTest,and identify the ideasascompleteor incomplete.Draw the vertical line between the words film and in. The phrase Director RyusukeHamaguchireleasedafilmisacompleteidea,andthephrasein2015calledHappyHourisanincompleteidea.Toconnectacompleteideawithanincompleteideanopunctuationisneeded,soeliminate(A),(C),and(D).Thecorrectansweris(B).
37. C Note thequestion!Thequestion askswhich choice ismost consistentwith the previousexamples in the sentence, so it is testing consistency. The previous examples in thesentencearerapid-fireeditsandglamoroussuperstaractors,whicharemovieproductionqualities thatcharacterize speedier films.Therefore, it canbepredicted that the correctchoicewillbeaquality thatcouldcharacterizespeedier films.While long ticketholderlinesmightbeoutsideoftheatersshowingspeedierfilms,theyarenotqualitiesofthefilmsthemselves;eliminate (A).Englishsubtitlesarecharacteristicsof filmswithnon-Englishdialogue,butnotnecessarilyspeedierfilms;eliminate(B).Explosivespecialeffectsmatchthe prediction of a speedier movie production quality, so keep (C). Professionaladvertisingcampaignscanaccompanyaspeedierfilm,butarenotactuallyacharacteristicofafilmitself;eliminate(D).Thecorrectansweris(C).
38. B Apostrophes are changing in the answer choices, so the question is testing apostropheusage. From the meaning of the sentence, it can be predicted that theworks belong toHamaguchi, so there should be an apostrophe and then an “s” appended toHamaguchi;eliminate (A) and (D).Thework, however, does not possess anything, so eliminate (C).Thecorrectansweris(B).
39. A Note thequestion!Thequestion askswhich sentence conclusion logically completes thediscussion of Happy Hour and provides an effective transition into this paragraph’sdiscussion,soitistestingconsistency.Ifthecontentofananswerchoiceismoreconsistentwith the ideassurrounding it, then it shouldbeadded;otherwise, it shouldnotbeadded,because leaving the sentence as is will be the most consistent option. The end of theprevious paragraph states thatHamaguchi’swork…can almostmake it feel thatwe areexperiencinglifeitself,sothecorrectchoicewillsaysomethinglike“infactHappyHourislikelifeitself.”ThatHappyHourissorealisticthatviewerscanwonderwhetherthisfictional film is itself a kind of authentic reality matches the prediction, so keep (A).There is no reason tomention thatHappyHour is too long to be shown in traditional
theaters, atypical of the kind of movies coming out of Japan, or the work of anaccomplisheddirector,soeliminate(B),(C),and(D).Thecorrectansweris(A).
40. D Thevocabularyischangingintheanswerchoices,sothisquestionistestingwordchoice.Look for awordwhosedefinition is consistentwith theother ideas in the sentence.Thesentencesays that idea[whether this fictional film is itselfakindofauthenticreality]hasbeenonethatartistshave insomewaydealtwithallalong.Fromthecontextof thesentence, the underlined word should be something like “look at” or “think about.”Research is too scientific aword forwhat artists do in their artwork, so eliminate (A).Huntandscoutbothmean“tolookfor”not“tolookat”or“thinkabout,”soeliminate(B)and(C).Toexploreanideaistothinkaboutit.Thecorrectansweris(D).
41. C Transitionsarechangingintheanswerchoices,sothequestionistestingtheconsistencyofthat transition. The sentence around the transition asks if audiences 70 years from nowwatchour filmswithasimilarsenseofsuperiority,whatwouldthatmeanforourownsense of reality? This question responds to the statement in the prior two sentencesindicatingthatwatchingafilmfromthe1940s,wemayconsidertheactingawkwardandstilted and that the films today seem much more realistic. Since the films seem morerealisticbutthequestioninthesentenceindicatestheymightnotalways,itcanbepredictedthat a change-direction transition isneeded.Therefore,moreover,andso are each same-directiontransitions,soeliminate(A),(B),and(D).Thecorrectansweris(C).
42. B Notethequestion!Thequestionaskswhichmosteffectivelysetsupthemainideaoftheremainderoftheparagraph,soitistestingconsistency.Ifthecontentofananswerchoiceis more consistent with the ideas surrounding it, then it should be added; otherwise, itshouldnotbeadded,becauseleavingthesentenceasiswillbethemostconsistentoption.The paragraph to this point says that the convergence of documentary and fictionfilmmakingisoneofthemostinterestingculturaldevelopmentsofourtimeandhasgreatconsequences for the medium itself. The remainder of the paragraph discusses onlinepersonalitiesandourin-the-worldpersonalities,sothecorrectanswerwillbridgethegapbetween these two concepts. There is no other discussion ofHollywood films, the waypeople watch movies today, nor a patience on the part of the audience that is rare,eliminate(A),(C),and(D).Couldimpacthowpeoplegenerallyinteractwiththeworldaddresses themanner inwhich the convergenceof documentaryand fiction filmmakingcould impact our online personalities and our in-the-world personalities. The correctansweris(B).
43. C Verbs are changing in the answer choices, so the question is testing the consistency ofverbs.Averbmustbeconsistentwithitssubjectandwiththeotherverbsinthesentence.Theverbwerecreating isbeingpaired incontextwith the idea thatperhapsour in-the-worldpersonalitiesare justas fabricatedasouronlineavatars.Therefore, the correctanswershouldmatchthesimplepasttenseoffabricated.Werecreatingisnotpasttense,soeliminate(A).Wouldcreateandwouldhavecreated introduceaconditionalphrasingthatdoesnotmatch the restof the sentence, soeliminate (B)and (D).Havecreatedmatchesfabricated.Thecorrectansweris(C).
44. A Thewords are changing in the answer choices,with the option to delete the underlinedportion in (D). This question is testing precision and concision. Consider the option todeletecarefully,asitisoftencorrectbecauseitisthemostconciseanswer.Thesentenceoffers a comparison of online personalities for ourselves and the personalities of ouronlineavatars.Thoseaccuratelyrefersbacktothepersonalitiesofouronlineavatars,sokeep(A).Themreferstoagroupbeingactedupon,soeliminate(B).That issingularandpersonalities are plural, so eliminate (C).Deleting thosewould result in an illegitimatecomparison between our in-the-world personalities and of our online avatars, soeliminate(D).Thecorrectansweris(A).
Section3:Math(NoCalculator)1. A Tofindthesumofcomplexnumbers,justaddthemtogether,treatingilikeavariable.The
sumis6+2i+3+5i.Combineliketermstofindtheanswer.Add6and3toget9.Then,addtheimaginaryterms,2iand5i,toget7i.Addthesetwotermstoget9+7i.Thecorrectansweris(A).
2. C ReadtheFullQuestion.Thequestionasksforthemeaningof14intheequation.Next,labeltheequation.Crepresentsthetotalcostandhrepresentshoursofwork.Next,useProcessofElimination.14 isnotassociatedwithhoursofwork, soeliminate (A)and (D).14 isaddedto9htodeterminethetotalcost,soitcannotbethetotalcostforanyamountofwork;eliminate(B).Thecorrectansweris(C).
3. A UseBite-SizedPiecesandProcessofElimination todetermine thecorrectanswer.Sincethisquestiondealswithpercentages,30%and70%mustbeconvertedtodecimals,0.3and0.7, respectively. Eliminate (C) and (D), since the percentages are not converted todecimals.TrailMixX is30%peanutsbyvolumeand is representedbya; therefore, thecorrectrelationshipwilltake30%ofa.Likewise,TrailMixYis70%peanutsbyvolumeandisrepresentedbyb;therefore,thecorrectrelationshipwilltake70%ofb.Choice(B)hasreversedthisrelationship,soeliminateit.Thecorrectansweris(A).
4. D Thisquestionalreadystatesthatqisequalto12,soplug12intothefirstexpressiontogetp= (12)=9.Don’tstophere,because9isnotthecorrectanswer.MakesuretoReadthe
FullQuestiontoseethatitasksforthevalueof3p−4.Plugin9forptoget3(9)−4=27−4,whichequals23.Thecorrectansweris(D).
5. B Theequationofthelinegiveninthisquestionisiny=mx+bform,wheremistheslopeandbisthey-intercept.Sincethey-interceptis6,eliminate(C)and(D),whichbothhavenegativey-intercepts.Theslopeforthisequationis−3,whichmeansthatthegraphoftheline will slope downward from the upper left quadrant to the lower right quadrant.Eliminate(A),sincethisgraphhasapositiveslope.Thecorrectansweris(B).
6. D Whentherearenumbersintheanswerchoices,tryPluggingIntheAnswers.Thesechoicesrepresentpossiblevaluesofz.Startwith(C),whichis4.Ifzis4,thentherightsideoftheequationbecomes(4y+r)(4y−r).ExpandthisexpressionusingFOILtofindthefirstterm,
which will be 16y2. Since this doesn’t match 9y2 from the left side of the equation,eliminate(C).Since16isbiggerthan9,thecorrectanswerneedstobesmallerthantheonein(C).Therefore,eliminate(A)and(B).Choice(D)mustbethecorrectanswer.Testthisby plugging in 3 for z.Notice that the first termof (3y + r)(3y − r) is 9y2. The correctansweris(D).
7. D The question asks for a specific value, so Plug In the Answers. The answer choicesrepresentvaluesofk.Becausethevaluesforfandginthetabledonotfollowanyeasilydiscernable pattern, work systematically through the answers rather than starting in themiddle.Startwith(A).Ifx=2, then f(2)−g(2)=2.Nowuse the table todeterminethevaluesforf(2)andg(2).Thevalueoff(2)is1,andthevalueofg(2)isalso1.Since1–1doesnotequal2,eliminate(A).Next,try(B)andcontinuetousethetabletofindthevaluesforthefunctions.Ifx=1,f(1)−g(1)=1.Thevalueoff(1)is−1,andthevalueofg(1)is2.Since−1−2doesnotequal1,eliminate(B).For(C),f(0)−g(0)=0.Thevalueoff(0)is1,andthevalueofg(0)is3.Since1–3doesnotequal0,eliminate(C).For(D),f(−1)−g(−1)=−1.Thevalueoff(−1)is3,andthevalueofg(−1)is4.Since3−4=−1,(D)mustbetheanswer.
8. B Sincethequestionasksforaspecificvalue,itcanbesolvedbyPluggingIntheAnswers;
however,becausethequestioninvolvesroots,itmaybeeasiertosolveinstead.Since
=2and =6,rewritetheexpressiontoread +2=6.Isolatetbyfirstsubtracting2
frombothsidestoget =4.Next,squarebothsidestocleartheradical:t=42,whichis
16.Thecorrectansweris(B).
9. B Whentherearevariablesintheanswerchoices,PluggingInisanoption.However,since
thereare3variablesinthequestion,itisprobablyeasiertojustdoalgebraicmanipulation.
The answer choices indicate that the equationmust be solved form. The variablem is
multipliedbyboth10andh,sotoisolatem,dividebothsidesby10h: = .The
10andthehontherightsideoftheequationcancel,leaving =m.Thecorrectanswer
is(B).
10. C Sincetherearevariablesintheanswerchoices,usePluggingIn.Letb=2.Theexpression
becomes = = = = .Nowpluginb=2ineachanswer
choiceandeliminateanychoicethatdoesnotequalthetargetvalueof ,or2.5.Eliminate
(B)and(D)sincetheanswermustbeafraction;(B)and(D)equal2and5,respectively.
Check(A),whichbecomes2− =2− =2− =1.5.This is toosmall,so
eliminate(A).Check(C),whichbecomes2+1− =3− =3− =2.5.This
matchesthetargetvalue,sothecorrectansweris(C).
11. A Tofindanaverage,usetheAveragePie.Findthetotalandputitinthetopsection.Inthisquestion,thereare5terms,oneforeachmonthofTaylor’straining:39,46,48,49,andh.Therefore,thetotalis39+46+48+49+h.Althoughthiscanbesimplified,leaveitasistokeepit inasimilarformto theanswerchoices.Sincethereare5 terms,puta5 in thelowerleftsectionofthepie.Thisresultsinthefollowingpie:
The total of these 5 termsmust be divided by 5 in order to calculate Taylor’s average.
Therefore,heraveragecanbeexpressedas .Shewantsthisvalueto
beatleast45,sowritethisastheinequality ≥45.Thisdoesn’tmatch
anyof theanswerchoices,but (B)and (D)canbeeliminated since theydonothave the
correctnumeratorortotal.Lookat(A),whichcorrectlysumsupall5termsandsaysthey
mustbeequal toorgreater than5timeshergoal.Noticethat thisanswerchoiceis justa
resultofmultiplyingbothsidesoftheinequalityby5.Thecorrectansweris(A).
12. C Theparabolainthegraphopensdownwardbecausethereisanegativeterm(−a)infrontofx2.However,theequationinthequestiondoesnothaveanegativeterminfrontofx2,whichmeansthatthegraphofy=a(x+m)2+nwillopenupward.Eliminate(A)and(B). Inaparabola,addingorsubtractingatermdirectlyfromthevalueofxbeforesquaringitwillshifttheparabolaleftorright,respectively.Thismeansthatforthegraphofy=a(x+m)2+n,theadditionofmtoxwillcausetheentireparabolatoshifttotheleftadistanceofm.Therefore,thenewvertexoftheparabolay=a(x+m)2+nwillbe(−m,n).Thecorrectansweris(C).
13. B The key to finding the correct system of equations or inequalities is to translate theinformationusingBite-SizedPiecesanduseProcessofEliminationateachstep.Chooseapieceofstraightforwardinformationtotranslatefirst,suchasthateachpoundofpotatoes,p,costs$3.25andeachpoundofcarrots,c,costs$2.47.Eliminate(C)and(D),sincethoseanswers do not relate the coefficients to the correct variables. To determine the correctinequality that relates to the number of pounds of vegetables, refer to the statement theownerneedstobuyatleastthreetimesasmanypoundsofpotatoesaspoundsofcarrots.Translate this statement into an inequality. The owner needsmore potatoes than carrots.Whatevernumberofpoundsofpotatoesshebuys,thatnumberneedstobeatleast3timesmorethanthenumberofpoundsofcarrots.Therefore,thecorrectinequalityisp≥3c.Thecorrectansweris(B).
14. B There are variables in the answer choices, so Plug In to solve this question. Since
calculatoruseisnotallowed,picknumbersthatwillmakethematheasy,suchasr=3and
s=6.Theexpression in thequestionbecomes = (3+2)2= (5)2=25.The target
value is25.Checkeachanswerchoiceandeliminateanyanswer thatdoesnotequal25.
Choice(A)becomes32+ + ,whichsimplifiesto9+ + .Thisbecomes9+
18+12,whichequals39.Thisdoesnotequal25,soeliminate(A).Choice(B)becomes32
+ + ,whichsimplifiesto9+ + .Thisbecomes9+12+4,whichequals
25. Keep (B), but check (C) and (D) just in case. Choice (C) becomes 32 + , which
simplifies to9+ .Thisbecomes9+12,whichequals21.Eliminate (C).Choice (D)
becomes 32 + , which simplifies to 9 + . This becomes 9 + 4, which equals 13.
Eliminate(D).Thecorrectansweris(B).
15. D ThismayseemlikeanidealquestionforPluggingIntheAnswers,however,doingsowillquickly result in a messy and complicated situation. Instead, study the expression byplugginginvaluesforxtofindvaluesfordinordertomakeasketchofthegraph.Whenx=1,3(1)2+6(1)=9=d.Whenx=2,3(2)2+6(2)=24=d.Nowexaminewhathappensasxdecreases.Whenx=0,3(0)2+6(0)=6=d.Whenx=−1,3(−1)2+6(−1)=−3=d.Whenx=−2,3(−2)2+6(−2)=0=d.Usethesepointstomakeasketchofthegraph.
Thismeans that the equation only has real solutions for values ofd that are equal to orgreaterthan−3.Therefore,theonlyvalueofdthatwouldresultinanequationwithnorealsolutionsis−4.Thecorrectansweris(D).
16. or5.25
Tosolveforn,startbymovingitintothenumeratorofthefractionontherighttoget =
.Cross-multiplytoget4n=21.Dividebothsidesby4togetn= .Thecorrectansweris
or5.25.
17. 7.5 Startbytranslatingtheproblemintoanequation.5pintsofa5%solutionis5 or0.25
unitsof sugar.Theamountof30%added isunknown, socall theamountx.Therefore,x
pintsof30%solutionisx or0.3xunitsofsugar.Thenewsolutionis20%sugar,which
is or0.2.Percentagesrepresent ,sotheleftsideoftheequationwillbethetwo
solutionsofsugaraddedtogether,0.25+0.3x,overthetotalamount,whichwillbe5+x.
Thisisequalto0.2,theresultingsolutionpercent.Thisgives =0.2.Solveby
multiplyingbothsidesby5+xtoget0.25+0.3x=0.2(5+x).Distributeontherightside
of theequation toget0.25+0.3x=1+0.2x.Gather like termsby first subtracting0.25
frombothsidestoget0.3x=0.2x+0.75.Subtract0.2xfrombothsidestoget0.1x=0.75.
Finally,isolatexbymultiplyingbothsidesby10togetx=7.5.Thecorrectansweris7.5.
18. 1,2,3,4,6,or12
Plug In to answer this question. First, try to think of the integers that can be raised to a
power to equal 81.Try thinking of the factors of 81. For example, 92 = 81. Thatwould
meanthat =2andy=6.Onepossibleanswertothequestionis6.Anotherpossibilityis
that34=81.Therefore, =4andy=12.Thebasecouldsimplybe81itself,as811=81.
Thus, = 1 and y = 3.A less obvious but still valid optionwould be for x to have a
fractionalexponentthatdoesn’treduce.Ify=1,then =81andcubingbothsidesgivesx
=531,441.Ify=2,then =81,x2=531,441,andx=729.Finally,ify=4,then =81,
x4=531,441,andx=27.Althoughthecorrectanswercouldbe1,2,3,4,6,or12,gridin
thefirstanswerthatworks.
19. or1.25
SincecircleOhasaradiusof2,usetheformulaA=πr2tofindtheareaofthecircle.A=
π(2)2=4π.Theareaoftheentirecircleis4πandtheareaofthesectoris π.Tofindwhat
fractionoftheareaofthecircleistheareaofthesector,dividethesectorbythewholeto
get .Canceltheπinbothpartstoget .Divideby4bymultiplying bythereciprocal
of4: × = .Thecorrectansweris .
20. 24 SinceGI isparallel toFJ, GIH isalsoa rightangle.The lengthofHIcanbefoundby
either using the Pythagorean Theorem or by noticing the Pythagorean triple 5-12-13.
Therefore,HI=12.TriangleFHJandtriangleGHIaresimilartrianglesbecausetheyhave
thesameangles.Thesidesofsimilar trianglesareproportional,sosetuptheproportion
tofindthelengthofHJ.Plugintheknownvaluestosolvetheproportion: =
.Tomake thematheasier, reduce to .Therefore, = .Cross-multiply to get
HJ=(2)(12)=24.Thecorrectansweris24.
Section4:Math(Calculator)1. B ThequestionasksforthedifferencebetweenthedistanceofRebecca’stripandNatalie’s
trip.BothRebeccaandNataliebicycletoadestinationthatis2,400yardsfromNatalie’s
home.However,theydonotbeginatthesameplace.Nataliebeginsat0,butRebeccadoes
not.Thedifferencebetweentheirstartingpointsisthedifferencebetweenthedistancesof
theirtrips.Goto0onthex-axisandfindRebecca’sstartingpointbytracingstraightupto
thelinelabeledRebecca.Thislinetoucheshalfwaybetween600and1,200onthey-axis,
sohertripis =900yardsshorterthanNatalie’s.Thecorrectansweris(B).
2. C Alejandrodrivesandthenstopsatastore.Whileheisstoppedinthestore,hedoesn’taddanydistancetraveled.Therefore,aportionofthegraphmustbeflat.Eliminate(A),whichisalwaysincreasingwithnoflatportion.Hethenproceedsataslowerspeed.Althoughthespeed is slower, the total distance traveled still increases, so eliminate (B). Speedcorrelatestoslope.Therefore,theslopeofthefirstportionmustbegreaterthantheslopeoftheendportion.Eliminate(D),whichreversesthis.Thecorrectansweris(C).
3. D When subtractingpolynomials, useBite-SizedPieces.Combine like termsone at a time,eliminatingchoicesateachstep.Usethechoicestohelpdecidewheretostart.Therearethreepossibilitiesfortheconstanttermandonlytwopossibilitiesforeachoftheothertwoterms,sostartwiththeconstant.The−11inthesecondpolynomialmustbesubtractedfromthe−5inthefirstpolynomialtoget−5−(−11)=−5+11=11−5=6.Eliminate(A),(B),and(C),whichdonotinclude6.Onlyonechoiceremains.Thecorrectansweris(D).
4. C Thequestion asks for an equivalent inequality.The inequalities in the choices are in thesame form as the original. The only difference is the coefficients. This indicates thatfactoringisthekey.Alltermsintheoriginalinequalityaremultiplesof3.Dividebothsidesby3toget4a+3b<12.Thecorrectansweris(C).
5. A Thequestionaskshowmanyofthosesurveyedbelievethatthemostimportantissueinthe
electionistheeconomyorcrime.Accordingtothetable,54%believethattheeconomyis
themostimportant,and15%believecrimeisthemostimportant.Therefore,atotalof54%
+ 15% = 69% of those surveyed responded that the economy or crime was the most
importantissue.Thereareatotalof1,800respondersinthepoll,sotake69%of1,800to
get ×1,800=1,242.Thecorrectansweris(A).
6. A Becausethequestionasksforthevalueofx,PlugIntheAnswers,startingwithoneofthemiddlechoices.Startwith(B).Ifthemonthlyfeeis$55,thenitcosts$55×18=$990.Thisisalreadytoohigh,evenwithouttheinstallationfee,soeliminate(B).Choices(C)and(D)will be greater still, so eliminate those answers aswell.Only (A) is left, so itmust becorrect. If themonthly fee is$45, then18monthscosts$45×18=$810.Add the$150installationfeetoget$810+$150=$960.Thisisthecorrecttotalcharge,sothecorrectansweris(A).
7. B Thequestion asks for probability,which is . Because
thequestionasksof thepeoplewhoselectmilk, the total # of possible outcomes is the
totalnumberofpeoplewhoselectmilk.TakethesumofthetwonumbersunderYesformilk
toget5+6=11.The#ofoutcomesthatfittherequirementsisthenumberofpeoplewho
selectbothmilkandsugar,whichis5.Therefore,theprobabilityis .Thecorrectanswer
is(B).
8. B Thesampleofthesurveywasmadeupofstudentswhoplayasport.Thesestudentswouldbemorelikelythantheaveragestudenttowantincreasedfundingtotheathleticdepartment,so thesamplingdoesnot likelyreflect thepreferenceof thestudentbodyasawhole.Gothrougheachchoiceoneata time.Choice(A)wouldonlyfurther theproblem.Eliminate(A).Choice(B)reflectstheproblemdiscussedabove.Keep(B).Choice(C)appearstobetheresultofthesurvey.However,theresultsmaybeskewedbecauseofthesamplechosen,so this conclusion cannot necessarily be reached. Eliminate (C). Choice (D) would beunrepresentativeforadifferentreason:Thesestudentswouldbelesslikelythantheaveragestudenttosupportincreasedfundingtotheathleticdepartment.Eliminate(D).Thecorrectansweris(B).
9. C Therearenumbersinthechoices,soPlugIntheAnswers,startingwithoneofthemiddlechoices.ThequestionaskshowmanydaystheFirstOpiumWarlasted.Startwith(B).IftheFirst OpiumWar lasted 1,180 days and was 218 days shorter that the second, then theSecondOpiumWarlasted1,180+218=1,398days.Therefore,thetwotogetherlastedatotalof1,180+1,398=2,578days.Thisistoosmall,soeliminate(A)and(B).Try(C).Ifthefirstwarlasted1,260days, thenthesecondlasted1,260+218=1,478days,andthetwotogetherlasted1,260+1,478=2,738days.Thisisconsistentwiththeinformationinthequestion,sothecorrectansweris(C).
10. C StartbydeterminingthepopulationofTorontoin2001bysubtractingtheincreasefromthe
2011population:2.615−0.134=2.481millionpeople.To find thenumberof residents
servedperhospital,dividethepopulationbythenumberofhospitals: ≈57,700.
Thecorrectansweris(C).
11. C Todetermine the periodwith the greatest change in rate, check theweeks in the answerchoicesandBallpark.Agreatincreasewouldbealinethatslopesupsharplyfromlefttoright.Choice(A)showsarelativelyflat linefromWeek0 toWeek12,soeliminate(A).Choice (B) shows a slight increase fromWeek12 toWeek24, sokeep (B).Choice (C)showsasharpincreasefromWeek30toWeek39,sokeep(C).Sincetheincreasein(C)isgreaterthanthatin(B),eliminate(B).Choice(D)showsanincreasefromWeek39toWeek42,butitisnotincreasingassharplyas(C),soeliminate(D).Thecorrectansweris(C).
12. C Thequestionasksforthebestlinearmodelfortheweight,inounces,fromWeek33toWeek39.Pickavalue fromthe tableduring thisperiodandplug it into theanswers.Since theweightinWeek33was67.68,plugt=33intoeachchoice,andeliminateanyforwhichwisnotcloseto67.68.Choice(A)isw=2.5(33)−220=−137.5.Thisisnotcloseto67.68,soeliminate(A).Choice(B)isw=5.8(33)−180=11.4.This isnotclose to67.68,soeliminate(B).Choice(C)isw=8.1(33)−200=67.3.Thisiscloseto67.68,sokeep(C).Choice(D)isw=12.4(33)−150=259.2.Thisisnotcloseto67.68,soeliminate(D).Thecorrectansweris(C).
13. B Thequestionasksforthemeaningofcinthefunctionw(t)=ct+d.Labelwhatisknownintheequation.Thefunctionwistheweight,inounces,ofthefetus.Thevariabletrepresentsthe number of weeks since conception. Next, use Process of Elimination. Constant c ismultipliedbyt.Inalinearequation,thecoefficientonthevariableistheslope,whichistherate of change.Choices (A), (C), and (D) refer to a specific amount, not the changeperweek.Only(B)indicatesthatcistherateofchange.
14. C Tosolveasystemoflinearequations,stacktheequationsandthenaddorsubtract.Sincethecoefficientsontheytermshaveoppositesigns,addtheequationstogethertomaketheytermsdisappear.
Dividebothsidesof theresultingequationby11 togetx=1.Plugx=1 intooneof the
equationsandsolvefory.Plugitintothefirstequationtoget6(1)+5y=9.Simplifytoget
6+5y=9.Subtract6frombothsidestoget5y=3.Dividebothsidesby5togety= .
Therefore,x−y=1− = .Thecorrectansweris(C).
15. D Whenaquestionprovidesthefiguresoftwotriangles,checktoseewhethertheyaresimilartriangles.TrianglePQRhasa56°angleanda90°angle,sodeterminethemeasureofthethirdangle.Themeasuresofthethreeanglesofatrianglehaveasumof180°,so56+90+a=180.Add56and90toget146+a=180.Subtract146frombothsidestogeta=34.Since Rhasameasureof34°,whichisthemeasureof XintriangleXYZ,thetrianglesare similar. Therefore, corresponding sides, which are opposite congruent angles, areproportional.Thecorrespondingsideswouldbeeasiertoseeif thetriangleswerefacingthesameway,soredrawtriangleXYZtomatchtrianglePQR.
Thequestionaskswhichchoice isequal to theratio .SegmentPQ isoppositea34°
angle,soitcorrespondswithYZ.PR isoppositea90°angle,so itcorrespondswithXZ.
Therefore, = .Thecorrectansweris(D).
16. C The table gives points in the relationship, and the answer choices provide possible
equations for the relationship. Plug points from the table into the answer choices, and
eliminateanyforwhichtheequationisnottrue.Plugx=1andy= intoeachchoice.For
(A), = · .Thisisfalse,soeliminate(A).For(B), = (1)−4.Thisistrue,so
keep(B).For(C), = (1)+ .Thisistrue,sokeep(C).For(D), =2· .Thisis
false,soeliminate(D).Twochoicesremain,sopluginanotherpoint.Pluginx=2andy=
.For(B), = (2)−4.Thisisfalse,soeliminate(B).For(C), = (1)+ .This
istrue,sokeep(C).Thecorrectansweris(C).
17. B Julietminesat least 4 ounces of gold, so eliminate (D),which allows for less than this
amount.Although(C)mayseemliketheobviousanswer,thefactthatatleast14ouncesof
silvermustbeminedmayfurtherrestricttheamountofgoldthatcanbemined.Plugs=14
intotheequation3g+s=35toget3g+14=38.Subtract14frombothsidestoget3g=
24.Divideboth sides by3 to getg = 8.The information in the question says that Juliet
wishestogetatleast14ouncesofsilver.Astheamountofsilverincreases,theamountof
golddecreases.Tobetterseethis,plugins=15toget3g+15=38.Subtract15fromboth
sidestoget3g=23.Dividebothsidesby3togetg= =7.6.Therefore,theamountof
goldminedcannotbegreaterthan8.Eliminate(A)and(C).Thecorrectansweris(B).
18. A Johnnywants tomine6poundsofgoldandwants to takebetween10and15ouncesper
round.First,convertthe6poundsintoounces.Becausethereare16ouncesin1pound,set
up the proportion . Cross-multiply to get x = 96. Johnnywants to
takebetween10and15ouncesofgoldperround.IfJohnnytakes10ouncesperround,it
wouldtake =9.6roundstoget96ounces.IfJohnnytakes15ouncesperround,itwould
take =6.4roundstoget96ounces.Therefore,thenumberofroundsmustbebetween
6.4and9.6.Sincetheremustbeanevennumberofrounds,thereare8roundsinthegame.
Ifthereare8roundsinthegame,Johnnytakes =12ouncesofgoldperround.Plugthis
intotheequationtoget3(12)+s=38.Simplifytheleftsidetoget36+s=38.Subtract36
frombothsidestogets=2.Thequestionasksfortheamountofsilverminedperround,so
thecorrectansweris(A).
19. D Thequestionasksfortheamountofgoldminedeachroundintermsoftheamountofsilver
minedthatround.Becausetheamountofgoldminedisrepresentedbyg,solvetheequation
3g+s=38forg.Subtractsfrombothsidestoget3g=38−s.Dividebothsidesby3.
Makesuretoputtheresultinthesameformasthechoices.Becausethechoicesallinclude
,dividebothsidesby3bymultiplyingbothsidesby togetg= (38−s).Thecorrect
answeris(D).
20. A Thesurveywasconductedonfourth-gradegirlsinthecounty,sorestricttheconclusiontothatgroup.Choice(A)restrictstheconclusiontofourth-gradegirls,sokeep(A).Choices(B), (C), and (D) all refer to all fourth-graders ingeneral, not just fourth-gradegirls, soeliminatethesechoices.Thecorrectansweris(A).
21. B Tofindthesolutionstoanequationinfactoredform,seteachofthefactorsequalto0.Ifx+5=0,subtract5frombothsidestogetx=−5.Ifx−0.4=0,add0.4tobothsidestogetx=0.4.Therefore,thetwosolutionsare−5and0.4,sothesumofthesolutionsis−5+0.4=−4.6.Thecorrectansweris(B).
22. B The question asks for the percent decrease. For percent difference, use the formula
× 100. The difference is $91.94 − $86.53 = $5.41. Because it is a percent
decrease,thelargervalueistheoriginal.Therefore,thepercentdecreaseis ×100
≈5.884.Thequestionaskstoroundtothenearesttenthofapercent,sothecorrectanswer
is(B).
23. C The question asks for the median year of entry for the 27 countries. The median is themiddlenumberwhenallthenumbersarelistedinorder.Becausethereisanoddnumberofcountries,tofindthemiddlecountry,dividethetotalnumberofcountriesby2androundup.Because27÷2=13.5, themiddlecountry is the14thcountry. (Note that ina listof27,there are 13 countries above and 13 countries below the 14th country.) Find the 14thcountry.Therewere6countriesadmittedin1957.Thereare3countriesadmittedin1973,sothereare6+3=9countriesadmittedby1973.Therewas1countryadmittedin1981,sotherewere9+1=10countriesadmittedby1981.Therewere2countriesadmittedin1986, so there were 10 + 2 = 12 countries admitted by 1986. There were 3 countriesadmittedin1995,sotherewere12+3=15countriesadmittedin1995.Therefore,the14thcountrywasadmittedin1995,sothemedianis1995.Thecorrectansweris(C).
24. D Thequestionasksforthenumberoftimesthatthependulumwas1centimetertotheleftoftheequilibriumpoint.Accordingtotheinformationinthequestion,distancetotherightisindicatedbyanegativenumber.Therefore,findthehorizontallinerepresentingadistanceof−1.Traceacrossandcountthenumberoftimesithitsthegraph.Ithitsfourtimes,sothecorrectansweris(D).
25. D Tofindtheradius,gettheequationintothestandardformforacircle:(x−h)2+(y−k)2=r2,where(h,k)isthecenterandristheradius.Gettheequationinthisformbycompletingthesquare.Thatprocessismucheasieriftherearenocoefficientsonthesquaredterms,sodividetheentireequationby2togetx2+x+y2−5y=42.5.Tocompletethesquareonthex-terms,takehalfthecoefficientonx,squareit,andaddittobothsidesoftheequation.Thecoefficientis1,halfis0.5,andthesquareis0.25.Add0.25tobothsidestoget(x2+x+0.25)+(y2−5y)=42.75.Tocompletethesquareofthey-terms,takehalfthecoefficientonthey-term,square it,andadd it tobothsides.Thecoefficient is−5,half is−2.5,and thesquareis6.25.Add6.25tobothsidestoget(x2+x+0.25)+(y2−5y+6.25)=49.Factorthe right side toget (x+0.5)2+ (y−2.5)2 = 49.The equation is now in standard form.Sincer2=49,takethesquarerootofbothsidestogetr=7.Thecorrectansweris(D).
26. A Accordingtothequestion,gisalinearfunction,sotheequationofgisintheformg(x)=
mx+b,wheremistheslopeandbisthey-intercept.Tofindtheslope,plugtwopointsinto
theformulam= .Plug in (0,−3)and(3,3) togetm= = =2.They-
interceptisthevalueofthefunctionwhenx=0.Accordingtothetable,g(0)=−3,sob=
−3.Therefore,g(x)=mx+b=2x−3.Thequestionasksforg(4).Pluginx=4togetg(4)
=2(4)−3=5.Thecorrectansweris(A).
27. A TheratioofvolumeofContainerXtothevolumeofContainerYis10:70=1:7.Therefore,
theratioofthepressureinContainerXtothepressureinContainerYis7:1.Becausethe
pressure in Container X is 300 torr, find the pressure in Container Y by setting up the
proportion = .Cross-multiplytoget7y=300.Dividebothsidesby7togety= .
The ratio of the volume of Container Y to the volume of Container Z is 70:30 = 7:3.
Therefore, the ratioof thepressure inContainerY to thepressure inContainerZ is3:7.
SincethepressureinContainerYis ,setuptheproportion = .Cross-multiplyto
get3z=300.Dividebothsidesbyztogetz=100.Alternatively,becausetheamountofgas
isalwaysthesame,usetheratioofthevolumeofContainerXandthevolumeofContainer
Z,bypassing theneed touseContainerY.Theratioof thevolumesofContainerX to the
volumeofContainerZis10:30=1:3.Therefore,theratioofthepressureinContainerXto
thepressureinContainerZis3:1.Setuptheproportion = .Cross-multiplytoget3z
=300.Dividebothsidesby3togetz=100.Eitherway,thecorrectansweris(A).
28. C Therearevariablesinthequestionandanswerchoices,soPlugIn.Let t=5tomakethe
matheasier. If t=5, thend=10 =10 = 250.Therefore, after 5 seconds, the
glucosetravels50micrometers.Tofindtheaveragespeed,dividethetotaldistancebythe
totaltimetoget =10.Therefore,thetargetvalueis10.Plugt=5intoeachchoiceand
eliminate any that are not equal to 10. Choice (A) becomes 10(5) = 250, so
eliminate (A). Choice (B) becomes = 2, so eliminate (B). Choice (C) becomes
=10,sokeep(C).Choice(D)becomes =100, soeliminate (D).The
correctansweris(C).
29. A Plugginginpointscouldwork,buttheequationsallinvolveawkwarddecimals.Sincethechoices are all quadratic equations, use the rules of quadratics instead. A graph of aquadraticintheformy=ax2+bx+cisaparabolainthexy-plane.Ifa<0,theparabolaopensdownward.Sincethisparabolaopensdownward,eliminate(B)and(D),whichhavea>0.Ifthey-interceptispositive,thenc>0.Therefore,eliminate(C),whichhasc<0.Onlyonechoiceremains.Thecorrectansweris(A).
30. D Thequestionasksfor theequationforwhichthesolutionsarebothpoints thatare2unitsawayfrom−5.Determinethetwopoints.Thepointthatis2totheleftof−5is−5−2=−7.Thepointthatis2totherightof−5is−5+2=−3.Plugthesepointsintotheequationsintheanswerchoices,andeliminateanychoiceforwhichoneofthepointsisnotasolution.Startwith(A).Plugx=−7into(A)toget|−7−2|=5.Thisisfalse,soeliminate(A).Try(B).Plugx=−7into(B)toget|−7+2|=5.Thisistrue,sotryx=−3.Plugx=−3into(B)toget|−3+2|=5.Thisisfalse,soeliminate(B).Try(C).Plugx=−7into(C)toget|−7⁄5|=2.Thisisfalse,soeliminate(C).Only(D)isleft,soitmustbecorrect.Pluggingx=−7andx=−3into(D)resultsintwotruestatements,sothecorrectansweris(D).
31. 163,164,165,166,167,168,169,or170
Thequestionasksforthepossiblevolumeofacylindricalpool.Thevolumeofacylindercan be found using the formulaV =πr2h,where r is the radius andh is the height. The
questionsaysthattheradiusis3feet,sopluginr=3.Thequestionalsosaysthattheheightisbetween5.75and6feet,sopickaheightbetweenthesetwovalues.Pluginh=5.8.Ifr=3 and h = 5.8, thenV = πr2h = π(3)2(5.8) ≈ 163.99. The question asks for the volumeroundedtothenearestcubicfoot,sogridin164.Becausethequestionasksforonepossiblevalue,thisanswerisallthatisneeded.However,togettheotherpossibleanswers,pluginh = 5.75 andh = 6 into the volume formula to getV ≈ 163 andV ≈ 170. The possiblecorrectanswersare163,170,andanyintegerinbetween.
32. 12 Itmaybehardtocreateanequationtosolvehere.AlthoughPluggingInworksbestwhen
youhaveanswerchoices toworkwith, thestrategycanstillwork foraGrid-Inquestion
like this one. Try 10 roommates. If the rent was $6,000, then the rent per person was
=$600.If4roommatesmoveout, therewouldbe10−4=6remaining,eachof
whomwouldhavetopay =$1000.Therentwouldthusincreaseby$1,000−$600
= $400. This increase is too large. To make the increase less, increase the number of
roommates,makingtheeffectof4movingoutproportionallyless.Since11doesnotdivide
into $6,000 evenly, it is unlikely that the difference could be an integer.Try 12. If there
were12 roommates, then the rentperpersonwas =$500. If4 roommatesmove
out, therewould be 12 − 4 = 8 remaining, each ofwhomwould have to pay =
$750.The rentwould thus increase by$750−$500=$250.This is consistentwith the
informationinthequestion,sothecorrectansweris12.
33. 24 Distributethe5ontheleftsidetoget15y−60−(23+11y)=13.Distributethenegativesigntoget15y−60−23−11y=13.Combineliketermsontheleftsidetoget4y−83=13.Add83tobothsidestoget4y=96.Dividebothsidesby4togety=24.Thecorrectansweris24.
34. or3.5
Thequestionasksforthey-intercept,whichisthepointatwhichx=0.Plugx=0intotheequationtoget (0)+ y=1.Simplifytheleftsidetoget y=1.Dividebothsidesby ,
whichisthesameasmultiplyingby ,togetx= .Thecorrectansweris .
35. 3.2 First, find themean of Jennifer’s six semesters.Draw theAverage Pie.Get the total byaddingtheindividualGPAstoget3.5+3.2+2.7+3.7+3.6+3.1=19.8.Placethisinthe
topsectionoftheAveragePie.Thereare6semesters,soplace6asthenumberofthingsinthebottomleft:
Togettheaverage,divide19.8by6toget3.3.ThequestionsaysthatMichael’smeanwas0.2less,sohismeanwas3.1.DrawanotherAveragePie,placing3.1inthebottomright.Michaelalsohas6semesters,soplacethisinthebottomleft:
Multiply3.1by6togetatotalof18.6.Thus,thesumofMichael’sGPAsis18.6,so2.8+3.3+2.9+3.3+3.1+y=18.6.Simplifytheleftsidetoget15.4+y=18.6.Subtract15.4frombothsidestogety=3.2.Thequestionasksforthevalueofy¸sothecorrectansweris3.2.
36. 7 Ifthetwographsintersectat(0,0)and(−k,k),then(0,0)and(−k,k)aresolutionsofbothequations.Tofind thevalueofk,plug(−k,k) into they=2x2+13x equation to getk =2(−k)2+13(−k)ork=2k2−13k.Subtractkfrombothsidestoget0=2k2−14k.Factortherightsidetoget0=2k(k−7).Setbothfactorsequalto0.If2k=0,dividebothsidesby2togetk=0.Ifk=0,then(−k,k)=(0,0).However,thisistheotherpointofintersectiongiveninthequestion.Tofindtheothersolution,setk−7=0.Add7tobothsidestogetk=7.Thecorrectansweris7.
37. 3 Thequestionaskshowmanymoremembersvotedtoraisefinesthantolowerfines.Find
thetotalnumberofmemberswhovoted.Thequestionsaysthattheremaining15votedto
eliminatefines,sofindoutwhatpercentisremaininggiventhat35%votedtoraisefines,
10%votedtokeepthefinesthesame,and30%votedtolowerthefines.Thisisatotalof
35%+10%+30%=75%.Therefore,theremainingvotersmakeup100%−75%=25%
of thememberswhovoted.Let thenumberofmemberswhovotedbe representedbym.
Since15ofthemembersvotedtoeliminatethefinesandthisamountrepresents25%,
m=15.Rewritethisas0.25m=15anddividebothsidesby0.25togetm=60.Ofthis
total,35%votedtoraisefines,sothisis ×60=21.Ofthetotal,30%votedtolower
fines, so this is ×60=18.Therefore, therewere21−18=3morememberswho
votedtoraisefinesthanwhovotedtolowerfines.Thecorrectansweris3.
38. 25 The question talks about something tripling over time, so use the exponential growthformula:finalamount=originalamount(multiplier)numberofchanges.Becausetherewerepsupporters in 2006 and 675 supporters in 2009, the original amount is p and the finalamount is 675. The final date is 2009, which is 3 years after 2006, so the number ofchangesis3.Becausethenumbertripleseveryyear,themultiplieris3.Plugtheseintotheformulatoget675=p(3)3.Simplifytherightsidetoget675=27p.Dividebothsidesby27togetp=25.Withouttheformula,itisstillpossibletosolvethequestion.Thenumberofpeoplewho support thehighway systemon January1, 2009was675.Since this numbertripledeveryyear, thenumberofsupportersoneyearpriorwasone-thirdof thisnumber.Therefore,thenumberofsupportersonJanuary1,2008was675÷3=225.ThenumberofsupportersonJanuary1,2007was225÷3=75.ThenumberofsupportersonJanuary1,2006 was 75 ÷ 3 = 25. The question asks for the value of y, which is the number ofsupportersonJanuary1,2006,sotheansweris25.Eitherway,thecorrectansweris25.
ReadingTest65MINUTES,52QUESTIONS
TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassageorpairofpassagesbelowisfollowedbyanumberofquestions.Afterreadingeachpassageorpair,choosethebestanswertoeachquestionbasedonwhatisstatedorimpliedinthepassageorpassagesandinanyaccompanyinggraphics(suchasatableorgraph).
Questions1–10arebasedonthefollowingpassage.
Thepassagethatfollowsisadaptedfroman1859novelthatfollowsthelivesofbothEnglishandFrenchcharactersduringtheFrenchRevolution.
1. TheprimarypurposeofthepassageasawholeistoA) describethehistorybetweenCartonandStryver.B) characterizelifeattheShrewsburySchool.C) revealCarton’scharacter.D) showthatStryverhasbeenexploitingCarton.
2. Basedontheinformationinthepassage,Cartonisbestcharacterizedas
A) unsound.B) mercurial.C) unlucky.D) imperceptive.
3. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines10–11(“Up…despondency”)B) Lines13–14(“Even…own”)C) Lines35–36(“Atthis…laughed”)D) Lines45–46(“It’sa…breaking”)
4. Asusedinline11,“spirits”mostnearlymeansA) soul.B) liquor.C) essence.D) jubilation.
5. Basedonlines17–22(“squaringhimself….shoulderhimintoit”),itcanbereasonablyinferredthatA) StryverisfrustratedwithCarton’sbehavior.B) StryverisplanningtopushCartonintothefireplace.C) StryverbelievesCartontobecomparativelyolder.D) StryverwishestobullyCartonashedidatShrewsbury.
6. Theuseofitalicsinline55primarilyservestoemphasizeCarton’sA) incredulity.B) confusion.C) annoyance.D) affection.
7. ThepassagesuggestswhichofthefollowingaboutStryver?A) HeisinlovewithMissManette.B) HebelievesthatCartonlackstheintelligencerequiredtobesuccessful.C) HedoesnotbelievethatCartonfindsMissManetteunattractive.D) Hewasbornintoawealthyfamily.
8. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines32–33(“Ihad…wasI”)B) Line41(“Andwhose…that”)C) Lines58–59(“Why…Court”)D) Lines63–68(“Doyou…doll”)
9. Incontext,“desert”inline79referstoA) Styver’scolddemeanor.B) London’slandscape.C) Carton’swindows.D) sunlitdunes.
10. The“tears”referredtoinline85are“wasted”becauseA) MissManettewillneverloveCarton.B) Cartonisunlikelytochangehisways.C) Carton’shomeisoneofsqualor.D) StryverwillcontinuetoexploitCarton’slabor.
Questions11–21arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromPriitVesilind,TheSingingRevolution.©2008bySkyFilmsIncorporated.
DiagramofEuropefollowingtheNazi-SovietPactof1939,alsoknownastheMolotov-RibbentropPact.ImageadaptedfromCQResearcher.
11. ThepointofviewfromwhichthepassageiswrittenisbestdescribedasA) condemnatoryoftheSovietUnion’streacherousactions.B) sympathetictotheBalticstates’struggleforfreedom.C) dismissiveoftheideaofnon-violentrevolution.D) conflictedabouttheunderlyingcauseoftherevolution.
12. Asusedinline18,“collusion”mostnearlymeansA) conspiracy.B) impact.C) separation.D) danger.
13. Inlines33–36,theauthordrawsadistinctionbetweenA) thetoneofEstoniansongsandthepeople’struefeelings.B) thethemesofEstonianfolksongsandanthems.C) themilitarystrengthofEstoniaandthatoftheSovietUnion.D) songfestivalsinEstoniaandthoseinLatviaandLithuania.
14. Inthecontextofthepassage,thephrase“theirreluctancetobeabsorbed”suggeststhatEstoniansA) refusedtospeakRussianwiththemanyforeignerssettlersinEstonia.B) wantedtohaveanindependentnation.C) workedtoensuretheirculturestayeddistinctfromthoseoftheotherBalticstates.D) wereunwillingtodevotetheamountofconcentrationtosongfestivalsthatthe
Sovietsdemanded.
15. TheauthorincludesstatisticsaboutthesizeofthesongstageinTallinn(lines47–49)primarilytoA) provideasenseofhowlargetheamphitheateris.B) indicatethepopularityofthetributestoStalinandLenin.C) comparethesizetothatofsimilarstagesinLatviaandLithuania.D) illustratethewideappealofthemasssongfestivalsinEstonia.
16. Asusedinline66,“burden”mostnearlymeansA) weight.B) travail.C) responsibility.D) need.
17. TheprimaryrhetoricaleffectofthelastsentenceofthepassageistoA) conveythesenseofdreadthathungoverEstoniaattheheightoftheSinging
Revolution.
B) indicatethedepthofdisagreementbetweenviolentandnon-violentrevolutionaries.C) showhowcrucialmusicandpoetryweretoEstonia’sfightforindependence.D) communicatethesenseofoptimistictensionthatEstoniansfeltaftertheNightSong
Festivals.
18. WhichofthefollowingdoesthepassagesuggestaboutEstonia’srelationtotheSovietUnion?A) EstoniahadaricherculturaltraditionofsingingthantheSovietUnionhad.B) EstoniahadthepoliticalleveragenecessarytofreeitselffromtheSovietUnion.C) EstoniawassmallerandweakerthantheSovietUnion,makingviolentrevolution
impractical.D) EstoniaheldsongfestivalsduringtheSovietoccupationprimarilytopaytributeto
Communisticons.
19. TheauthorimplieswhichofthefollowingaboutEstoniansongfestivals?A) TheyaffordedEstoniansamediumthroughwhichnationalandculturalpridecould
beexpressed.B) TheywerestartedduringtheSovietoccupationtopreserveEstoniancultureand
language.C) Theywereuniqueinsizeandformattothecountrywheretheywerefounded.D) Theyprovidedanopportunitytosingsongsthatweremoreupliftingthanthosesung
whileworking.
20. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines19–21(“So…‘divorce’”)B) Lines44–46(“Thefestivals…Lithuania”)C) Line62(“Bythelate…simmering”)D) Lines79–82(“This…music”)
21. Whichofthefollowingclaimsissupportedbythediagram?A) Inthe1939pact,GermanygainedtheentiretyofPoland.B) TheSovietUniondoubledinsizeafterthepact.C) LithuaniaandEstoniaarecontiguouscountries.D) TheSovietUnion’sgainsstretchedfromtheBalticSeatotheBlackSea.
Questions22–31arebasedonthefollowingpassage.
Thispassageisanexcerptadaptedfromaspeechgivenin1917byAmericanSenatorRobertLaFollette.Inthespeech,LaFolletteexplainsthespecialimportanceoffreespeechduringtimesofwarandtherelationbetweenfreespeechanddemocraticgovernance.
22. ThepositionthatLaFollettetakesisbestdescribedasA) alaw-makersuggestinganewpieceoflegislation.B) animpartialobserverarbitratingalegalissue.C) adissenterarguingforacause.D) apacifistarguingagainstinternationalconflicts.
23. Inthepassage,LaFollettedrawsadistinctionbetweenA) rightsthatareappropriatelyandinappropriatelysacrificedduringwar.B) momentswhenfreespeechisandisnotnecessary.C) justwarsandwarssoughtforeconomicinterest.D) theinterestsoftheNationandtheinterestsofhumanity.
24. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines6–11(“Ihave…crime”)B) Lines21–27(“Ithink…war”)C) Lines30–31(“Hemust…power”)D) Lines50–57(“Iam…humanity”)
25. Asusedinline8,“incommunicado”mostnearlymeans
A) justified.B) sequestered.C) luxuriously.D) available.
26. Lines32–36suggestthatA) somerightsarenecessarilygivenupduringwartime.B) restrictionsoncivilpowersarealwaysarbitrary.C) theGovernmentmustbewatchfulofthemilitary.D) temporaryrestrictionsmaybecomepermanent.
27. Basedontheinformationinthepassage,citizengovernanceisnecessaryinallofthefollowingsituationsEXCEPTA) electinglegislatorsandexecutives.B) negotiatingapeacetreaty.C) declarationsofwar.D) decisionsaboutmilitarystrategy.
28. Theprincipalrhetoricaleffectofthephraseinlines48–50,(“itscauses…peaceshouldbemade”)istoA) argueagainstgrantingfreespeechduringwarbyemphasizingthedifficultiesfaced
bythemilitaryandthePresident.B) suggestthenumerouspointsatwhichcitizensshouldexercisetheirfreespeech
duringtimesofwar.C) discussthreereasonswhymembersofthepressarecurrentlyunabletospeak
franklywithoutfear.D) showthatLaFollettebelievesthatthecitizensunderstandthedynamicsofwarfar
betterthanthePresident.
29. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines11–15(“Private…violated”)B) Lines16–20(“Itappears…war”)C) Lines30–36(“Hemust…restored”)D) Lines37–41(“Morethan…unclogged”)
30. Theauthor’sattitudetoward“theattempttostifle”(line63)canbedescribedasA) sympathetic.
B) apathetic.C) frustrated.D) morose.
31. Asusedinline83,“inviolable”mostnearlymeansA) secretly.B) freely.C) unbreakable.D) personally.
Questions32–41arebasedonthefollowingpassageandsupplementarymaterial.
ThefollowingisfromapassageaboutcontinentaldriftandplatetectonicsfromScienceWorld.
Thisimageshowsthethreemaintypesofplateboundaries:divergent,convergent,andtransform.ImageadaptedfromtheU.S.GeologicalSurvey.
32. BasedontheinformationinthepassageitcanbereasonablyinferredthatA) geologicaltheoriesareonlyprovenwiththehelpoftechnologicaladvances.B) improvementsinsatellitetechnologyadvancedplatetectonicstheory.C) theplatetectonicstheorywascreatedin1965.
D) theSanAndreasFaultprovedtheveracityofplatetectonicstheory.
33. Inthethirdparagraph(lines20–25),whatisthedistinctiontheauthordrawsbetweencontinental-drifttheoryandplatetectonics?A) FluidityversusimmobilityB) DriftingalongversuspushingwithpurposeC) MovingthroughversusmovingwithD) Sailingonoceansversusraftingthroughstreams
34. Asusedinline42,“convection”mostnearlymeansA) liquefying.B) melting.C) mobilizing.D) transferring.
35. Inline56,whatisthemostlikelyreasontheauthorintroducesYellowstone’shotsprings?A) Asanexampleofamid-platevolcanoB) AsproofthatplatesslidepasteachotherC) AssupportforanopposingtheoryD) Asanexampleofamid-oceanridge
36. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines3–5(“Itwas…activity”)B) Lines54–55(“Thevolcanoes…northeast”)C) Lines60–62(“Asthe…activity”)D) Lines65–67(“Plate…them”)
37. Asusedinline64,“compatible”mostnearlymeansA) consistent.B) adaptable.C) opposed.D) skewed.
38. WhatisthemostlikelyreasontheauthormentionsIceland?A) Toofferanexampleofanislandcreatedatamid-oceanridgeB) Toshowacontrastbetweenanislandandacontinent
C) ToprovethatanislandcanalsobeavolcanoD) ToassertthattheMid-AtlanticRidgeconnectstwoplates
39. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines9–12(“Plates…other”)B) Lines41–44(“Scientists…Earth”)C) Lines49–52(“Most…center”)D) Lines69–72(“As…islands”)
40. Theprincipalrhetoricalpurposeofthephrase“Somegeologists…separate”(lines80–84)istoA) suggestthatscientistsarestillinvestigatingplatetectonictheory.B) emphasizethelackofdatasupportinghowfracturesseparate.C) revealthatsomescientistsdisagreewiththemajortenetsofplatetectonics.D) exposeaweaknessinthecontinental-drifttheory.
41. ItcanbereasonablyinferredfrominformationinthepassageandthediagramthatA) continentalriftzonesalwaysoccurbesidetheocean.B) hotspotsaremoltenplumesthattravelthroughthelithospheretothesurface.C) mid-oceanridgesarecausedbythepresenceofsubductingplates.D) oceaniccrustismorerigidthancontinentalcrust.
Questions42–52arebasedonthefollowingpassages.
Passage1isadaptedfromTheodoreS.Melis,Ed.,“EffectsofThreeHigh-FlowExperimentsontheColoradoRiverEcosystemDownstreamfromGlenCanyonDam,Arizona,”publishedin2011bytheU.S.GeologicalSurvey.Passage2isadaptedfromPaulE.Grams,“ASandBudgetforMarbleCanyon,Arizona—ImplicationsforLong-TermMonitoringofSandStorageChange,”publishedin2013bytheU.S.GeologicalSurvey.
42. TheauthorofPassage1mostlikelybelievesthattheGlenCanyonDamA) isausefultoolformanagingscarcewaterresources.B) wasbuiltwithalackofforesight.C) hasdecimatednativefishpopulations.D) hashadacalmingeffectontheaquaticecosystem.
43. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–4(“Atthetime…Park”)B) Lines17–23(“Thehumpback…Canyon”)C) Lines24–25(“Annual…regime”)
D) Lines30–34(“Pre-damfloods…transported”)
44. TheauthorofPassage1mentionsscientistsandriverrecreationistsprimarilytoA) providesupportfortheideathatthepost-damriverlooksdrasticallydifferent.B) drawacontrastbetweenscientificobservationsandcasualobservationsofriver
conditions.C) emphasizethespiritofcollaborationbetweenthesciencecommunityandthepublic
inconservationefforts.D) provethattheGlenCanyonDamhashadaruinouseffectontheriver.
45. Passage1suggeststhatthehumpbackchubA) isnowextinctintheGrandCanyon.B) hasasmall,depressedskull.C) cansurviveinchangingenvironments.D) thrivesinhighvelocityriverchannels.
46. Asusedinline25,“regime”mostnearlymeansA) government.B) tenure.C) system.D) management.
47. Asusedinline65,“suspended”mostnearlymeansA) stopped.B) mixed.C) withheld.D) hanging.
48. ItisreasonabletoconcludethatcontrolledfloodsA) successfullysimulatepre-damsnowmeltfloods.B) containlargeamountsofsuspendedsediment.C) maybedetrimentaltothehealthoftheColoradoRiver.D) shouldbedoneduringthemonthsthatsnowmeltfloodstypicallyoccur.
49. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines58–59(“Normal…sandbars”)
B) Lines66–68(“Thesuspended…velocity”)C) Lines71–73(“Newly…sand”)D) Lines77–79(“Scientists…low”)
50. TheauthorofPassage1wouldmostlikelyrespondtotheHighFlowExperimentsdescribedinPassage2byA) appreciatingtheeffortsofscientiststomaintainthesandsupplybelowthedam.B) warningofthecalamityofinterferingwiththeriverecosystem.C) questioningtheabilityofcontrolledfloodstobuildupsandbars.D) worryingthatreshapedhabitatswillharmnativefish.
51. Whichofthefollowingbestdescribesthestructureofthetwopassages?A) Passage1introducesaproblem,andPassage2proposesasolutiontotheproblem.B) Passage1offersahistoricaldiscussion,andPassage2describestheimplicationsof
ascientificpractice.C) Passage1givesbackgroundinformation,andPassage2detailsrecentchanges.D) Passage1describesanexperiment,andPassage2offerssuggestionsforfuture
action.
52. WhichofthefollowingstatementsistrueofPassage1,butnotofPassage2?A) Thepassagegivesdetailsofscientificstudiesconductedontheriver.B) Thepassageoffersdocumentedevidenceoftopographicchangeintheriver.C) Thepassageindicatestheimportanceoffloodstotheriverecosystem.D) Thepassagegivesspecificexamplesofspeciesaffectedbythedam.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
WritingandLanguageTest35MINUTES,44QUESTIONS
TurntoSection2ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassagebelowisaccompaniedbyanumberofquestions.Forsomequestions,youwillconsiderhowthepassagemightberevisedtoimprovetheexpressionofideas.Forotherquestions,youwillconsiderhowthepassagemightbeeditedtocorrecterrorsinsentencestructure,usage,orpunctuation.Apassageoraquestionmaybeaccompaniedbyoneormoregraphics(suchasatableorgraph)thatyouwillconsiderasyoumakerevisingandeditingdecisions.
Somequestionswilldirectyoutoanunderlinedportionofapassage.Otherquestionswilldirectyoutoalocationinapassageoraskyoutothinkaboutthepassageasawhole.
Afterreadingeachpassage,choosetheanswertoeachquestionthatmosteffectivelyimprovesthequalityofwritinginthepassageorthatmakesthepassageconformtotheconventionsofstandardwrittenEnglish.Manyquestionsincludea“NOCHANGE”option.Choosethatoptionifyouthinkthebestchoiceistoleavetherelevantportionofthepassageasitis.
Questions1–11arebasedonthefollowingpassage.
AndJusticeforAll
Herfathergotherthejob.Amandawasbetweensemestersatcollege,andher 1 workatthemallwouldn’tdomuchforherwhenshegotoutofschool.Itwastimetodosomethingmoreserious,somethingthatmeantmoretoher.Manyofherfriendsweregettinginternshipsinthecity,workingforthisorthatpublishinghouseorTVstudio.Amanda,however,wantedsomethingdifferent.Shewouldstartapplyingtolawschools 2 soonandshewantedtoknowwhatthelawlookedlikeinaction.
1.A) NOCHANGEB) work,atthemall,wouldn’tdomuchforherwhenC) workatthemallwouldn’tdomuchforher,whenD) work,atthemall,wouldn’tdomuchforher,when
2.A) NOCHANGEB) soonand,C) soon,andD) soon,
Fortunately,herdadknewsomeonefromhighschool,afriend 3 namedEllen,whohadthengoneontostudyatDukeUniversity.Itwasathanklessjob,andalthoughtheDepartmentbuildingitselfcoveredalmostonehundredacres(inNewYorkCity,therewasanentireislanddevotedtoit),noonepaidtheDepartmentofCorrectionsmuchmind.Mostpeoplenevercomenearajailcell,so 4 it’seasyforthemtodismissinmatesastotallyremovedfromsociety.
3. Whichofthefollowingtruestatementscontainsinformationmostinkeepingwiththemainideaofthispassage?A) NOCHANGEB) whohadgoneontolawschoolandnowworkedattheCountyDepartmentof
Corrections.C) withwhomhehadnotspokenintwenty-fiveyears,thoughwithwhomhestillfelt
veryclose.D) DELETEtheunderlinedportion.
4. Whichofthefollowingbestconcludesthisparagraphbyreinforcingideaspresentedinthissentenceandtheprecedingone?A) NOCHANGE
B) peopleoftenknowliterallynothingaboutprisonlife,thoughtheyareendlesslyfascinated.
C) moviestudiosarefamousfortheirsordidbutoftenwrongdepictionsofprisonlife.D) incarcerationratesintheUnitedStatesaresomeofthehighestintheworld.
[1]AttheDepartment,however,Amandalearnedaboutprisoners’rights.[2]Or,bythesametoken,whenwastheuseofforceappropriatefromtheofficers?[3]ThereisaclearprovisionintheConstitutionthatprohibits“cruelandunusualpunishment.”[4]Themeaningofthesefourwords 5 werenowheremoreambiguousthaninprisons.[5]Everyonewithinthesewallshadbeenconvictedofacrimeandwasnowpaying 6 they’redebttosociety,buthowcouldagovernmentensurethattheplacewoulddeliverthe“reform”inareformatoryorthe“penitence”inapenitentiary?[6]Shouldinmateswith,forexample,mentalillnessesbetreateddifferentlyfromothers? 7
5.A) NOCHANGEB) havebeenC) areD) is
6.A) NOCHANGEB) theirC) thereD) hisorher
7. Inthesequenceoftheparagraph,thebestplacementforsentence2wouldbeA) whereitisnow.B) beforesentence1.C) aftersentence3.D) aftersentence6.
WhileAmandadidnotgainanyanswersfromhersummerattheDepartmentofCorrections,she 8gatheredtogetherawholenewsetofquestions.Shehaduncoveredquestionsandconundrumsabouttheprisonsystemitself,butshehadbeguntoseeprisoners’rightsascentraltothequestionoffreerightsaswell.Shebegantowonderexactlywhatitwasthatagovernmentoweditspeopleandhowmuchfreedomwastoomuch.Herinternshipthatsummermadeherrealizethatpoliticsandthelaw 9 wasalivingthing.Assheappliedtolawschoolsthefollowingfall,Amandawrotepassionatelyaboutwhatshehaduncovered.“Althoughlawhaslongbeenconsideredaprofessionofprivilegeandprestige,”sheconcludedheressay,“Ihaveseenfirsthandhowitaffectsthelivesofallofus.Wemaybelievethatwe
nevercomeintocontactwiththe 10 law;however,itiswrittenintoeverythingaroundus,includinghowweseeourselves.”
8.A) NOCHANGEB) gatheredupC) collectedupD) gathered
9.A) NOCHANGEB) werelivingthings.C) wasathingthatwasalive.D) werethingsthatwereliving.
10.A) NOCHANGEB) law,howeverC) law,however;D) law,however,
Question 11 asksaboutthepreviouspassageasawhole.
Thinkaboutthepreviouspassageasawholeasyouanswerquestion11.
11. Supposethewriter’sgoalhadbeentowriteanessaythatcriticizestheAmericanjusticesystem.Wouldthisessayfulfillthatgoal?A) Yes,becauseitreferstomuchofwhatAmandalearnsas“conundrums.”B) Yes,becauseitshowsthattheU.S.justicesystemhassomeproblems.C) No,becauseittellsthestoryofonepersonbecominginterestedinthejusticesystem.D) No,becauseitsuggeststhatworkinginthejusticesysteminspiredoneperson’s
entirecareer.
Questions12–22arebasedonthefollowingpassageandsupplementarymaterial.
Alexander’sEmpireofCulture
AlexandertheGreatisanameknowntoall,butnotallknowtheextentofAlexander’saccomplishments.Nowthatthestudyofthe“classics”(mainlyRomanandGreekcivilizations)has 12disappearedbothfromhigh-schoolandcollegecurricula,AlexandertheGreat’slegendisnotonthetongueofeveryschoolboy,thoughhisaccomplishmentshavenot 13 diminishedforallthat.
12.A) NOCHANGEB) disappearedfrombothC) disappearedbothD) frombothdisappeared
13.A) NOCHANGEB) amelioratedC) gonedownD) subsided
AlexanderwasborninPella,Macedonia,in356BCE.Hisfather,KingPhilipII,astrongmilitaryking 14 inhisownwrite,believedthathissonwasbornpartmanandpartgod.Alexandercametocultivatetheimagehimself,bolsteredbyhiskeenintellectandlearning,quickenedinpartbyhistutor,thegreatGreekphilosopherAristotle.PellawasatthattimeabackwaterofGreekculture,and 15 hisarrivalannouncedaneweraofwhathistorianswouldlatercall“enlightenedmonarchy,” 16 eventhoughthattermisusedmuchmoretodescribemonarchiesintheeighteenthcentury.
14.A) NOCHANGEB) inhisownright,C) inhisownrite,D) byhisownrite,
15.A) NOCHANGEB) Aristotle’sC) theirD) the
16. WhichofthefollowingtruestatementswouldbestconcludetheparagraphbyemphasizingthechangethatAlexander’srulebroughttoMacedonia?A) NOCHANGEB) althoughthosewhosuffereddefeatatAlexander’shandsmightnothaveseenitthat
way.C) suggestingastyleforthereignsofbothJuliusCaesarandNapoleonBonaparte.D) underliningfurtherthatPhilip’sformermilitaristicstatewasenteringanewage.
Still,theagewasnotentirelynew.Alexanderspentnearlyallhistimeabroad,firstunitingtheGreekkingdomthatthreatenedtofallapartatPhilip’sdeath,thenmovingontobroadermilitaryconquests. 17Alexanderhadconqueredanincredibleamountoflandbythetimeofhisdeathin323BCE, 18 ashisempirestretchedfromGreecetomodern-dayIndia,sometwomillionsquaremiles.WhenhisarmiesconqueredPersia(nowIranandIraq)onceandforall,hetookonthetitlebywhichheisstillknowntoday:KingofBabylon,KingofAsia,KingoftheFourQuartersoftheWorld.
17. TheauthorwantstoinsertanintroductoryphraseorclauseatthebeginningofthissentencethatwillemphasizethecontinuityAlexander’sreignhadwiththepreviousone.Whichofthefollowingchoiceswouldmosteffectivelygivethisemphasis?A) Inwhatmusthavebeentrulyexhausting,B) Withgreatambition,C) Ashisfatherhadbeforehim,D) Justashistorianshavenoted,
18. Whichofthefollowingchoicesgivesinformationconsistentwiththemapshownbelow?A) NOCHANGEB) whilehetraveledonfootthroughoutmostofmodern-dayEurope,C) becausehecircledtheentireMediterraneanSeaandmuchoftheIndianOcean,D) asheconqueredallofItalyhundredsofyearsbeforeCaesarhaddoneso,
ExtentoftheempireofAlexandertheGreat
Alexander’shistoricalimportanceisnotmerelyoneofmilitarymight,however. 19 Hemovedtothesedifferentpartsoftheworld,hebroughtGreekculturewithhim,andhisreignmarks 20 anunprecedentedinstanceofcontactbetweentheancientEastandWest.Overtwentycitiesthroughouttheempirebearhisname.Alexandria,Egypt,perhapsthemostfamousofthesecities,continuesto 21thrive.Itisthesecond-largestcityinthemodernnationofEgypt.
19.A) NOCHANGEB) AsheC) AlthoughheD) Moreover,he
20. WhichofthefollowingalternativestotheunderlinedportionwouldNOTbeacceptable?A) anunparalleledB) apioneeringC) anahistoricalD) aneverbeforeseen
21. Whichofthefollowingisthemosteffectivewaytocombinethesetwosentences?A) thrive;itisB) thrive,is
C) thrive.It’sD) thriveandis
PerhapshistoryisthewrongplacetounderstandtheaccomplishmentsofAlexandertheGreat.Epicpoetryseemsmoresuitable.Afterall,Alexander’sgreatteacherAristotleshowedhimHomer’sIliadandOdyssey,anditseemsthatAlexanderhimselfunderstoodhislifeasashuttlingbackandforthbetweenmanandgod,theindividualandtheworld,andthenatural 22 andtheunnatural.
22.A) NOCHANGEB) versusC) fromD) but
Questions23–33arebasedonthefollowingpassage.
Brother,CanYouSpareaDime?
Althoughprintedcheaplyandforquickconsumption, 23 today’sexperienceofcultureislargelyshapedbydimenovels.Formuchofthenineteenthcentury,Americansconsumedfiction,poetry,andnon-fictionbywayofliteraryperiodicals.Someofourbest-knownauthorsfromthisperiod, 24 thoughtherewerealsosomenotableexceptions,publishedsomethingclosetotheircompleteworksbetweenthepagesofcountlessperiodicals.
23.A) NOCHANGEB) weexperienceculturethewaywedobecauseofdimenovels.C) dimenovelshaveshapedthewayweexperienceculturetoday.D) theshapeofdimenovelsinfluencesofculturalexperiences.
24. Whichofthefollowingtruephrasesgivesthemostspecificinformationinthecontext?A) NOCHANGEB) someofthebest-knownauthorsofalltime,C) andsomewhowerenotsowell-known,D) especiallyEdgarAllanPoeandNathanielHawthorne,
ThingsstartedtochangearoundtheCivilWar.HarrietBeecherStowe’sgreat 25 novel,UncleTom’sCabinhadbeenanenormouslypopularserialnovelintheabolitionistperiodicalTheNationalEra.Bythetimethenovel’sforty-weekrunhadconcluded,however,publisherswereclamoringforanactualbook. 26 ThatbookwentontobecomethefirstAmericanbestseller.AnditshowedthatAmericanswerewillingtopayforbooks,whichhad,tothatpoint,beentooexpensivetoprintandsubsequentlytobuy. 27
25.A) NOCHANGEB) novel,UncleTom’sCabin,C) novelUncleTom’sCabin,D) novelUncleTom’sCabin
26. Iftheauthorweretoremovethephrase“foranactualbook”(endingthesentenceatthewordclamoring),thesentencewouldloseA) specificinformationthatclarifiesthesubjectofthenextsentence.B) adescriptionofthegreedofpublishersinthenineteenthcentury.
C) detailsthatshowhowStowe’sworkcametobesopopular.D) nothing,becausethisinformationisimpliedintheword“clamoring.”
27. Atthispoint,thewriterisconsideringaddingthefollowingtruestatement:
TheaverageannualincomeformeninNewEnglandfrom1820-1850wasamere$323.25.
Shouldthewritermakethisadditionhere?A) Yes,becauseitmakesclearhowexpensivebooksmusthavebeenintheperiod.B) Yes,becauseitshowsthateventhoseinNewEnglandcouldnotaffordbooks
printedthere.C) No,becauseitstraysfromtheparagraph’sfocusonthechangesinbookpublishing.D) No,becauseitsuggeststhatpeopleinNewEnglandwerenotwealthyenoughto
read.
In1860,IrwinandErastusBeadlepublishedthefirstinalongseriesofwhat 28 wouldbecomeknownasBeadle’sDimeNovels.ThefirstwascalledMalaeska,TheIndianWifeoftheWhiteHunter.Bytheturnofthenineteenthcentury,dimenovelswereeverywhere.
28.A) NOCHANGEB) becomesC) isD) wouldhavebecome
The 29 affectsaredifficulttochart,butwecanactuallyseetheinfluenceofthesedimenovelseverywhere.MuchofthemythologyoftheOldWest,forexample,wasconcretizedinthesedimenovels,andWilliamBonneyandJamesButlerHickokbecamethefolkheroesBillytheKidandWildBillHickokasthedimenovelschartedtheir(largelyimagined)adventures. 30
29.A) NOCHANGEB) effectsC) effect’sD) affect’s
30. Theauthorisconsideringdeletingthenames“BillytheKidandWildBillHickok”fromtheprecedingsentence.Shouldthenamesbekeptordeleted?A) Kept,becausetheyarespecificnamesinasentencethatspeaksingeneralities.
B) Kept,becausetheydemonstratethetransformationdescribedinthesentence.C) Deleted,becausetheyarenicknamesofpeoplewhosetruenamesarealreadylisted
inthesentence.D) Deleted,becausetheyencouragethefrontierbehaviorthatmadetheWildWestsuch
aviolentplace.
Thenewmediaofthetwentieth-century—film,radio,andcomicbooks—mayhavereplacedthedimenovel,buttheydidsowithmuchtheyhad 31 beentaughtfromthedimenovel’spopularity.Allthreemedia,forinstance,borrowedcharactersthathadbecomepopularindimenovels—characterssuchasFrankReadeandNickCarter,MasterDetective.Then,incomicbooksandradio,anewgenerationofsuperheroes—TheShadow,Superman,andPopeye—wascreatedinthemoldoftheoldswashbucklingromanciersofthedime-novelera.
31.A) NOCHANGEB) gotC) learnedD) brought
Sotoday,asweenjoysuperheroactionfilmsorboy-wizardseriesofnovels,weshouldbeawarethatthereisnothingnewunderthesun.Indeed, 32 forourhopelesslymass-mediauniverse,thisnowforgottenformlaidthefoundation,pushingthesamebooksontocountlessreaders.Suchafeatmaybecommonplaceasfilmsgrossmanybillionsofdollarsattheboxoffice,butinthenineteenthcentury,thedimenovelbroughtanew 33 frameofreferenceandabeliefthatthesmallworldwasgettinglargerbitbybit.
32. Ifthepunctuationisadjustedaccordingly,thebestplacementfortheunderlinedportionwouldbeA) whereitisnow.B) afterthewordform.C) afterthewordfoundation.D) attheendofthesentence.
33. WhichofthefollowingalternativestotheunderlinedportionwouldNOTbeacceptable?A) paradigmB) integrationC) frameworkD) context
Questions34–44arebasedonthefollowingpassageandsupplementarymaterial.
TheTigerMoth’sPhantomTarget
—1—
Batshavealwaysseemedmysteriouspredators.Whilemanyotheranimalpredatorsusemethods34 similartohumanhunters,batshaveevolvedaseriesofuniquemethodsofcapturingprey. 35 Themaincuriosityamongthebat’sweaponryisitsuseofecholocation,orsonar.
34.A) NOCHANGEB) similartothatofhumanhunters,C) similartothoseofhumanhunters,D) likehumanhunters,
35.A) NOCHANGEB) Theecholocation,sonar,ofthebat’sweaponryisitsmaincuriosity.C) Thebathasacuriousweaponry,mainamongwhichisitsecholocationandsonar.D) Thebat’sweaponryismainlycuriousinitsuseofecholocationofsonar.
—2—
Becausebatshuntinthedark,theyarenotoftenabletoseetheirprey.Instead,theyuseaprocesswhereintheyemitsoundsandlistenfortheechoes.If 36 theyare,say,standingatopamountainandshout,youcanfigureoutthedistanceacrossthecanyonusingthespeedofsoundwavesandaseriesofprecisecalculations.Usingitsinnatesenses,abatdoesthesesame 37 calculationsinstinctively.Withextremeprecision,abatcanidentifyitsprey’slocationandsizeinthedarkandcaptureitsprey.Whileabatdoeshaverelativelyacutevision, 38 thoughnotnearlyasacuteassomespeciesofshrimp,itsecholocationiswhatmakesitsuchaneffectivepredator.
36.A) NOCHANGEB) they’re,C) oneis,D) youare,
37.
A) NOCHANGEB) calculationsbyinstinct.C) calculationswithitsinstincts.D) calculations.
38. Thewriterintendstoinsertaphraseorclausethatemphasizesacommonmisunderstandingaboutbats’vision.Whichofthefollowingwouldbestsuitthatintention?A) NOCHANGEB) underminingthecliché“blindasabat,”C) despitethepitchdarknessinwhichithunts,D) inadditiontoitsincrediblehearing,
—3—
However,scientistshaverecentlydiscoveredaspeciesthatcandisruptthebat’susuallyfailsafeecholocation.Thetigermoth,avictimofbatpredationforover50millionyears,hasfiguredoutawayto“jam” 39 itssystemofecholocation.Mosttigermothscanemitclicksthatwarnbatsawayfromthemoths,suggestingthatthemothsmightbeinedibletoxiccompounds. 40
39.A) NOCHANGEB) thebats’C) thebat’sD) thebats
40. Ifthewriterweretodeletethewordsinedibleandtoxicfromtheprecedingsentence,thesentencewouldprimarilyloseA) anindicationthatthetigermothisnotconsumedbyanypredators.B) aspecificdescriptionofthecompoundthatpreventsthebatfromeatingthetiger
moth.C) adetailedanalysisofthemechanismoftheclicksthatproducethisparticular
compound.D) nothing,becausetheinformationisstatedelsewhereinthepassage.
—4—
Inthelonghistoryofbatresearch,scientistshaveneverseenthelikeofthesetigermoths.Althoughhumanmethodsofwarfarehaveusedsonicdeceptionforaslongassuchwarfarehasexisted,thetigermothand 41 theirsonarjammingprovideoneofthefirstinstancesofauralcamouflageintheanimal
kingdomthatscientistshavediscovered.Itseemsthatnomatterhowancienttheconflict,batsandtigermothscontinuetoattack, 42 counterattack,andadaptinawarasoldastime.
41.A) NOCHANGEB) it’sC) itsD) its’
42.A) NOCHANGEB) counterattack,and,adaptC) counterattackandadaptD) counterattackandadapt,
—5—
Onespecies,thetigermothBertholdiatrigona,hasdoneevenbetter.Thisspeciesemitsahigh-frequencyclickingnoisethatthrowsoffthebat’ssonaraltogether.WhilenooneiscertainexactlyhowtheseclickscamouflagetheB.trigona,theclickshavebeenremarkablysuccessfulindefendingthemothsfrombatattacks.Somesuggestthattheclicksforcebatstomisinterprettheirsensorydata,takingthemothclicksfortheirownechoes.Asaresult,bats 43 misstheirpreyatthemomentofattemptedcapture,andthetigermothsflitawayunharmed. 44
ThisimageisadaptedfromtheJournalofExperimentalBiology©2011.
43. Whichofthefollowingprovidesaccurateinformationbasedonthediagrams?A) NOCHANGEB) attackotheranimalstheyfindeasiertodetect,C) flyafteroneanother,bonkingtheirheadstogether,D) hearnosoundsatall,
44. Inthecontextofthepassageasawhole,thebestplacementforparagraph5wouldbeA) whereitisnow.B) afterparagraph1.C) afterparagraph2.D) afterparagraph3.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–NoCalculator25MINUTES,20QUESTIONS
TurntoSection3ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–15,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions16–20,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion16onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorisnotpermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Whichofthefollowingequationshasavertexof(3,–3)?A) y=5(x–3)2–3B) y=5(x+3)2–3C) y=5(x–3)2+3D) y=5(x+3)2+3
2. Abeveragestorechargesabasepriceofxdollarsforonekegofrootbeer.Asalestaxofacertainpercentageisappliedtothebaseprice,andanuntaxeddepositforthekegisadded.Ifthetotalamount,indollars,paidatthetimeofpurchaseforonekegisgivenbytheexpression1.07x+17,thenwhatisthesalestax,expressedasapercentageofthebaseprice?A) 0.07%B) 1.07%C) 7%D) 17%
3. Syedtookoutacashadvanceofddollarsfromafinancingcompany.Thecompanydeductsafeeof oftheoriginaladvancedamountalongwithawiretransferfeeof
$30.00.WhichofthefollowingrepresentsthefinaladvancedamountthatSyedreceivesafterallappliedfees,indollars?
A) d–30
B) (d–30)
C) (d–30)
D) d–30
4. Whatistheequationofalinethatcontainsthepoint(1,6)andhasay-interceptof4?
A) y= x+4
B) y=x+4C) y=2x+4D) y=4x+2
5. Thenumberofbonuspoints,B(p),thatacreditcardholderreceivesisgivenbythefunctionB(p)=4p+7,whereprepresentsthenumberofpurchasesmade.Ifthenumberofpurchasesisincreasedby3,byhowmuchdoesthenumberofbonuspointsincrease?A) 3B) 4C) 12D) 19
6. Jefftestshowthetotalvolumeoccupiedbyafluidcontainedinagraduatedcylinderchangeswhenroundmarblesofvarioussizesareadded.Hefoundthatthetotalvolumeoccupiedbythefluid,V,incubiccentimeters,canbefoundusingtheequationbelow,wherexequalsthenumberofidenticalmarblesJeffadded,oneatatime,tothecylinder,andristheradiusofoneofthemarbles.
Ifthevolumeofthegraduatedcylinderis96μcubiccentimeters,then,whatisthemaximumnumberofmarbleswitharadiusof3centimetersthatJeffcanaddwithoutthevolumeofthefluidexceedingthatofthegraduatedcylinder?A) 1B) 2C) 3D) 4
7. Ifbistwomorethanone-thirdofc,whichofthefollowingexpressesthevalueofcintermsofb?
A) c=
B) c=
C) c=3(b–2)
D) c=3(b–6)
8. Therotationrateofamixingblade,inrotationspersecond,slowsasaliquidisbeing
addedtothemixer.Thebladerotatesat1,000rotationspersecondwhenthemixerisempty.Therateatwhichthebladeslowsisfourrotationspersecondlessthanthreetimesthesquareoftheheightoftheliquid.Ifhistheheightofliquidinthemixer,whichofthefollowingrepresentsR(h),therateofrotation?A) 4–9h2
B) 1,000–(4–3h)C) 1,000–(9h–4)D) 1,000–(3h2–4)
9. Adentalhygienecompanyiscreatinganew24-ouncetubeoftoothpastebycombiningitsmostpopulartoothpastes,CavityCrusherandBadBreathObliterator.CavityCrushercontains0.25%ofsodiumfluorideasitsactiveingredient,andBadBreathObliteratorcontains0.30%oftriclosanasitsactiveingredientforatotalof0.069ouncesofactiveingredientsinbothtoothpastes.SolvingwhichofthefollowingsystemsofequationsyieldsthenumberofouncesofCavityCrusher,c,andthenumberofouncesofBadBreathObliterator,b,thatareinthenewtoothpaste?
A) c+b=0.0690.25c+0.3b=24
B) c+b=240.0025c+0.003b=0.069
C) c+b=240.025c+0.03b=0.069
D) c+b=240.25c+0.3b=0.069
10.
Intheequationabove,whatisthevalueofd?A) –4B) 2C) 4D) 6
11. Whichofthefollowingisapossibleequationforacirclethatistangenttoboththex-axisandthelinex=4?
A) (x+2)2+(y+2)2=4B) (x+2)2+(y–2)2=4C) (x–2)2+(y+4)2=4D) (x–6)2+(y–2)2=4
12. ReactantAisplacedinabeaker,towhichReactantBwillbeadded.ReactantsAandBwillnotreactunlessBgetstoacertainconcentration.Oncethereactionstarts,bothconcentrationsdecreaseuntilBhasbeenconsumed.Whichofthefollowinggraphs,showingconcentrationinmolesasafunctionoftimeinseconds,representsthereaction?A)
B)
C)
C)
D)
14.
IfrectangleABCDhasanareaof48andthetangentof BCA(notshown)is ,then
whichofthefollowingisthelengthofBD(notshown)?A) 5B) 10
C) 13D) Itcannotbedeterminedfromthegiveninformation.
15. Whichofthefollowingisequivalentto ?
A)
B)
C)
D) m–6
DIRECTIONS
Forquestions16–20,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpretedas
,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
16. Arectangularboxhassides3,4,andxandavolumeof18.Whatisthevalueofx?
17. JeannebabysitsChuyonedayeachweek.Jeannechargesa$20feefortheday,plus$5.50forevery30minutesofbabysitting.HowmuchhasJeanneearnedafterthreehoursofbabysitting?(Disregardthe$signwhengriddingyouranswer.)
18. Theparabolay=–x2+5x+6isintersectedbytheliney= x+12.Whatisthey-
coordinateoftheintersectionclosesttothex-axis?
19.
Basedonthesystemofequationsabove,whatisthesumofrandv?
20. Agardenerhasacultivatedplotthatmeasures4feetby6feet.Nextyear,shewantstodoubletheareaofherplotbyincreasingthelengthandwidthbyxfeet.Whatisthevalueofx?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–Calculator55MINUTES,38QUESTIONS
TurntoSection4ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–30,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions31–38,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion31onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorispermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Thepopulation,P,ofTownYsince1995canbeestimatedbytheequationP=1.0635x+3,250,wherexisthenumberofyearssince1995and0≤x≤20.Inthecontextofthisequation,whatdoesthenumber1.0635mostlikelyrepresent?A) TheestimatedpopulationoftownYin1995B) TheestimatedpopulationoftownYin2015C) ThefactorbywhichthepopulationoftownYincreasedyearlyD) ThefactorbywhichthepopulationoftownYdecreasedyearly
2. Ifx2+12x=64andx>0,whatisthevalueofx?A) 2B) 4C) 8D) 16
3. Saiisorderingnewshelvingunitsforhisstore.Eachunitis7feetinlengthandextendsfromfloortoceiling.ThetotallengthofthewallsinSai’sstoreis119feet,whichincludesalengthof21feetofwindowsalongthewalls.Iftheshelvingunitscannotbeplacedinfrontofthewindows,whichofthefollowinginequalitiesincludesallpossiblevaluesofr,thenumberofshelvingunitsthatSaicoulduse?
A) r≤
B) r≥
C) r≤119–21+7rD) r≥119+21–7r
4. TruffulaTreeFruitWeight
Thescatterplotaboveshowstheweight,inounces,ofthefruitsonacertaintruffulatreefromdays55to85afterflowering.Accordingtothelineofbestfitinthescatterplotabove,whichofthefollowingistheclosestapproximationofthenumberofdaysafterfloweringofatruffulafruitthatweighs5.75ounces?A) 63B) 65C) 77D) 81
5. Hannahplacedanonlineorderforshirtsthatcost$24.50pershirt.Ataxof7%isaddedtothecostoftheshirts,beforeaflat,untaxedshippingrateof$6ischarged.WhichofthefollowingrepresentsHannah’stotalcostforsshirts,indollars?A) 0.07(24.50s+6)B) 1.07(24.50+6)sC) 1.07(24.50s)+6D) 1.07(24.50+s)+6
6. Onceacertainplantbeginstogrow,itsheightincreasesatalinearrate.Aftersixweeks,theplantis54centimeterstall.Whichofthefollowingfunctionsbestmodelstherelationshipbetweenh(w),theheight,incentimeters,oftheplant,andw,thenumberofweeksthattheplanthasbeengrowing?A) h(w)=6wB) h(w)=9w
C) h(w)=54wD) h(w)=54+w
7. Whichofthefollowingisequivalentto(12x2+4x+5y)+(3x2–2x+3y)?A) 2x2–2x+8yB) 2x2+15x+8yC) 15x2–2x+8yD) 15x2+2x+8y
8. AnadvertisementforRoyalRatRationsstates:“7outof8veterinariansrecommendRoyalRatRationsforyourfancyrat.”Nootherinformationaboutthedataisprovidedbythecompany.
Basedonthisdata,whichofthefollowinginferencesismostvalid?A) RoyalRatRationsprovidesthebestnutritionforfancyrats.B) IfyoudonotfeedyourratRoyalRatRations,yourratwillbeunhealthy.C) OnlyoneveterinariandoesnotrecommendRoyalRatRationsforyourfancyrat.D) OftheveterinarianssurveyedbyRoyalRatRations,themajorityrecommendRoyal
RatRationsforyourfancyrat.
9.
t+4= t–5
Intheequationabove,whatisthevalueoft?A) 4B) 9C) 18D) 36
10. Dogsneed8.5to17ouncesofwatereachdayforevery10poundsoftheirweight.Everetthastwodogs—Ringoisa35-poundblacklabmix,andElvisisa55-poundbeagle.Whichofthefollowingrangesrepresentstheapproximatetotalnumberofouncesofwater,w,thatElvisandRingoneedinaweek?A) 77≤w≤153B) 109≤w≤218C) 536≤w≤1,071
D) 765≤w≤1,530
11. PriyaisplanningtosendherfavoritedryrubrecipetoafriendwholivesinFrance.Beforesendingtherecipe,PriyawantstoconverttheAmericancustomaryunitsintheinstructionsintometricunitssothatherfriendwilleasilybeabletounderstandthemeasurements.Iftherecipecallsforaratiooffourouncesofpaprikatoeverysevenouncesofchilipowder,andifPriya’sfriendisplanningtomakealargebatchofdryrubwith91totalouncesofchilipowder,approximatelyhowmanytotalgramsofpaprikaandchilipowderwillthereciperequire?(1ounce=28.3grams)A) 4,047gramsB) 4,521gramsC) 4,925gramsD) 5,149grams
12. Lucianomeasuredtheamountofwaterthatevaporatedoveraperiodoftimefromacontainerholdingwouncesofwater,wherewisgreaterthan12.Bytheendofthefirstday,thecuphadlost2ouncesofwater.Bytheendofthe7thday,thecuphadlostanadditional8ouncesofwater.Bytheendofthe11thday,thecuphadlosthalfofthewaterthatremainedafterthe7thday.Whichofthefollowingrepresentstheremainingamountofwater,inounces,inLuciano’scontainerattheendofthe11thday?
A)
B) –10
C) w–10
D)
Questions13and14refertothefollowinginformation.
Inthe1990s,theparkrangersatYellowstoneNationalParkimplementedaprogramaimedatincreasingthedwindlingcoyotepopulationinMontana.Resultsofstudiesofthecoyotepopulationintheparkareshowninthescatterplotbelow.
13. Basedonthelineofbestfitinthescatterplotabove,whichofthefollowingistheclosesttotheaverageannualincreaseincoyotesinYellowstoneParkbetween1995and2000?A) 22B) 24C) 26D) 28
14. Accordingtothedatainthescatterplot,whichofthefollowingbestrepresentsthepercentincreasebetweenthemedianoftheresultsofthestudiesfrom1995andthemedianoftheresultsofthestudiesfrom1996?A) 50%B) 100%C) 150%D) 200%
15. Bailey’sBoutiqueClothingishavinga20%offsaleduringwhichshirtscost$30.00and
pantscost$60.00.Onthedayofthesale,Bailey’ssellsatotalof60shirtsandpantsand
earnedatotalof$2,250.Onaregularday,Bailey’ssells thenumberofshirtsandpants
soldduringthesaleandearnsatotalof$1,875.Solvingwhichofthefollowingsystemsof
equationsyieldsthenumberofshirts,s,andthenumberofpants,p,soldduringaregular
day?
A) s+p=4037.5s+75p=1,875
B) s+p=4030s+60p=2,250
C) s+p=6030s+60p=2,250
D) s+p=2,25030s+60p=60
16. Bryan,whoworksinahigh-endjewelrystore,earnsabasepayof$10.00perhourplusacertainpercentcommissiononthesalesthathehelpstobrokerinthestore.Bryanworkedanaverageof35hoursperweekoverthepasttwoweeksandhelpedtobrokersalesof$5,000.00worthofjewelryduringthatsametwo-weekperiod.IfBryan’searningsforthetwo-weekperiodwere$850.00,whatpercentcommissiononsalesdoesBryanearn?A) 1%B) 2%C) 3%D) 4%
17. If ,whichofthefollowingcouldbeanexpressionofCintermsofx?
A) 3(1+x)B) x2+2x–24
C) (x+6)(x–4)
D) (x–3)(x+8)
18. Lennonhas6hourstospendinHaHaTonkaStatePark.Heplanstodrivearoundtheparkatanaveragespeedof20milesperhour,lookingforagoodtrailtohike.Oncehefindsatrailhelikes,hewillspendtheremainderofhistimehikingit.Hehopestotravelmorethan60milestotalwhileinthepark.Ifhehikesatanaveragespeedof1.5milesperhour,whichofthefollowingsystemsofinequalitiescanbesolvedforthenumberofhoursLennonspendsdriving,d,andthenumberofhourshespendshiking,h,whileheisatthe
park?A) 1.5h+20d>60
h+d≤6B) 1.5h+20d>60
h+d≥6C) 1.5h+20d<60
h+d≥360D) 20h+1.5d>6
h+d≤60
19. Inacertainsportinggoodsmanufacturingcompany,aqualitycontrolexperttestsarandomlyselectedgroupof1,000tennisballsinordertodeterminehowmanycontaindefects.Ifthisqualitycontrolexpertdiscoveredthat13oftherandomlyselectedtennisballsweredefective,whichofthefollowinginferenceswouldbemostsupported?A) 98.7%ofthecompany’stennisballsaredefective.B) 98.7%ofthecompany’stennisballsarenotdefective.C) 9.87%ofthecompany’stennisballsaredefective.D) 9.87%ofthecompany’stennisballsarenotdefective.
20. If– <–3z+6<– ,whatisthegreatestpossibleintegervalueof9z–18?
A) 6B) 7C) 8D) 9
21.
Whichofthefollowingorderedpairs(j,k)isthesolutiontothesystemofequationsabove?A) (6,–6)B) (3,0)C) (0,2)D) (–4,1)
22. UnitedStatesInvestmentinAlternativeEnergySources
ThetableaboveshowstherelativeinvestmentinalternativeenergysourcesintheUnitedStatesbytype.Onecolumnshowstherelativeinvestmentin2007of$75milliontotalinvestedinalternativeenergy.Theothercolumnshowstheprojectedrelativeinvestmentin2017givencurrenttrends.Thetotalprojectedinvestmentinalternativeenergyin2017is$254million.Supposethatanewsourceofalternativeenergy,ColdFusion,isperfected.Itisprojectedthatby2017that$57millionwillbeinvestedinColdFusionintheUnitedStates,withoutanycorrespondingreductionininvestmentforanyotherformofalternativeenergy.WhatportionofthetotalinvestmentofalternativeenergyintheUnitedStateswillbespentonbiofuels?A) 0.18B) 0.22C) 0.28D) 0.34
23.
(x–2)2+y2=36y=–x+2
Theequationsaboverepresentacircleandalinethatintersectsthecircleacrossitsdiameter.WhatisthepointofintersectionofthetwoequationsthatliesinQuadrantII?A) (−3 ,3 )
B) (–4,2)C) (2+ ,2)
D) (2−3 ,3 )
24.
Thegraphoff(x)isshownaboveinthexy-plane.Thepoints(0,3),(5b,b),and(10b,–b)areonthelinedescribedbyf(x).Ifbisapositiveconstant,whatarethecoordinatesofpointC?A) (5,1)B) (10,–1)C) (15,–0.5)D) (20,–2)
25. Melanieputs$1,100inaninvestmentaccountthatsheexpectswillmake5%interestforeachthree-monthperiod.However,afterayearsherealizesshewaswrongabouttheinterestrateandshehas$50lessthansheexpected.Assumingtheinterestratetheaccountearnsisconstant,whichofthefollowingequationsexpressesthetotalamountofmoney,x,shewillhaveaftertyearsusingtheactualrate?A) x=1,100(1.04)4t
B) x=1,100(1.05)4t–50
C) x=1,100(1.04)t/3
D) x=1,100(1.035)4t
26.
Iftheradiusofthecircleaboveisx, AOB=120°,andOisthecenterofthecircle,whatisthelengthofchordAB,intermsofx?A) x
B) x
C)
D) x
27. Studentsinaphysicsclassarestudyinghowtheangleatwhichaprojectileislaunchedon
levelgroundaffectstheprojectile’shangtimeandhorizontalrange.Hangtimecanbe
calculatedusingtheformula ,wheretisthehangtimeinseconds,vistheinitial
launchvelocity,θistheprojectileanglewithrespecttolevelground,andgisthe
accelerationduetogravity,definedas9.8m/s2.Horizontalrangecanbecalculatedusing
theformula ,whereRisthedistancetheprojectiletravelsfromthelaunchsite,in
feet.Whichofthefollowinggivesthevalueofv,intermsofR,t,andθ?
A)
B)
C)
D)
28. If(i413)(ix)=1,thenwhatisonepossiblevalueofx?A) 0B) 1C) 2D) 3
29. Thefunctiongisdefinedbyg(x)=2x2–dx–6,wheredisaconstant.Ifoneofthezerosofgis6,whatisthevalueoftheotherzeroofg?A) 2
B)
C) –
D) –2
30. Theflushotforafluseasoniscreatedfromfourstrainsofthefluvirus,namedStrainA,B,C,andD,respectively.Medicalresearchersusethefollowingdatatodeterminetheeffectivenessofthevaccineoverthefluseason.Table1showstheeffectivenessofthevaccineagainsteachofthesestrainsindividually.Thegraphbelowthetableshowstheprevalenceofeachofthesestrainsduringeachmonthofthefluseason,representedasapercentageoftheoverallcasesoffluthatmonth.
Table1
Forthestrainagainstwhichtheflushotwasthemosteffective,approximatelyhoweffectivewastheshotoverallduringthemonththatstrainwasleastprevalent?A) 13%B) 20%C) 27%D) 48%
DIRECTIONS
Forquestions31-38,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpretedas
,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
31. If9>3v–3,whatisthegreatestpossibleintegervalueofv?
32. Intheexpression =1,whatisthevalueofy?
33. Duringapresidentialelection,ahighschoolhelditsownmockelection.StudentshadtheoptiontovoteforCandidateA,CandidateB,orseveralothercandidates.Theycouldalsochoosetospoiltheirballot.Thetablebelowdisplaysasummaryoftheelectionresults.
614studentsvotedforCandidateA.Approximatelyhowmanystudentsattendtheschool?
34. Iftanθ= ,thencosθ=
35. MarcellusistravelingabroadinGhanaandusingtraveler’schecks,whichhehasacquiredfromEasyTraveler’sSavingsBank.EasyTraveler’sSavingsBankchargesa7%feeontraveler’schecks,whichcanthenbeusedlikecashatanylocationoverseasatthesameexchangerate,andanychangewillthenbereturnedtoMarcellusinlocalcurrency.Forthistrip,Marcellusboughta651Ceditraveler’scheckandpaidafeeof32.30USD(UnitedStatesdollars)forthecheck.
WhileinGhana,MarcellusfindsLeon’sPawnshopandBarter,whichoffersstorecreditforMarcellus’sbriefcaseequaltoitsvalueinCedis.IfMarcellus’sbriefcaseisworth5,000USDatthesameexchangerateatwhichheboughthistraveler’scheck,thenhowmuchstorecredit,totheclosestCedi,willMarcellusreceiveforthebriefcase?
36. Asquareisinscribedinacircle.Theareaofthesquareiswhatpercentoftheareaofthecircle?(Disregardthepercentsymbolwhengriddingyouranswer.)
Questions37and38refertothefollowinginformation.
Professor Malingowski, a chemist and teacher at a community college, is organizing his
graduatedcylindersinthehopesofkeepinghisofficetidyandsettingagoodexampleforhis
students.Hehasbeakerswithdiameters,ininches,of , , ,1,and .
37. ProfessorMalingowskinoticesoneadditionalcylinderlyingontheground,andcanrecallcertainfactsaboutit,butnotitsactualdiameter.Ifheknowsthatthevalueoftheadditionalgraduatedcylinder’sdiameter,x,willnotcreateanymodesandwillmakethemeanofthesetequalto ,whatisthevalueoftheadditionalcylinder’sdiameter?
38. Withhisoriginalfivecylinders,ProfessorMalingowskirealizesthatheismissingacylindernecessaryforhisupcominglabdemonstrationforThursday’sclass.Heremembersthatthecylinderheneeds,whenaddedtotheoriginalfive,willcreateamediandiametervalueof forthesetofsixtotalcylinders.Healsoknowsthatthe
measureofthesixthcylinderwillexceedthevalueoftherangeofthecurrentfive
cylindersbyawidthofanywherefrom inchesto inches,inclusive.Basedonthe
abovedata,whatisonepossiblevalueofy,thediameterofthismissingsixthcylinder?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
SATEssay
ESSAYBOOK
DIRECTIONS
Theessaygivesyouanopportunitytoshowhoweffectivelyyoucanreadandcomprehendapassageandwriteanessayanalyzingthepassage.Inyouressayyoushoulddemonstratethatyouhavereadthepassagecarefully,presentaclearandlogicalanalysis,anduselanguageprecisely.
Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteinprintsothatwhatyouarewritingislegibletothosereaders.
Youhave50minutestoreadthepassageandwriteanessayinresponsetothepromptprovidedinsidethisbooklet.
REMINDER
— Donotwriteyouressayinthisbooklet.Onlywhatyouwriteonthelinedpagesofyouranswerbookletwillbeevaluated.
— Anoff-topicessaywillnotbeevaluated.
Asyoureadthepassagebelow,considerhowtheauthoruses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
Excerptedfrom“MakingABrainMapThatWeCanUse”byAlvaNoë.OriginallypublishedJanuary16,2015.
1 Itisnowconventionalwisdomthatthebrainistheseatofthemind;itisalonethroughthebrain’sworkingsthatwethinkandfeelandknow.
2 Butwhatisabrain,anyway?
3 MythoughtsturnedtothisquestionasIwasreadingarecentNewYorkTimespieceaboutSebastianSeung’sprojecttomapthebrainbytracingouteachofthetrillionsoflinksbetweenindividualneurons.Thisundertakingtomapthesystemofconnectionswhichmakeuswhatweare—tomapwhatSeungcalledtheconnectomeinhis2011book—canseem,fromacertainpointofview,likeagloriousandheroicstepbackward.
4 Tryingtounderstandhowthebrainworksbylookingatthebehaviorofindividualcells—soobservedDavidMarr,oneofmoderncognitivescience’sfoundationalfigureswritinginthelate1970s—wouldbeliketryingtounderstandhowabirdfliesbyexaminingthebehaviorofindividualfeathers.Tounderstandflight,youneedtounderstandaerodynamics;onlyonceyougetahandleonthatcanyouaskhowastructureoffeathers,oranyotherphysicalsystem—suchasamanufacturedairship—canharnessaerodynamicsintheserviceofflight.
5 Andsoitiswiththebrain:Beforewecanunderstandhowitworks,itwouldseemthatweneedtounderstandwhatit’sdoing.Butyoucan’treadthatofftheactionofindividualcells.Justtry!
6 Imagineyouweretostumbleonedayuponacomputeronthebeachandimagine(veryunrealistically)thatyouhaveneverseenorheardofacomputerbefore.Howwouldyougoaboutfiguringouthowitworks?Well,onethingyoucoulddowouldbetomakeamapofhowallthedetachablepartsofthemachineareconnected.Thispieceofmetalissolderedtothispiece,whichisstapledtothispieceofplastic.Andsoon.Supposeyoufinishedthejob.Wouldyouknowwhatthethingisbeforeyou?Orhowitworks?Wouldyourcomplicated,Rube-Goldberg-esquemapoftheconnectionsbetweenthepartsevencountasamodelofthecomputer?Keepinmindthattherearelotsofdifferentkindsofcomputers,madeoflotsofdifferentmaterials,withlotsofdifferenttypesofpartsandnetworksofconnections.Infact,ifAlanTuringwasright(andTuringwasright),thebasicandessentialjobofacomputer—thecomputingofcomputablefunctions—canbespecifiedinentirelyformalterms;thephysicalstuffofthecomputingmachineisirrelevanttothequestionofwhatcomputationsarebeingcomputedand,so,really,itisalsoirrelevanttothequestionofhowthis—oranyothercomputer—works…
7 I’mraisingbothapracticalpointandapointofprinciple.Thepracticalpointisthatweneedsomeconceptionofwhatthewholeisforbeforewehaveaghostofachanceoffiguringouthowitworks.ThisisMarr’spointaboutfeathersandflight.Butthereisalsoamatterofprinciple:Whenitcomestocomplexfunctionalsystems—likecomputers,forsure,and,probably,likebrains—thelawsandregularitiesandconnectionsthatmatterarethemselveshigher-level;theydon’tbottomoutinlawsframedintermsofneuronalunitsanymorethantheydoinlawsframedintermsofquantummechanicalprocesses.Thepointisnotjustthatitishardtounderstandthebrain’sholisticoperationintermsofwhatcellsaredoingbut,instead,thatitmightbeimpossible—liketryingtounderstandthestockmarketintermsofquantummechanics.Surely,naturalismdoesn’tcommitustotheviewthatitoughttobepossibletoframeatheoryofthestockmarketinthetermsofphysics?
8 GarethCook,whowrotetherecentNewYorkTimesMagazinearticleonSeung’squest,waswisetorefertoArgentinianwriterJorgeLuisBorges’scautionarytale,OnExactitudeInScience,aboutamapbeingbuiltasanexact,to-sizereplicaofthedomainbeingmapped.Suchamapcan’tserveanyexplanatorypurposewhatsoever.Itwon’tbeausefulmap.MyworryisthatwealreadyknowthatexactlythesamethingistrueofSeung’sconnectome.
WriteanessayinwhichyouexplainhowNoëbuildsanargumentagainsttheideaofcell-by-cellbrainmapping.Inyouressay,analyzehowNoëusesoneormoreofthefeatureslistedabove(orfeaturesofyourownchoice)tostrengthenthelogic and persuasiveness of his argument. Be sure that your analysis focuses on the most relevant aspects of thepassage.
Your essay should not explain whether you agree with Redford’s claims, but rather explain how the author builds anargumenttopersuadehisaudience.
PRACTICETEST2ANSWERKEY
Section1:Reading
1. C2. B3. A4. D5. A6. A7. C8. D9. B10. B11. B12. A13. A14. B15. D16. C17. D18. C19. A20. D21. D22. C23. A24. B25. B26. D27. A28. B29. D30. C31. C32. B33. C
34. D35. A36. C37. A38. A39. D40. A41. B42. B43. A44. A45. C46. C47. B48. C49. D50. A51. B52. D
Section2:Writing&Language
1. A2. C3. B4. A5. D6. D7. D8. D9. B10. A11. C12. B13. A14. B15. B16. D17. C
18. A19. B20. C21. D22. A23. C24. D25. D26. A27. C28. A29. B30. B31. C32. C33. B34. C35. A36. D37. D38. B39. C40. B41. C42. A43. A44. D
Section3:Math(NoCalculator)
1. A2. C3. D4. C5. C6. B7. C8. D9. B
10. C11. D12. B13. A14. B15. D
16. 1.5or
17. 5318. 10
19. or3.66or3.67
20. 2
Section4:Math(Calculator)
1. C2. B3. A4. C5. C6. B7. D8. D9. D10. C11. A12. D13. B14. D15. A16. C17. C18. A19. B20. C21. A22. C23. D
24. B25. A26. B27. C28. D29. C30. D31. 3
32. or0.83
33. 1,279
34. or0.384or0.385
35. 7,05436. 63.6or63.7
37. or0.7
38. 1≤y≤1.25
PRACTICETEST2EXPLANATIONS
Section1:Reading1. C Thekey to thisquestion is thephrase thepassageasawhole.Choice (A)describes the
purposeofasectionofapassage,butitistoospecificanddoesnotdescribethepurposeofthepassageasawhole.Therefore, (A) is incorrect.Similarly,while thespeakersbrieflydiscuss the Shrewsbury School, the discussion occupies very little space, and is not themain point of the passage. Therefore, (B) is incorrect. Because the passage focuses onCarton, it is accurate to say that its purpose is to reveal his character.Therefore, (C) iscorrect.BecausethereisnoevidenceinthepassagethatStryverhasexploitedCarton,(D)cannotbecorrect.
2. B Because Stryver describes Carton as sound in the first paragraph, (A) is incorrect.Mercurial means “subject to sudden changes.” Because Carton rapidly changes fromgrowling to laughing to crying, (B) accurately describes him. Carton’s luck is neverdescribedasbad,so(C)is incorrect.BecausethereisnoindicationthatCartondoesnotnotice the things occurring around him, (D) does not describeCarton.Choice (B) is thecorrectanswer.
3. A In the previous question, it is clear that Carton’s personality and emotional state aresomewhat easilychangeable, so thecorrect answer for thisquestionneeds to reflect thattheme.Thequote in line10,Uponeminuteanddownthenext,accurately illustrates theideathatCartonismercurial;therefore,theanswermustbe(A).Noneoftheotheranswerchoicesarerelevant.
4. D Intheparagraphinquestion,inspiritsdescribesCarton,andtheparagraphsaysthatcartonisuponeminuteanddown thenext.Becausedespondencymeans “depression,” spiritsmustmeantheoppositeofdepression,likehappiness.Choices(A),(B),and(C)allmeanthingsotherthanhappiness.Onlyjubilationistheoppositeofdespondency.Therefore,(D)iscorrect.
5. A Intheparagraphinquestion,StryvercallsCartonunmotivatedandlame,soitisclearthatStryverdislikesCarton’sbehavior.Therefore,(A)iscorrect.BecauseCartonandStryverare friends, it is clear that thedescription shouldnotbe taken literally;Stryverdoesnotwant to literally push Carton into the fireplace. Therefore, (B) is wrong. Similarly, thephrase theoldSydneyCarton hasnothing todowithCarton’sactual age,but rather is atermof endearment.Thus, (C) is incorrect.BecauseStryver andCartonarepresentedasschoolfriends,andthereisnoreasontobelieveStryvereverbulliedSydneyatschool,(D)shouldbeeliminated.
6. A Twolinesaftertheparagraphinquestion,CartonexplicitlystatesthathedoesnotfindMissManette pretty. Because incredulity means “disbelief,” (A) is a good description ofCarton’sattitudeandthecorrectanswer.BecauseCartonsaysthatsheisnotattractiveand
Stryver says that she is attractive,Carton is not confused.He knowswhat he thinks andwhatStryverthinks.Therefore,(B)isincorrect.BecausethereisnoindicationthatCartonisannoyedbyStryver in the lines inquestion, (C) shouldbeeliminated.BecauseCartonthinksMissManetteisnotpretty,hedoesnotfeelaffection towardher.Therefore,(D)isincorrect.
7. C WhileStryversaysthatMissManetteispretty,tosaythatheisinlovewithherwouldbeextreme.Therefore,(A)isincorrect.ThoughCartonisnotsuccessful,Stryversaysthatitisa lack of motivation that holds him back, not a lack of intelligence. Therefore, (B) isincorrect. In lines63–68,Stryver says that it looked likeCarton sympathized withMissManette,whichindicatesthatStryverbelievesCartonwaspayingattentiontoherandsawwhathappenedtoheratcourt.Hewaspayingattentionbecauseshe’sattractive.Therefore,(C)iscorrect.BecauseStryverandCartonneverdiscusseitherman’sfamily,(D)cannotbecorrect.
8. D TheanswertothepreviousquestionisthatStryverdoesnotbelievethatCartonfindsMissManetteunattractive.Becausetheparagraphsindicatedby(A)and(B)makenomentionofMissManette, thesechoicesareincorrect.Sincethelinesindicatedby(C)stateonlythatthe court foundMissManette attractive andmakesno reference toCarton, this choice isincorrect.Theparagraphindicatedby(D)saysthatCartonsympathizedwithMissManette,which contradicts Carton’s assertion that she is not attractive. Therefore, (D) providessupport for the statement that Stryver does not believe that Carton finds Miss Manetteunattractive,andisthecorrectanswer.
9. B Because lifelessdesert describes thewhole scene, it refers to the physical landscape atwhichCartonislooking.Choices(A)and(C)donotdescribealandscape,sobothcanbeeliminated.BecauseCartonislookingatthecity’slandscape,notsanddunes,(D)shouldbeeliminated,leaving(B),whichisthecorrectanswer.
10. B ThereisnoindicationofMissManette’sfeelings,positiveornegative,towardCarton,so(A)isnotcorrect.SinceCartonisdescribedasincapableandresigned,itisclearthathecannot change his behavior. Therefore, (B) is correct. The passage does not provide aphysicaldescriptionofCarton’sapartment,so(C)isincorrect.ThereisnoindicationthatStryverisexploitingCarton,soeliminate(D).
11. B UsePOEtofindtheanswerchoicethatisconsistentwiththepassage.Sincetheauthorisinsupportoftherevolution,(B)isagoodfit.Althoughtheauthordoesn’tseemtosupporttheSoviet Union in the passage, (A) is still too extreme. Eliminate (C) and (D), since theauthorisneitherconflictednordismissive.Choice(B)iscorrect.
12. A Use the context from earlier in the passage, in which a secret non-aggression treatybetweentheSovietUnionandNaziGermanyisdiscussed.Lookforawordorphrasethatmatchesthisdescription,suchas“scheme.”Choice(A)isthebestfit,andthusthecorrectanswer.
13. A The author describes the songs asgrim, but states that people hadhope in their hearts.
Choice(A)matchesthiscontrastratherwell.Choice(B)doesn’tworkbecausethereisnodistinctionmade between the themes of the songs and the anthems; rather, they are bothcategorizedcollectivelyashavinggrimandsorrowfulthemes.ThemilitaryofEstoniaisn’tdiscussed, so eliminate (C).Song festivals arementioned in the followingparagraph, soeliminate(D).You’releftwith(A),whichiscorrect.
14. B Basedon the informationearlier in thepassage, it’s clear thatEstoniawanted tobe freefrom the SovietUnion, or to have a legal“divorce,” as stated at the end of the secondparagraph. This phrase directly correlates with this desire. Choice (B) is a good fit.Eliminate (A) because there is nomention of speakingRussian. Choice (C) is incorrectbecause it’s never stated that Estoniawanted to be culturally separate from otherBalticnations. Eliminate (D) because the passage implies the opposite: Estonians took thefestivalsveryseriouslyandputalotofeffortandtimeintothem.Choice(B)iscorrect.
15. D Basedonthetoneoftheentirepassage,thesizeoftheamphitheaterisusedtoshowhowmuch support this revolution had. Choice (D) matches this tone well. Choice (A) isincorrectbecause thequestionasks for thepurposeof this fact,and thisanswerdoesnotaddress the purpose of including this statistic. Choice (B) is also incorrect because theauthor is not trying to show the popularity of the SovietUnion and its leaders.You caneliminate(C)becausenocomparisonismadetoothertheatersinthepassage.Thecorrectansweris(D).
16. C Crossoutthewordburdenandreplace itwithyourownword that isconsistentwith thetext.Theparagraphbeginsbystatingthathistoriansweredefying“freespeech,”but thatlateritwasmusicianswhoneededtodothis.Soagoodreplacementforburdenwouldbe“authority”or“leadership.”Choice(C)isthebestmatchandthereforethecorrectanswer.
17. D Thefinalparagraphstates that therevolutionwaspowerfuland thatseditionhung in thewind,sofindananswerchoiceconsistentwiththesedescriptions.Choice(A)isincorrect,asdread is tooextreme,andtherewerepositiveoutcomesfromtherevolution.Eliminate(B)becausedisagreementamongrevolutionariesisdiscussedinthepassage.Choice(C)isincorrect becausemusic andpoetry is too broad. Itwas specifically these festivals thatincludedmusicandpoetrythatwerevital.Therefore,(D)istheanswer.
18. C UsePOE to findananswer that is supportedby information in thepassage.Thepassagedoesnotdiscuss theSovietUnion’ssinging traditions,soeliminate (A).Choices (B)and(D)aredirectlycontradictedbythepassage,sogetridofthosechoicesaswell.Choice(C)issupportedbythethirdparagraph,whichstatesthatEstoniacouldnotthreatentheSovietUnionmilitarily.Choice(C)iscorrect.
19. A UsePOEtofindananswerthatissupportedbyinformationinthepassage.Choice(A)isagoodmatch because lines 39–46 discuss the impact of the song festivals. Choice (B) isincorrectbecausethefestivalstartedover100yearsago,notduringtheSovietoccupation.Eliminate(C),asit’snotstatedthatthesongfestivalswereunique.Choice(D)isincorrectbecause the passage doesn’t discuss whether these songs were sung while working.Therefore,theansweris(A).
20. D Thefestivalswereameansofdemonstratingnationalandculturalpride;usePOEtofindtheanswerthatbestexemplifiesthis.Choice(D)isthebestfitbecausethefestivalsunitedEstonians with poetry and music. Choices (A) and (C) are irrelevant to the festivals.Choice(B)discussesthefestivalsbutdoesnotmentionanythingaboutnationalorculturalpride.Thus,(D)iscorrect.
21. D According to the diagram, the Soviet Union acquired Estonia, Latvia, Lithuania,Bessarabia,andpartofPolandinthepact.ThislandmassstretchesfromtheBalticSeatotheBlackSea;therefore,(D)isthecorrectanswer.AlthoughGermanydidreceiveaportionofPoland,theSovietUnionalsoreceivedasignificantchunk.Therefore,(A)isincorrect.As depicted in the diagram, the Soviet Union is much larger than the part of Poland itacquired; eliminate (B).Andcontiguousmeans sharing a commonborder;Lithuania andEstoniaareseparatedbyLatvia,sotheyarenotcontiguous,soeliminate(C).
22. C Thefourthparagraphstates,Butsir,therighttocontroltheirownGovernmentisnotoneoftherightsthatthecitizensofthiscountryarecalledupontosurrenderintimeofwar.Theauthorisobjectingtotherestrictionsplacedonthosewhohaveprotestedthewar,andonly (C) captures the author’s dissenting views. While it is true that LaFollette is alawmaker,nolegislationisproposed,soeliminate(A).SinceLaFollettearguesforasinglepoint of view throughout the text, eliminate (B). While it is true that LaFollette wasdissentingagainstthewar,thisisnothisprimarypurpose,soeliminate(D).
23. A The fourth paragraph states,…all men recognize that in time of war the citizen mustsurrender some…But sir, the right to control their own Government according toconstitutional forms isnotoneof therights….Therefore,LaFollettebelieves thatsomerights are appropriately given up and some are not. Only (A) describes this distinction.LaFollette describes free speech as a fundamental personal right and never describes amomentinwhichitmightbeunnecessary,soeliminate(B).LaFolletteneverdiscusseswhatwouldandwouldnotjustifyawar,soeliminate(C).LaFollettedoesmentiontheinterestsofhumanity (howwars are ended) and the interestsof this country (enduringpeace),butdoesnotdrawadistinctionbetweenthem,soeliminate(D).Choice(A)iscorrect.
24. B The answer to the previous question states that LaFollette draws a distinction betweenrights that are appropriately and inappropriately given up in times of war. Neither thisdistinction nor any other distinction is mentioned in (A), so it can be eliminated. Theaforementioneddistinctionismentionedinthelinesreferencedin(B),whichisthecorrectanswer.Neitherthisdistinctionnoranyotherdistinctionismentionedin(C)or(D),sotheycanbeeliminated.
25. B Thepassagestatesthatpeoplearebeingunlawfullyarrested,thrownintojail…onlytobeeventuallydischargedwithouteverhavingbeentakenintocourt.Agoodwaytodescribethese individualswould bedetained and separated. The only answer choice thatmeanssomethingsimilartothisis(B),sequestered.Thus,(B)isthecorrectanswer.
26. D Thepassagestatesthatcitizensmustbewareof thoseprecedentsinsupportofarbitraryactionbyadministrativeofficials,whichexcusedon thepleaofnecessity inwar time,
become the fixedrulewhen thenecessityhaspassedandnormalconditionshavebeenrestored.Thus,LaFolletteisconcernedthatofficialsmayrestrictfreespeechduringtimesofwarbut thenfail to remove thoserestrictionswhenwartimehaspassed.Moresimply,LaFolletteisworriedthatexceptionsmaybecomerules.Choice(D)matchesthisideamostclosely. LaFollette does grant that the citizen must surrender some rights, but this ismentioned in paragraph 4. Thus, (A) can be eliminated.While LaFollette does say thatsome restrictions are arbitrary, paragraph 4 explicitly denies that all restrictions arearbitrary.Thus, (B)canbeeliminated.WhileLaFollettedoesseemtobeconcernedwithmilitaryaction,(C)isnevermentionedinthepassageandcanbeeliminated.Choice(D)iscorrect.
27. A The passage states that the right of the citizens…to discuss…every important phase ofthiswar; its causes, themanner inwhich it should be conducted, and the terms uponwhichpeace shouldbemade. In this paragraph,LaFollette explicitlymentionsdeclaringwar,whichisreferencedin(C);howtoconductwar,(D);andhowtoendawar,(B).Thus,eachofthesecanbeeliminated.WhileLaFolletteprobablybelievesthatcitizensoughttoelectlegislatorsandexecutives,itisnevermentionedinthepassage.Thus,(A)iscorrect.
28. B The beginning of the sentence in question states that it is the right of the citizens…todiscuss…every importantphaseof thiswar.The list that followsservesasexamplesofthe importantphasesof awar inwhichcitizenoversightmightbenecessary.Choice (B)best matches this description and is the correct answer. LaFollette’s main point in thepassage is to argue against the restriction of free speech during war, so (A) can beeliminated.LaFollettedoesofferreasonswhythepressmightbeafraidtospeakout,butnotin the referenced paragraph; eliminate (C). LaFollette does not believe that citizensunderstandwars better than the president, only that the country needs the counsel of allcitizens,so(D)canbeeliminated.
29. D The answer to the previous question states that LaFollette believes that free speech isnecessary for theconductofwar.Choice (D) introduces this ideaexplicitly.The lines in(A) reference reasons that people are currently afraid to publicly discuss the issues inquestion,butdonotprovidereasonswhyspeechisnecessaryandcanbeeliminated.Thelinesin(B)explainwhysomeareattemptingtorestrictspeechandcanbeeliminated.Thelines in (C) give reasons why we should be concerned by the attempts to restrict freespeech,buttheyprovidenoexplicitmentionofwhyfreespeechisnecessaryduringtimesofwar;eliminate(C).Choice(D)isthecorrectanswer.
30. C The lastparagraphof thepassagestates thatnowisprecisely the timewhen thecountryneeds counsel of all its citizens. Therefore, LaFollette believes that attempts to stiflediscussionabout issuesofwar arehighlyundesirable andcontrary to themajorgoalsofAmericandemocracy.Only(C)expressesanattitudethatmatchesthisposition.LaFollettedoes not offer any sympathetic explanations for suppressing free speech, so (A) can beeliminated. LaFollette clearly cares about the suppression of free speech, so (B) can beeliminated. Choice (D),morose, is a negative attitude, but it is overly negative and toopassive for the toneof thepassage.LaFollette isdispleasedwith thesuppressionof freespeech,butheisnotsadordepressedaboutit.
31. C ThefirstsentenceofthelastparagraphstatesthatItisnoanswertosaythatwhenthewarisoverthecitizenmayoncemoreresumehisrights….Thus,LaFolletterejectseventheidea of a temporary restriction of free speech, a right that he calls precious andfundamental.LaFollettethinksthatfreespeechshouldneverbewithheldbutinsteadshouldbemaintainedwithout interruption or restriction.Choice (C)bestmatches thismeaningandisthecorrectanswer.
32. B Choice(B)isthecorrectanswer,assatellitephotosgaveevidenceofthefaultlinesattheedgesoftheEarth’splates.Choice(A)isincorrectbecauseit’stooextreme.Choice(C)isalso wrong because it says that the theory was created in 1965, whereas the passageindicates that there had been investigations of the theory before then. Choice (D) is toonarrow;theSanAndreasFaultisusedasanexample,butitalonedoesn’tprovethatplatetectonicsisavalidtheory.
33. C The author states in paragraph 3 that continental-drift theory described the continents asmobilechunksthatmovedthroughtheoceanfloor,whileplatetectonicshasthecontinentsmovingwiththesurroundingseabed.Therefore,(C)iscorrect.Choice(A)istooextremebecausethecontinentsdon’tfloworstayimmobileineithertheory,nordotheymovewithor without purpose in either theory, as (B) states. Choice (D) looks very similar to themetaphorgiven,buttheactualdistinctionistheideaofplowingthroughversusmoving inconjunctionwith.Thus,(D)isalsoincorrect.
34. D Theconvectioncurrentstransferordiffuseheatfromthemoltenrock,andthisleadstotheplatemovements.Thus,(D)iscorrect.Choices(A)and(B)areincorrectbecausethewordconvection doesn’t mean to liquefy ormelt. Choice (C) is incorrect because, while theplatesaremoving,convectiondoesn’tmeantomoveasinamilitaryendeavor.
35. A TheauthorintroducesYellowstone’shotspringsasanexampleofhowvolcanoescanexistmid-plate when hot spots push lava up through the plate, so (A) is the correct answer.Choice (B) is incorrect because it is too extreme—one example doesn’t prove anything.Choice (C) is incorrect because Yellowstone isn’t used in this passage to support anopposingtheory.Choice(D)isincorrectbecauseit’sreferringtoamid-oceanridge,whichoccursatthebordersofplates.
36. C ThepassagesaysthatTheseplumesofmoltenrock,oftencalledhotspots,riseanderuptthroughthecrustofamovingplate,whichsuggeststhehotspotsarepunchingupthroughacompletepieceofthecrusttocreatevolcanoes,asthere’snofractureforittoflowthrough.Thus,(C),Asthecrustalplatemoves,thehotspot“punches”upalineofvolcanicandhot-springactivity,iscorrect,andyoucaneliminate(A),(B),and(D).
37. A TheHawaiianIslandsareconsistentoronalinewiththemovementofthePacificplate,so(C)and (D),whichstate theopposite,are incorrect.The islandsarecreatedas theplatemoves, but then the plate moves on and the islands don’t change to suit it, so (B) isincorrect.Choice(A)istheanswer.
38. A Choice(A)iscorrectbecauseitmatchesthepassage,whichstatesthatIcelandwascreatedby lava flow that bubbled up from between two tectonic plates at a mid-ocean ridge.Choice(B)contrastsanislandandacontinent,whichthepassagedoesnot,while(C)statesthattheauthormentionsIcelandtoprovethatanislandcanbeavolcano.Theauthorneversaysthatanislandcan’tbeavolcano,so(C)isincorrect.Choice(D)istrue,butitdoesn’tanswer thequestion. Icelanddoes straddle themid-Atlantic ridge,but the reason that theauthormentionsIcelandistogiveanexampleofanislandthatwascreatedbylavaflowatahotspot.
39. D The passage says that the lava flows more abundantly in certain spots, producingvolcanicislands(lines70–72)andunderliethelarge,highlyvolcanicislandofIceland,whichstraddlestheMid-AtlanticRidge(lines74–76).Thus,(D)iscorrect.Choices(A),(B),and(C)donotcoordinatewithanyanswerchoicesinthepreviousquestions.
40. A The author uses the phrase Some geologists propose to show that plate tectonics are atheory,andtherearestillthingsaboutitthatscientistsdon’tknowandwanttolearn.Thus,(A)iscorrect.Thepassagenevermentionsalackofdata,so(B)canbeeliminated,while(C)impliesthatthephraseisintroducinganopposingviewpoint,whichitdoesnot.Choice(D)mentionsthecontinental-drifttheory,whichisnotpartofthelogicofthisparagraph,soitisincorrect.
41. B The passages states that plumes of molten rock, often called hot spots, rise and eruptthroughthecrustofamovingplate.Thediagramdepictsthisprocesswithalinetravelingupthroughthelithospheretothesurface.Therefore,(B)iscorrect.Whilethediagramdoesdepictacontinentalriftzonebytheocean,thereisnoevidenceinthegraphorthepassagethatthisisalwaysthecase.Therefore,(A)isincorrect.Thepassagestatesthatmid-oceanridges mark boundaries where plates are forced apart as new ocean floor is beingcreated between them; thus, (C) can be eliminated. There is no mention in either thepassageorthediagramoftherelativerigidityofoceanicandcontinentalcrust,so(D)canbeeliminatedaswell.
42. B Theauthor’smainpoint in the firstparagraph is that theconstructionof theGlenCanyonDam did affect downstream resources, including the loss of large beaches used forcamping and the addition of several animals to the endangered species list. Choice (B)matches the context of this passage, so keep it.Eliminate (A), as nomention ismadeofmaintainingwater resources.According to thepassage, the fishwereadapted to thepre-damera,so(C)doesn’tworkbecausedecimatedistooextreme.Choice(D)istheoppositeofwhatthefirstparagraphsuggests,soeliminateit.Choice(B)istheanswer.
43. A The correct answer to the previous questionwas that the damwasbuilt with a lack offoresight.This isshownbestwith(A),since it’smentionedthat littleconsiderationwasgiven to howdamoperationsmight affect downstream resources.Choices (B) and (D)both show consequences but don’t necessarilymatch the phrase little consideration, soeliminatethem.Choice(C)isn’tnegativeatall,sogetridofit.Thecorrectansweris(A).
44. A The passage states that the scientists and recreationists observed the physical
transformation of the river inGrandCanyon, so the correct answer shouldmatch thisinformation.Choice(A)isagoodfit,sokeepit.Eliminate(B),asnomentionismadeofcasual observation, as well as (C) because the passage never hints at collaborationbetween scientists and the public.Choice (D) is too extreme because the passage neverprovesanything.Choice(A)iscorrect.
45. C ThefirstparagraphofPassage1discussesthehumpbackchubandmentionsthatithasbeenlistedasendangered,aswellasthatthedamanditsoperationjeopardizedthecontinuedexistenceofhumpbackchub inGrandCanyon.Choice (A) is incorrect because it’s tooextreme. The chub is endangered, not extinct. Choice (B) refers to the fish later in thepassage insteadof thechub,soeliminate it.Choice (D) isnevermentioned,soeliminatethis choice as well. This leaves (C), which is correct; it can be inferred the chub cansurviveavarietyofenvironmentsbecauseit’sstillalive.
46. C Go to the first sentence of the second paragraph in Passage 1 and cross out the wordregime. Replace it with your own word using the context of the paragraph. A goodreplacementwouldbe“process,” so findaword in theanswerchoices thatmatches thismeaning. Choice (C) fits, so keep it for now. Choice (A) is a dictionary definition ofregime,soeliminateit.Choices(B)and(D)arenotrelatedto“process”inanyway,sogetridofthemaswell.Choice(C)isthereforecorrect.
47. B Go to the second sentenceof the secondparagraph inPassage2 and cross out thewordsuspended. Replace it with your own word using the context of the paragraph. Theparagraphmentions that sand is included at high concentration in the flow, so a goodreplacementwouldbe“combined.”Choice(B)isthebestmatchandthereforethecorrectanswer.
48. C UsePOEtofindananswerconsistentwiththepassage.Controlledfloodsarediscussedinthefinaltwoparagraphs,sothisshouldbethereferencewindow.Choices(A)and(D)areincorrectbecausesnowmeltismentionedonlyinthefirstpassage.Whilecontrolledfloodssometimesleadtothehigherconcentrationsofsuspendedsand,thisisnotalwaysthecase.Therefore,(B)canbeeliminated.Choice(C)worksbecausethefirstsentenceofthefinalparagraph states that the floodsmay erode sandbars if the concentration of suspendedsandduringacontrolledfloodistoolow.Therefore,(C)iscorrect.
49. D Thecorrectanswer to thepreviousquestiondealswith thenegativeeffectsofcontrolledfloodingonthehealthoftheriver,sotheanswertothisquestionshouldreflectthistheme.The lines referenced in (D) describe sandbar erosion,whichwould certainly qualify assomething“detrimental”; therefore, (D) is thecorrectanswer.The lines fromthepassagereferencedbytheotheranswerchoicesdonotillustrateanynegativeeffectsontheriver.
50. A The High Flow Experiments mentioned in Passage 2 refer to controlled floods used toincrease sandbars. Therefore, the author of Passage 1 would have a positive attitudetowards these floods because Sandbars, riverbanks, and their accompanying aquatichabitatswerereshaped,which isultimatelybeneficial to theecosystem.Choice (A) isagoodmatchforthisinformation.Eliminate(B),(C),and(D)becausetheyaretoonegative.
51. B Passage1 ismostly interested in thegeologichistoryof theGlenCanyonDam,whereasPassage2primarilydiscusses theuseof controlled floods.UsePOE to find the answer.Eliminate(A);eventhoughaproblemispresentedinPassage1,Passage2doesn’taddressthesameproblemorsolution.Choice(B)isagoodfit,sokeepitfornow.Choice(C)isprettyvague,andit’snotclearwhetherthechangesinPassage2arerecent,soeliminateit.NoexperimentisdiscussedinPassage1withanyspecifics,soeliminate(D).Choice(B)iscorrect.
52. D Use POE to find an answer that is applicable to both passages. Eliminate (A) and (B)becauseneitherpassagediscussesascientificexperimentortopographicchanges.Choice(C) is true of both passages, so eliminate it aswell. This leaves (D),which is correct:Passage2neverdiscussesanyspecificspecies,whereasPassage1mentionsthehumpbackchubandColoradopikeminnow.
Section2:WritingandLanguage
AndJusticeforAll1. A If you can’t cite a reason to use a comma, don’t use one. In this case, commas are not
necessary because the fact that sheworks at themall is important as a contrast tomoreserious.Therefore,theansweris(A).
2. C The idea before the punctuation (She would start applying to law schools soon) iscomplete.The idea after the commaand conjunction (shewanted to knowwhat the lawlooked like inaction) is also complete.Remember theSTOPpunctuation rules.Choices(A) and (D) canbe eliminatedbecause twocomplete ideas cannot be joinedwith just aconjunctionorjustacomma;bothareneeded.Thecommain(B)isinthewrongplace,sotheansweris(C).
3. B Notice the question! It askswhich statement ismost in keepingwith themain idea. ThepassagecentersontheDepartmentofCorrections,andtheonlychoicethatintroducesthisinformation is (B). The next sentence doesn’t even make sense without the specificinformationin(B).
4. A Noticethequestion!Itasksforastatementthatreinforcesideasinthissentenceaswellastheprecedingsentence.Theideasinthesesentencesareaboutnoonepayingmuchattentionto theDepartmentofCorrections.Choice (B) contradicts this idea.Choices (C) and (D)containthewrongfocus.Therefore,(A)istheanswer.
5. D The subject of this sentence ismeaning, which is singular. Eliminate the choices withpluralverbs—(A),(B),and(C)—becausetheyareinconsistent.Thecorrectansweris(D).
6. D The underlined pronoun refers to Everyone, which is singular. Choice (D) is the onlypossibleanswerbecauseitisconsistentinnumber.
7. D Thesentenceshouldcomeafteranotherquestionaboutthetreatmentofinmatesinorderto
makesenseof thephrasebythesametoken.Thisquestionappears insentence6,so thissentenceshouldgoaftersentence6,as(D)suggests.
8. D Choices (A), (B), (C), and (D) all sayessentially the same thing,but (D)does so in themostconcisewaypossible.Therefore,(D)iscorrect.
9. B Thesubjectofthisverbispoliticsandthelaw,whichisplural, thuseliminating(A)and(C).Choice(B)isthecorrectanswerbecauseitismoreconcisethan(D).
10. A Theideabeforetheconjunction(Wemaybelievethatwenevercomeintocontactwiththelaw) is complete, and the idea after the conjunction (it is written into everything…ourselves) is also complete.Whena conjunctive adverb connects twocomplete ideas inonesentence, it isprecededbyasemicolonandfollowedbyacomma.Therefore,(A) iscorrect.
11. C ThisessayfocusesonAmanda’spersonaldiscoveriesaboutthelaw;itdoesnotthejusticesystem.Eliminate(A)and(B).Choice(D)isincorrectbecausethepassagedoesn’tdiscussherentirecareer,justthesummerbeforesheappliedtolawschools.Choice(C)iscorrect.
Alexander’sEmpireofCulture12. B The correct idiom is disappear from. The sentence as written implies two things have
disappearedwhen it shouldbe just thestudyof theclassics.Eliminate (A).Choices (C)and(D)arenotthecorrectformoftheidiom.Choice(B)isthecorrectanswer.
13. A Thissentenceiscorrectaswritten.Althoughthephraseforallthatmightsoundforeign,itis being used correctly here.Choice (B) does notmake sense.Choices (C) and (D) arebasically thesameas(A),andremember, if there isnogrammaticalreasontochangetheoriginal,don’t.Therefore,(A)iscorrect.
14. B The correct idiomuses thewords in and right, so (A), (C), and (D) can be eliminated.Choice(B)iscorrect.
15. B The correct answer will feature words or phrases that are as precise as possible. Thesentence aswrittendoesnotmake clear towhom thepronoun is referring:AlexanderorAristotle. Choice (B) clears up this pronoun ambiguity. Choice (C) can be eliminatedbecause Alexander was born in Pella, and his arrival as a newborn would not haveannouncedanenlightenedera,norisitlikelytheyarrivedtogether.
16. D Noticethequestion!Itasksforaconcludingstatementthatemphasizesthechangebroughtabout by Alexander’s rule. Choices (A), (B), and (C) do not address the change frommilitaristicPhiliptoenlightenedAlexander.Only(D)hasthecorrectemphasis.
17. C Noticethequestion!Itasksforanintroductoryphrasethatemphasizescontinuityfromthepreviousrule.Theonlychoicethatreferstothepreviousruleandexplainshowthesecondsentenceconnectstothefirstintheparagraphis(C).
18. A Checktheanswerchoicesagainstthemap,andmakesurethattheinformationisconsistentwith the figure.Choices (B)and (D)contain information thatcannotbegleaned from themap,while(C)containsinformationthatcontradictsthemap.Choice(A)isconsistentwiththemap,soitisthecorrectanswer.
19. B As written, the first part of the sentence creates a comma splice, wherein a commaseparatestwocompleteideas.Choice(A)canbeeliminated.Choice(B)isthebestoftheremaininganswerchoicesbecauseitisthemostconcise.Aconjunctionsuchasalthoughormoreover is not needed due to the however in the preceding sentence. This sentence’spurposeistoexplaintheprecedingsentence.
20. C Unprecedentedmeans“neverdoneorknownbefore.”Choices(A),(B),and(D)havethesame definition, so they can be eliminated—the question asks for what would NOT beacceptable. Choice (C) means “lacking historical context” and is not an acceptablealternative.
21. D Theideabeforetheperiod(Alexandria,Egypt,perhapsthemost…continuestothrive)isacompleteidea.Theideaaftertheperiod(Itisthesecond…ofEgypt)isalsoacompleteidea.Therefore, the two cannot be joined togetherwith only a comma. (Remember yourSTOPpunctuationrules.)Eliminate(B).Oftheremaininganswerchoices,(D)isthemosteffectiveway to combine the two sentences because it eliminates the need to repeat thesubject,whichmakesthesentenceflowbetter.Therefore,(D)iscorrect.
22. A The sentence as written is consistent in structure with between man and god and theindividualandtheworld,bothofwhichuse theconjunctionand.As the last itemin thislist,andshouldbeusedbetweenthenaturalandtheunnatural.Allotherchoicesarenotconsistentandchangethemeaning.Therefore,(A)istheanswer.
Brother,CanYouSpareaDime?23. C Thecorrectanswerwillcontainphrasesthatareaspreciseaspossible.Itisthedimenovel
thatwasprintedcheaplyandforquickconsumption,sothewordsdimenovelneedtobeplacedimmediatelynexttothemodifierphrase.Choices(A),(B),and(D)allincludethismisplacedmodifier.Only(C)makesthesentenceprecise.
24. D Noticethequestion!Itasksforthephrasethatgivesthemostspecificinformation.Choice(D)providesspecificnamesofauthorswhowrotebywayofliteraryperiodicals.Choices(A),(B),and(C)refertotheauthorsonlyinvagueterms.
25. D ThetitleofStowe’sbookisnecessaryinformation,whichmeansitshouldnotbesuroundedbycommas, soeliminate (B).Choices (A)and (C)haveotherunnecessarycommas.Thecorrectansweris(D)becauseitcontainsnocommasatall.
26. A Thecorrectanswerwillsupportthepassagewhilebeingaspreciseaspossible.Thenextsentence beginswith the subjectThatbook, andwithout the phrase the publishers wereclamoringforanactualbook,thereaderwouldn’tknowwhatthatbookis.Thisreasoning
is summedup in (A).Choice (B) is incorrect because there is no support for publishersbeinggreedy.Choice(C)isincorrectbecausethepassagesaysStowe’sworkwasalreadypopularasaperiodicalseries.
27. C Theaverageannualincomeofamaninthisperiodisnotinlinewiththemainideaoftheparagraph, which discusses the shift from periodicals to novels. To add this statementwouldbeinconsistentwiththeparagraph’sfocus,whichisstatedin(C).
28. A Choices(B)and(D)usethewrongverbtense.Choice(C)isnotinlinewiththefocusoftheparagraph.Additionally,sinceyoudonotknowiftheseriesisstillknownthisway,(A)isthecorrectanswer.
29. B Effectisgenerallyanoun,whileaffect isaverbexceptincertainunusualcircumstances.Theunderlinedportionneedstobeanoun,soaffectsisincorrect.Eliminate(A)and(D).Thesentencediscussesmultipleeffects,notsomethingbelongingtotheeffects,sothepluralformoftheverbisneeded,notthepossessiveform.Eliminate(C).Thisleaves(B),whichisthecorrectanswer.
30. B The correct answer will feature words or phrases that make the passage as precise aspossible.Withouttheactualnames,thephraseWilliamBonneyandJamesButlerHickcockbecame the folk heroes does not make sense. You need the names of transformed folkheroes in order to make sense of the sentence. Eliminate (C) and (D). Choice (A) isincorrectbecausetherestofsentencedoesnotspeakingeneralities;itprovidestwonamesalready.Choice(B)iscorrect.
31. C Thecorrectidiomislearnedfrom,nottaughtfrom,soeliminate(A).Thenewmediahasnotbroughtanythingfromthedimenovel’spopularitybecauseitissomethingentirelynew,soeliminate(D).Learnedismoreprecisethangot,sothecorrectansweris(C).
32. C As written, the sentence is unclear for whom or what the foundation is being laid, soeliminate (A). The underlined portion needs to follow the word foundation in order toclarifythis.Thecorrectanswerwillmakethepassageaspreciseaspossible.Thisis(C).
33. B Aframeofreferenceisasetofcriteriaorstatedvaluesinrelationtowhichmeasurementsor judgments can bemade. Integration, (B), is the intermixing of people or groups thatwerepreviouslysegregated.Sincethisdoesnotserveasanacceptablealternativetoframeofreference,itisthecorrectanswer.
TheTigerMoth’sPhantomTarget34. C Besure tocomparesimilar things tomaintainconsistencyandprecision.Thesentenceas
written compares methods to humans. Compare methods to methods, or change theconstructionof thesentence.Eliminate (A)and(D)becausebothmake thesamemistake.Choice (B)uses thesingularpronoun that to refer to thepluralmethods, so eliminate it.Choice(C)usesthecorrectcomparisonandthepluralpronoun,soitiscorrect.
35. A Allfourchoicesusesimilarwords.Choosetheonethatexpressestheideamostclearly.In
this case, the clearest choice is (A). Choice (B) is passive and contains unnecessarycommas.Choice (C)contains theawkwardphrasemainamongwhich is its.Choice (D)usescuriousasanadjectiveinsteadofanoun,implyingthattheweaponryiscuriousaboutsomethinginsteadofbeingacuriosityitself.
36. D This sentence does not refer to the bats (bats cannot shout). Eliminate (A) and (B). Thesentenceusesthewordyou later,sothisunderlinedportionshouldbeconsistentwiththerestofthesentence.Eliminate(C).Choice(D)correctlyreplacestheywithyou.
37. D Allfourchoicesusesimilarwords.Choosetheonethatexpressestheideamostclearlyandconcisely.Inthiscase, theansweris(D).Instinctsdoesnotneedtoberepeatedbecausethewordinnatewasalreadyused.
38. B Notice the question! The question asks for a phrase that emphasizes a commonmisunderstandingaboutbats’vision.Choice(A)comparesbats’visiontoshrimp,whichisnotacommonmisunderstanding.Choices(C)and(D)describeaspectsofbats’huntingbutdonotemphasizeacommonmisunderstanding.Only(B)discussesthecommonthought(orcliché)aboutbatsbeingblind.
39. C Thepronounitsisambiguous,asitisunclearwhetheritreferstothetigermothorthebat.Thecorrect choice featureswords that are asprecise aspossible, so eliminate (A).Theother choices clear up the ambiguity, but only (C) has the correct possessive singularpronoun needed. Choice (B) uses a plural pronoun, but since only a single system ofecholocationisreferredto,thesingularbat’sisappropriate.
40. B Thewordsinedibleandtoxicspecificallyexplainwhythewarningwouldresultinthebatsnotgoingafterthemoths.Thisisbestsummarizedin(B).Choice(A)isincorrectbecauseyoudonotknowaboutanypredators, justbats.Choice(C) is incorrectbecause inedibleand toxic donot give any information about themechanismof the clicks.Choice (D) isincorrectbecausetheinformationisnotstatedelsewhere.Theansweris(B).
41. C The pronoun refers to the tiger moth, which is the name of a species and therefore acollectivenoun.Collectivenounsaresingular,soeliminate(A)becauseitisinconsistent.When dealing with pronouns, remember that possessives do not use apostrophes, whilecontractions do use apostrophes. Choice (B) contains a contraction. It would not makesense tosay the tigermothand it is sonar jamming, soeliminate (B).There isno suchword as its’, so eliminate (D). The sonar jamming belongs to the tiger moth, so apossessivepronounisneeded,asin(C).
42. A Allofthecommasarecorrectaswritten.Thereshouldbeacommaaftereachiteminalist.Acommaisneededaftercounterattack,butnotafterandoradapt.Choices (B)and(D)containunnecessarycommas,while(C)doesnotcontainany;therefore,(A)istheanswer.
43. A Checktheanswerchoicesagainst thefigures.Only(A)canbesupportedby thediagram.Thereisnoindicationofotheranimals,asin(B);whatsoundsareorarenotheard,asin(D);orbatsrunningintoeachother,asin(C).
44. D Paragraph 5 does not fit as a conclusion, so eliminate (A).This paragraph should comeafterthediscussionofthetigermothanditstacticsandbeforetheconclusionoftheessay.Thisindicatesthebestplacementisafterthethirdparagraph,so(D)istheanswer.
Section3:Math(NoCalculator)1. A Thevertexformofaparabolaisy=a(x−h)2+k,where(h,k)denotesthevertex.Plugin
thepoint(3,−3)intothevertexformtogety=a(x−3)2−3.Thecorrectansweris(A).
2. C YoucanPlugIntomakesenseofthisequation.Saythatx=$100.Theamountofthekegwouldthenbe$107+$17.The$17mustbetheuntaxeddepositsinceitisaflatfeeratherthan percentage based. Therefore, the tax is $7, which is 7% of the original $100 baseprice.Theansweris(C).
3. D Whenevertherearevariablesinthequestion,PlugIn.Besuretopluginanumberthatis
divisibleby3.Letd=300. oftheoriginalamountof$300is$100,andthatisdeducted
bythecompany,leavingSyedwith$200.Then,subtractthewiretransferfeetoget$200−
$30= $170,which is the target number. Plug in 300 ford in the answer choices to see
whichoneisequaltothetargetnumberof170.In(A), (300)−30=70.Thisisnotthe
targetnumber,soeliminate(A).Likewisein(B), (300−30)=90,andin(C), (300−
30)=180.Neitheroftheseisthetargetnumber,soeliminate(B)and(C).In(D), (300)−
30=170,whichisthetargetnumber.Thecorrectansweris(D).
4. C Allof theanswersarewritten in the slope-intercept formy=mx+b,whereb is the y-
interceptandxandyarepointson the line.Eliminate (D)because they-intercept in that
equationis2.Fortheremaininganswerchoices,pluginthex-andy-values todetermine
whichequationworks.Ifx=1andy=6,(A)becomes6= (1)+4.Solvebothsidesof
theequationtoget6=4 .Eliminate(A).Choice(B)becomes6=1+4,soeliminate(B).
Choice(C)becomes6=2(1)+4,or6=6.Therefore,thecorrectansweris(C).
5. C Whenevertherearevariablesinthequestionandtheanswerchoices,thinkPluggingIn.If2
purchasesweremade,thenp=2,andthenumberofbonuspointscanbecalculatedas4(2)
+7=8+7=15.Ifthenumberofpurchaseswerethenincreasedby3,thenewpequals5
and the number of bonus points can be calculated as 4(5) + 7 = 27. The bonus points
increasedby27−15=12.Thecorrectansweris(C).
6. B ThisisagoodPlugIntheAnswersproblem.Startwith(B)andplugin2forxand3forrin
theequationtogetV=24π+2 ,whichisequaltothetargetamountof96π,so(B)is
correct.
7. C Whenevertherearevariablesinthequestionandintheanswers,thinkPluggingIn.Letc=
30.Therefore,b=2+ (30)=2+10=12.Plug12inforbintheanswerstoseewhich
answerequalsthetargetnumberof30.Choice(A)becomes Eliminate
(A), since it does not equal the target number. Choice (B) becomes .
Eliminate(B).Choice(C)becomes3(12−2)=3(10)=30.Keep(C),butcheck(D)justin
caseitalsoworks.Choice(D)becomes3(12−6)=3(6)=18.Eliminate(D).Thecorrect
answeris(C).
8. D Treat this question as a translation problem. According to the question, R(h) = fourrotationspersecondlessthanthreetimesthesquareoftheheightoftheliquid.Theheightoftheliquidisrepresentedbyh.Therefore,threetimesthesquareoftheheightoftheliquid=3h2.Fourlessthanthisamountis3h2−4.Sincetheoriginalspeedwas1,000,subtractthisvaluefrom1,000togetthecurrentrateofrotation.Thecorrectansweris(D).
9. B StartwiththeeasierequationanduseProcessofElimination.Theeasierequationisrelatedtothetotalnumberofounces,c+b,inthetube.Accordingtothequestion,thetubehas24ounces, soc +b = 24. Eliminate (A), since it does not include this equation. The otherequationinthesetisrelatedtotheamountofactiveingredients.Accordingtothequestion,cincludes0.25%ofsodiumfluorideandbcontains0.30%triclosan.0.25%=0.0025and0.30%=0.003.Therefore,inthecorrectequation,cshouldbeassociatedwith0.0025andbshouldbeassociatedwith0.003.Eliminate(C)and(D)becausebothoftheseequationsgetthepercentageswrong.Thecorrectansweris(B).
10. C Whenever the question includes variables and the answer choices are numbers, think
Plugging In the Answers. In (A), d = −4, and the equation becomes
. Solve both sides of the equation to get
,or .Reducebothfractionstoget−13=−5.Thisis
not true, so eliminate (A). In (B), d = 2, and the equation becomes
. Solve both sides of the equation to get
,or .Reducebothfractions toget .Eliminate
(B). In (C), d = 4 and the equation becomes . Solve both
sidesoftheequationtoget ,or .Reducebothfractions
toget = .Thecorrectansweris(C).
11. D Alltheanswerchoicesareequalto4(whichisr2,makingr=2),soyouneedtofocusonwhere the center of the circle lies. If the circle is tangent to both the x-axis (which isequivalenttotheliney=0)andthelinex=4,thenthecentermustbe2unitsfromy=0and2unitsfromx=4.Choices(A)and(B)bothhavecenterswithanxvalueof−2(rememberthestandardformofthecircleequationis(x−h)2+(y−k)2=r2,where(h,k)isthecenterandristheradius),whichis6unitsfromx=4.Eliminate(A)and(B).Choice(C)hasacenterat(2,−4).Thex-valueis2unitsfromx=4;however,they-valueis4unitsfromy=0.Eliminate(C)andchoose(D).
12. B According to the question, Reactant A does not react unless B gets to a certainconcentration.Therefore, thecorrectanswerwillhavean initial flat line forAwhile theline forB is rising.Onlygraph(B)shows this initial relationship.Therefore, thecorrectansweris(B).
13. A Alloftheanswerchoiceshavethesamelinesgraphed,sothisquestionisreallyabouttheshading.PluggingInisprobablytheeasiestwaytoapproachthisproblem.Startwith(0,0)becausethisisaneasyvaluetocheck.Thisworksinallthreeequationssince0≤8,−3≤0,and1≥0.Therefore, thisvalueneeds tobeshadedasapossibleanswer.Eliminate(B),(C),and(D)becausetheydonotincludethispoint.Thecorrectansweris(A).
14. B Thequestionsaysthattan BCAis ,sodrawsegmentCA.Sincetan= .Let
AB=3xandBC=4x.Thequestionsaysthattheareaoftherectangleis48.Theformulafor
theareaoftherectangleisA=lw.PluginA=48,l=3x,andw=4xintotheformulatoget
48=(3x)(4x).Simplifytherightsidetoget48=12x2.Dividebothsidesby12toget4=
x2.Thentakethesquarerootofbothsidestogetx=2.Therefore,AB=3x=3(2)=6,and
BC=4x=4(2)=8.Thequestionasksfor thelengthofBD,whichis thediagonalof the
rectangle andequal todiagonalAC.Thediagonalof the rectangle is thehypotenuseof a
righttriangle.Sincethetwolegsare6and8,thisis6-8-10righttriangle,sothehypotenuse
is10.Theansweris(B).
15. D Whenevertherearevariablesinthequestionandanswers,thinkPluggingIn.Ifm=2,the
expression becomes
Plug 2
informintheanswerchoicestoseewhichoneequalsthetargetnumberof−4.Choice(A)
becomes This does not match the
targetnumber,soeliminate(A).Choice(B)becomes .Eliminate
(B).Choice(C)becomes .Eliminate(C).Choice(D)becomesm−6=2
−6=−4.Thecorrectansweris(D).
16. 1.5or
Plug the given values into the equation: 18 = (3)(4)(x). Multiply the right side of the
equationtofindthat18=12x.Dividebothsidesby12tofindthatx= .Both18and12
aredivisibleby6,sothisfractionreducesto .
17. 53 Jeannecharges5.50×2=$11perhourforbabysitting.Therefore,herentireearningsforthreehourscanbecalculatedas(3×11)+20=53.Thecorrectansweris53.
18. 10 To solve the problemwithout a graphing calculator, set the two equations equal to each
other:−x2+5x+6=− x+12.Multiplytheentireequationby2toget−2x2+10x+12=
−x+24.Rewritetheequationtoequal0,soitbecomes−2x2+11x−12=0.Multiplythe
entireequationby−1toget2x2−11x+12=0.Thenfactorthequadratictoget(2x−3)(x−
4)=0.Solveforthetwopossiblevaluesofx:If2x−3=0,thenx= ,andifx−4=0,
thenx=4.Becausetheslopeofthelineisnegative,thex-valueofthepointthatisfarthest
totherightalongthex-axismustalsobeclosertothex-axis.Plug4inforxinthesecond
equationtogety=− (4)+12=−2+12=10.Thecorrectansweris10.
19. or3.66or3.67
Whenevertherearetwoequationswiththesametwovariables,theequationscanbesolved
simultaneouslybyaddingorsubtracting them.Take thesecondequationandrewrite it so
thatthevariablesareontheleftsideoftheequation:17r+22v=63.Stacktheequations
andaddthemtogether.
Dividetheentireequationby30togetr+v= .Thisistoobigtogridin,soreduceitto
.
20. 2 Theareaofthecurrentplotis4×6=24squarefeet,sothenewplotwillbe24×2=48squarefeet.Accordingtothequestion,xfeetwillbeaddedtoeachsidetoobtainthenewareaof48feet.Sincethelengthisonly2feetmorethanthewidth,youneedtwofactorsof48thatdifferby2.Youmayrecognizethatthesefactorsare6and8.So,theincreasewas2feetineachdirection.Alternatively,youcanwriteaquadratic:(4+x)(6+x)=48.Expandtherightsideoftheequationtogetx2+10x+24=48.Settheequationto0bysubtracting48frombothsidestogetx2+10x−24=0.Factortheequationtoget(x+12)(x−2)=0.Therefore,x=−12orx=2.Sincelengthscanneverbenegativetheonlypossiblevalueisx=2.Thecorrectansweris2.
Section4:Math(Calculator)1. C UseProcessofElimination.Accordingtothequestion,Prepresentsthepopulation,sothe
outcome of the entire equation has something to do with the population. Therefore,eliminateboth(A)and(B)because1.0635can’trepresentthepopulationifPdoes.Inthegivenequation,theonlyoperationsaremultiplicationandaddition,whichmeansthatovertimethepopulationwouldincrease.Therefore,eliminate(D).Thecorrectansweris(C).
2. B Tosolvethequadraticequation,firstsettheequationequalto0.Theequationbecomesx2+12x − 64 = 0. Next, factor the equation to get (x + 16)(x − 4) = 0. Therefore, the twopossiblesolutionsforthequadraticequationarex+16=0andx−4=0,sox=−16or4.Since the question states thatx>0,x = 4 is the only possible solution.Anotherway toapproach this question is to Plug In theAnswers. Startwith (B), x = 4. Plug 4 into the
equationtoget42+12(4)=64.Solvetheleftsideoftheequationtoget16+48=64,or64=64.Sincethisisatruestatement,thecorrectansweris(B).
3. A TofigureoutthetotalnumberofshelvingunitsSaicoulduse,findthetotalavailablewall
spaceanddividebythelengthoftheunits.Thetotalamountofwallspacecanbecalculated
as119–21.Because the lengthof eachunit is 7 feet, themaximumnumberofunitsSai
couldputupcanbecalculatedas .Becausethisisthemaximumnumberofunits
Saicouldputup,rhastobelessthanorequaltothisnumber.Therefore,thecorrectanswer
is(A).
4. C Weight is shownon theverticalaxisof thegraph,given inounces.Makeyourownmarkindicating5.75onthisaxis;thendrawahorizontallinefromthatmarktothelineofbestfit.Once you hit it, draw a vertical line straight down to the horizontal axis. It should hitbetween 75 and 80 days, slightly closer to themark for 75. Thismakes (C) the correctanswer.Drawyourlinescarefully,usingyouranswersheetasastraightedgeifnecessary.
5. C Wheneverthequestionincludesvariables,PlugIn.Ifs=2,theshirtscost2($24.50)=$49.Thetaxontheshirtsis0.07($49)=$3.43.So,theshirtswithtaxandthe$6shippingfeecost$49+$3.43+$6=$58.43.Plugin2forsintheanswerstoseewhichanswerequalsthe target number of $58.43. In (A), 0.07[24.50(2) + 6] = 3.85. This is not the targetnumber,soeliminate(A).In(B),1.07(24.50+6)(2)=65.25.Again,thisisnotthetargetnumber,soeliminate(B).In(C),1.07[24.50(2)]+6=58.43.Thisisthetargetnumber,sokeep it,butbesure tocheck theremaininganswerchoice. In(D),1.07(24.50+2)+6=34.355,whichisnotthetargetnumber.Therefore,thecorrectansweris(C).
6. B Thequestionstatesthatafter6weekstheplantis54centimeterstall.Therefore,whenw=6,h(w)=54.Plugin6forw in theanswerchoices toseeinwhichoneequals the targetnumber of 54. In (A), h(w) = 6(6) = 36. Eliminate (A). In (B), h(w) = 9(6) = 54. Thecorrectansweris(B).
7. D Becausetheoperationbetweentheparenthesesisaddition,theparenthesescanberemoved,andtheresultingexpressionbecomes12x2+4x+5y+3x2−2x+3y.Reorderthetermssothatliketermsarenexttoeachother:12x2+3x2+4x−2x+5y+3y.Combineliketermstoget15x2+2x+8y.Thecorrectansweris(D).
8. D Youdonotknowhowthesurveyisconducted,nordoyouknowhowmanyveterinariansweresurveyed(itmaybethecasethatonly8weresurveyed).Therefore,youcannotinferthat the survey accurately measures all veterinarians’ beliefs about Royal Rat Rations.Choice(A)isnotsupported.First,youdonotknowwhatveterinariansbelieveingeneral,andsecond,veterinariansmayberecommendingRoyalRatRationsforareasonotherthanits nutrition. Choice (B) is similarly not supported: Besides not knowing veterinarians’
beliefs, this choice assumes that no other rat food is acceptable. Choice (C) is notsupported because you do not know the sample size of the survey, nor is there anyindicationthatthereisonlyoneveterinarianwhodoesnotrecommendRoyalRatRations.Choice(D)isthecorrectanswer:YouknowtheopinionsonlyoftheveterinarianssurveyedbyRoyalRatRations.
9. D Useacalculatortotranslatethefractionsintodecimals. t+4= t−5becomes0.5t+4=
0.75t−5.Subtract0.5tfrombothsidestoget4=0.25t−5,andthenadd5tobothsides.
Thisresultsin9=0.25t.Useacalculatortodivide!t=36;therefore,thecorrectansweris
(D).
10. C Takingthetwodogstogether,Everetthas35+55=90poundsofdog.Setupthefollowing
proportion to determine the lowest amount of water the dogs need per day:
.Cross-multiplytoget10x=765,sox=76.5.Multiplyby7daystoget
theweeklyamountofwaterthedogsneed:76.5×7=535.5ounces,orapproximately536
ounces.Only(C)includes536asthelow-endamount.Therefore,thecorrectansweris(C).
11. A In order to answer this question, you need to deal with the ratio as well as the unit
conversion.For the largebatchofdryrub,Priya’sfriend isplanning touse91ouncesof
chilipowder.Sincethepaprikaandthechilipowdermustbeusedinaratioof4to7,you
cansetupaproportiontodeterminehowmuchpaprikaisneeded: .Cross-multiply
andsolveforxtodeterminethatx (i.e.,paprika)=52ounces.Soyouhave52ouncesof
paprika and 91 ounces of chili powder for a total of 143 ounces.Multiply that by your
conversion number, 28.3, to determine that this is equivalent to 4,046.9 grams,which is
closestto(A).
12. D Whenevertherearevariablesintheproblemandintheanswerchoices,PlugIn.Ifw=20,
then Luciano’s cup has 20 − 2 = 18 ounces at the end of day 1. At the end of 7 days,
Luciano’scupwouldhave18−8=10ounces.After11days,Luciano’scupwouldhold10
−5=5ounces.Plugin20forwintheanswerchoicestoseewhichanswerisequaltothe
target number of 5. Choice (A) becomes . This does not match the
targetnumberof5,soeliminate(A).Choice(B)becomes =9−10
= −1. Eliminate (B). Choice (C) becomes ( )(20) − 10 = 10 − 10 = 0. Eliminate (C).
Choice (D) becomes . This matches the target number; therefore, the
correctansweris(D).
13. B Accordingtothelineofbestfit,in1995therewere20coyotesinthepark.In2000,there
were140coyotesinthepark.Thisisanincreaseof120coyotesoveraperiodof5years,
so =anaverageincreaseof24coyotesperyear,whichis(B).
14. D The median number of coyotes in the park in 1995 was 20, and the median number of
coyotesintheparkin1996was60.(BecarefultoRTFQ;thequestionwantsthemedian,
notthelineofbestfit!)Inordertocalculatethepercentincrease,itisnecessarytousethe
percent change formula: . The calculation here will be
=2×100=200%,whichis(D).
15. A StartwiththeeasierequationanduseProcessofElimination.Theeasierequationisrelated
tothetotalnumberofshirtsandpants,s+p,soldonaregularday.Thequestionstatesthat
onaregulardayBailey’ssells thenumberofpantsandshirtssoldduringasale. (60)
=40.Therefore,oneoftheequationsinthecorrectanswerwillbes+p=40.Eliminate
(C)and(D)sinceneitherincludesthisequation.Theotherequationisrelatedtothemoney
Bailey’searnsonaregularday.Accordingtothequestion,Bailey’searnsatotalof$1,875
onaregularday,sotheequationmustequal$1,875.Eliminate(B)becausethetotalinthe
moneyequationisincorrect.Thecorrectansweris(A).
16. C Thereareafewdifferentwaystoapproachthisquestion.Inanyapproach,thebestfirststep
is to figure out howmuch incomeBryan earned during the two-week periodwithout the
commission.Sinceheworkedanaverageof35hoursperweekfortwoweeks,heworkeda
totalof70hours.Atarateof$10.00perhourbasepay,thiswouldaddupto$700.00(70×
10=700).SinceBryan’searningswereactually$850.00,thatmeanshemusthaveearned
$150.00 of commission (850 − 700 = 150).At this point, you can calculate the percent
commission algebraically or simply work backwards from the answer choices.
Algebraically,youknowthat$150.00 isequal toacertainpercentof$5,000.00 insales,
whichcanberepresentedasfollows:150= (5,000).Solveforx,andyouget3,which
is(C).Ifinsteadyouwishtoworkbackwardsfromtheanswerchoices,youcantakeeach
choiceandcalculatewhat1%,2%,etc.of$5,000.00wouldbe,andthenaddthatbackto
$700.00toseewhichchoicematchesyourtargetof$850.00:(C).
17. C Cross-multiplytoget3(C+x)=(x−3)(x+8).Expandtherightsideoftheequationtoget
3(C+x)=x2+5x−24.Distributethe3toget3C+3x=x2+5x−24.Subtract3x from
bothsidesoftheequationtoget3C=x2+2x−24.Factortherightsideoftheequationto
get3C=(x+6)(x−4).Dividebothsidesby3togetC= = (x+6)(x
−4).Thecorrectansweris(C).Alternatively,youcanpluginforxtogetatargetvaluefor
C,andthenuseProcessofElimination.
18. A Startwiththeeasiestpieceofinformationfirst,anduseProcessofElimination.Sinceh isthenumberofhoursspenthikinganddisthenumberofhoursdriving,thetotalnumberofhoursLennonspendsintheparkcanbecalculatedash+d.ThequestionstatesthatLennonhasupto6hourstospendinthepark—“upto”means≤.So,h+d≤6.Eliminate(B),(C),and(D).Thecorrectansweris(A).
19. B Thequalitycontrolexpertdiscovered that13outof1,000randomlyselected tennisballs
weredefective. =0.013,whichisequivalentto1.3%.Thismeansthat100−1.3=
98.7%oftennisballstestedwerenotdefective,andthisdatamostsupports(B),whichis
thecorrectanswer.
20. C Whensolvinginequalities,thenaturalimpulseistoisolatethevariable.Inthiscase,though,
lookatwhatthequestionisasking.Thequestiondoesn’twantyoutofindjustthevalueofz,
butratherthevalueof9z−18.Togetfromthevalueof−3z+6givenintheinequalityto
this newvalue, the original inequalitymust bemultiplied by−3. Justmultiply the entire
inequality by this value, making sure to flip the inequality signs when multiplying by a
negative number. The equation becomes
. The
questionasksforthegreatestpossibleintegervalue,sofocusonthehighendofthegiven
values.Thevalueatthatend, ,equals8.57,sothegreatestintegerlessthanthatis8.The
answeris(C).
21. A Whenever there are variables in the question and numbers in the answer choices, think
Plugging In theAnswers. In (A), j = 6, and k = −6. Plug these two values into the first
equationtoget−24−8(6)=12(−6).Solveforbothsidesoftheequationtoget−24−48=
−72,or−72=−72.Therefore,thevaluesworkforthefirstequation.Plugthevaluesinto
thesecondequationtoget .Solvebothsidesoftheequationtoget3+
(−10)=−7,or−7=−7.Sincethevaluesgivenin(A)workinbothequations,thecorrect
answeris(A).
22. C Youknowthenewproportionmustbelessthanthecurrent0.34forbiofuels(becausethe
totalamountspentonalternativeenergyis increasing,but theamountspentonbiofuels is
remaining the same), so you can eliminate (D). Next, determine the amount that will be
spentonbiofuels in2017bymultiplying0.34by the totalof$254million:0.34×254=
$86.36million.Because 57million newdollarswill be spent on alternative energy, the
newtotalwillbe254+57=$311million.Divide$86.36millionby$311milliontoget
thenewproportion: =0.28,whichis(C).
23. D InQuadrant II, the x-coordinate is negative, and the y-coordinate is positive. Therefore,eliminate (C). Whenever the question includes variables and the answer choices arenumbers, thinkPluggingIn theAnswers.Of theremainingchoices, (B) iseasiest toworkwith. In (B), the x-value is −4 and the y-value is 2. Plug these values into the second
equationtoget−4=−2+2.Sincethisisnotatruestatement,eliminate(B).Trythevaluesin (A) in the second equation to get .This is also not true, so thecorrectansweris(D).
24. B Rightaway, (A)canbeeliminated,sincepointChasanegativey-coordinate.Given any
two points, the slope of the line can be determined using the equation .Use this
formulatofindthevalueofbbysettingtheslopeofABequaltotheslopeofBC.Usepoints
(0,3)and(5b,b)intheleftsideoftheequationandpoints(5b,b)and(10b,−b)intheright
sideof the equation to get . Simplifyboth sides of the equation to get
,or .Cross-multiplytoget5(3−b)=10b.Dividebothsidesby5
get3−b=2b,then3=3b,andfinallyb=1.Pluginb=1forpointCtoget[10(1),−(1)],
or(10,−1).Therefore,thecorrectansweris(B).
25. A TheformulaforcompoundinterestisA=P(1+r)t,wherePisthestartingprinciple,r is
therateexpressedasadecimal,and t is thenumberof times the interest iscompounded.
Melaniereceivedlessthan5%interest,soyoucaneliminate(B)because1.05=1+0.05,
which indicates that shewas receiving 5% interest.You can also eliminate (C) because
over the course of a year the interest is compounded 4 times, not of a time. Because
Melanieinvested$1,100atwhatshethoughtwas5%compounded4times(12monthsina
year ÷ 3 months per period), she expected 1,100(1 + 0.05)4 = $1,337.06 after a year.
Instead, she has 1,337.06 − 50 = $1,287.06 after one year. Because t is in years in the
answerchoices,make t=1 in (A)and (D)andeliminateanychoice thatdoesnot equal
1,287.06.Only(A)works.
26. B Youcanstartbyplugginginavalueforx;tryx=4.BecauseangleAOB is120°and the
triangleisisosceles,anglesAandBareeach30°.CuttriangleAOBinhalftomaketwo30-
60-90triangleswithahypotenuseof4andlegsof2and .Thelegwithlength lies
onchordAB.Doubleittogetthetotallength: orjust ,whichis(B)whenyouput
x=4intotheanswerchoices.
27. C Whenevertherearevariablesinthequestionandintheanswerchoices,thinkPluggingIn.
Thequestionstatesthevalueofg,butitisaconstantandaweirdoneatthat.Picknumbers
forallthevariablesthatwillmakethemathmorestraightforward.Ifv=4andg=2,then
, and . Plug
thesevalues into theanswerchoices to seewhichequationworks.Choice (A)becomes
.Simplifytherightsideoftheequationtoget or
. This will not simplify further, so eliminate (A). Choice (B) becomes
.Simplifytherightsideoftheequationtoget or
.Eliminate (B).Choice(C)becomes .Distribute the2
to get . Reduce the equation to get 4 = or 4 = 4. The correct
answeris(C).
28. D ia = 1 when a is a multiple of 4. Using your exponents rules, 413 + x must also be amultipleof4.PlugIntheAnswersandlookforwhatmakes413+xamultipleof4.Only(D)works.
29. C Thezeroofgisthevalueofthevariable,inthiscasex,whentheequationissetto0.This
isalsocalledtherootorsolutionofanequation.Settheequationto0toget0=2x2−dx−
6.Plug6inforxtoget0=2(62)−d(6)−6.Simplifytheequationtoget0=72−6d−6,or
0=66−6d.Solvefordtoget−66=−6d,so11=d.Plug11infordandsetthequadratic
to0toget0=2x2−11x−6.Factortheequationtoget0=(x−6)(2x+1).Theotherzero
of the equation iswhen2x+1=0.Solve forx toget2x = −1, or x = . The correct
answeris(C).
30. D The flu shot is most effective against Strain C, which is least prevalent in March. Todeterminetheoverallefficacyof theflushotat this time,multiply theprevalenceofeachstrainofflubytheefficacyoftheflushotagainstthatstrain,andthenaddthoseproductstogetaweightedaverageoftheefficacyoftheshot:(0.23×0.35)+(0.25×0.13)+(0.13×0.76)+(0.39×0.68)=0.477=47.7%,whichisclosestto(D).
31. 3 Solve theequation forv.Take9>3v −3 and add3 toboth sides toget 12>3v. Nowdividebothsidesby3tofindthat4>v.Therefore,thelargestintegerthatvcouldbeis3.
Gridin3.
32. or0.83
Start bymultiplying the second fraction in the denominator of the equation by to get
.Combinethefractionsinthedenominatortoget .Reducethefractionin
the denominator to get . Dividing by a number is the same as multiplying by its
reciprocal,sotheequationbecomes .Multiplybothsidesoftheequationby to
gety= .Thecorrectansweris .
33. 1,279 614 studentsvoting forCandidateA represents0.48of thepopulationout of 1.Set up a
proportion: , where x is the total number of students in the school. Cross-
multiply:0.48x=614.Dividebothsidesby0.48andyougetapproximately1,279.
34. or0.384or0.385
Drawarighttriangleandlabelanon-rightangleθ.SOHCAHTOAtellsyouthattangentis
,sothelegoppositeθis12andthelegadjacenttoθis5.Cosineis ,so
youneed tofind thehypotenuseof the triangle.Youcanuse thePythagoreanTheorem,or
you can recognize this as a 5-12-13Pythagorean triplet.The hypotenuse is therefore 13.
Thelegadjacenttoθisstill5,socosθ= .
35. 7,054 First,youneedtodeterminethecurrentexchangerate.The7%feeisthesame(relativeto
theexchangerate),whetheritwasappliedtotheCediorUSD.Therefore,7%of651Cedi
is equal to 32.30USD. Translate English tomath: 0.07(651) = 32.30, or 45.57 Cedi =
32.30USD.Next, youwant the value of an itemworth 5,000USD inCedi, so set up a
proportion: . Cross-multiply: (45.57)(5,000) = 32.30x, or
227,850=32.30x.Dividebothsidesby32.30andyougetx=7,054.18USD,whichrounds
to7,054.
36. 63.6or63.7
First,drawasquareinscribedinacircle.Becausethediameterofthecircleisequaltothe
diagonalof thesquare,youcanplug inanumber like2 for the lengthof thediameter.
Becausethediameterformsa45-45-90triangle,eachsideofthesquarehasalength
of2.Usingtheareaformulaforasquare(A=s2),plugin2forthestogetA=22,which
simplifies toA = 4. The area of the square is 4. To find the area of the circle, use the
formulaA=πr2.Becausethediameterofthecircleis2 ,r= .Plugthatintothearea
formulatoseethatA= ,whichsimplifiestoA=2π.Tofindthesolution,translate
thequestionfromEnglishintomath.Theareaofthesquareiswhatpercentoftheareaofthe
circlebecomes:4= ·2π.Solveforx:First,divideeachsideby2π,andthenmultiply
each side by 100. The answer is a non-repeating decimal beginning 63.66197….When
enteringyouranswer,simplycutoffthedecimal(donotround)soittakesupfourspaces.
Youshouldenter63.6.
37. or0.7
Ifthemeanofthenewsetis ,thenthesumofthediametersofthecylindersdividedbythe
numberofcylindersmustequal .Setuptheequation: = ,where
x is the unknown cylinder. Multiply both sides by 6 to simplify:
.Combineliketerms(useyourcalculator,butbecarefulwith
parentheses!):5= +x.Subtract frombothsidesandyouget .
38. 1≤y≤1.25
Asetwithanevennumberofelementswillhaveasitsmediantheaverageofthemiddle
twoterms.Inthecurrentset, and1haveanaverageof ,sothenewcylindermustbe
equaltoorgreaterthan1,sothemedianwillbetheaverageof and1.Therangeoftheset
offivecylindersisthegreatestminustheleast: − = .Becausethenewcylindermust
be inchesto greaterthan ,thecylindermustbebetween1and inchesindiameter.
ReadingTest65MINUTES,52QUESTIONS
TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassageorpairofpassagesbelowisfollowedbyanumberofquestions.Afterreadingeachpassageorpair,choosethebestanswertoeachquestionbasedonwhatisstatedorimpliedinthepassageorpassagesandinanyaccompanyinggraphics(suchasatableorgraph).
Questions1–10arebasedonthefollowingpassage.
ThispassageisadaptedfromJaneEyre,anineteenth-centuryEnglishnovelbyCharlotteBrontë.
1. Jane’sattitudetowardMr.RochesterisbestcharacterizedasA) sympathetic.B) uncaring.C) despising.D) reckless.
2. Basedontheinformationinthepassage,itcanbeinferredthatJanerefusesRochester’s
advancesbecauseA) shedoesnotlovehimasmuchashelovesher.B) itwouldviolateherpersonalideals.C) hethinksthatsheisweakandfrail.D) shewishestocausehiminjury.
3. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–3(“While…him”)B) Lines13–16(“Iwill…now”)C) Lines36–38(“Thesoul…eye”)D) Lines50–51(“Whatever…creature”)
4. Incontext,thephrase“Iaminsane—quiteinsane”inline23referschieflytoA) aseverementalillnessthatJanesuffersfrom.B) amentalstatebroughtonbyGod’slaw.C) afeelingthatcurrentlyurgesJanetorejectRochester.D) areductionofjudgmentduetoemotion.
5. Asusedinline29,“wrought”mostnearlymeansA) hammered.B) made.C) excited.D) wrung.
6. Thefourthparagraph(lines42–61)providesacontrastbetweenA) Jane’sbodyandherwill.B) Rochester’sloveandangertowardJane.C) abirdanditscage.D) Jane’spurityandimpurity.
7. TheinmateRochestermentionsinline53referstoA) acriminallockedawayinjail.B) Rochestertrappedinhisemotions.C) Janestuckinthetraditionsofhertime.D) thepossiblebehaviorofJane’sspirit.
8. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines38–41(“Myeye…exhausted”)B) Lines45–47(“Icould…her”)C) Lines55–57(“Andit…frame”)D) Lines63–65(“Thelook…now”)
9. Asusedinline63,“worse”mostnearlymeansA) lessdesirable.B) moredifficult.C) oflowerquality.D) unskillful.
10. Basedontheinformationinthefinalparagraph,itcanbereasonablyinferredthatJanevaluesA) heremotionsoverherreason.B) freedomoversocialconvention.C) herprinciplesoverherfeelings.D) trueloveaboveallelse.
Questions11–21arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromHillaryClinton’sremarkstotheU.N.FourthWorldConferenceonWomenPlenarySessionin1995inBeijing,China.
PovertyratesintheUnitedStates,dividedbyageandgender.ImagecourtesytheU.S.CensusBureau.
11. ThepositionthatClintontakesinherspeechcanbestbedescribedasthatofA) acriticcounteringaseriesofarguments.B) ascholaranalyzingsocialphenomena.C) anadvocateseekingaparticularoutcome.D) amediatorseekingafaircompromise.
12. Asusedinline23,“valued”mostnearlymeansA) increased.B) considered.C) bought.D) insured.
13. Inlines12–13,whatisthemostlikelyreasonthatClintonmentionstheprior“women’sconferenceinNairobi”?A) Toprovideanexampleofaprevious,failedattempttosolvetheproblemof
domesticviolenceB) TodisagreewiththosewhoquestionthereasonforthecurrentconferenceC) TocontendthatagreatnumberofwomenandtheirexperienceshavegoneunnoticedD) Toofferevidencefortheclaimthatconferencescompelpeopletoaddressproblems
14. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–2(“Thereare…conference”)B) Lines9–12(“Itis…problems”)C) Lines21–22(“Weare…elderly”)D) Lines30–32(“Women…treated”)
15. Inlines39–45,ClintondrawsadistinctionbetweenA) thosewhoworkatschoolsandhospitals.B) peoplewhocanandcannotspeakout.C) employedandunemployedwomen.D) womenwhocanandcannotvote.
16. Basedontheinformationinthepassage,womenfaceeachofthefollowingchallengesEXCEPTA) lackofaccesstohealthcare.B) violenceintheirhomes.C) limitedfinancialresources.D) widespreadunemployment.
17. Asusedinline40,“speak”mostnearlymeansA) talkaloud.B) scold.
C) advocate.D) gossip.
18. Theprincipalrhetoricaleffectofthephraseinlines73–75(“letitbethat…onceandforall”)istoA) argueagainstattemptstounderstandwomen’srightsasdistinctfromotherrights.B) showthatmanywomenwhoshouldbeattheconferenceareunabletoattend.C) emphasizethespecialnatureofwomen’srightsastheyrelatetohumanrightsat
large.D) suggestthattheneedtofocusonthespecificproblemsofwomenisnowpast.
19. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines57–59(“Butwe…protected”)B) Lines68–71(“Itis…rights”)C) Lines75–76(“Letus…heard”)D) Lines79–83(“Itis…part”)
20. BasedontheinformationpresentedinClinton’sspeech,itcanbeinferredthatsomeofthosewhohaveimportantpositionsofauthorityintheworldA) areactivelyworkingagainsttheprosperityofwomen.B) donotconsiderthelabordonebywomentobeofseriousimport.C) arereadytoensurethatmenandwomenhaveequallegalrights.D) havemadeitunacceptabletodiscusswomen’srights.
21. Usinginformationinthegraphandthepassage,itcanbereasonablyinferredthatA) inAmericaandacrosstheworldthegreatestgenderdisparityinpovertyratesis
amongthose65andolder.B) women18to64comprise15.4percentoftheworld’spoor.C) whileahighpercentageofchildrenarepoorinAmerica,theoppositeistrue
worldwide.D) povertyratesinAmericaareinlinewithaworldwidegenderdisparity.
Questions22–31arebasedonthefollowingpassages.
Passage1isadaptedfromGardner’sArtThroughtheAges.©1991byHarcourtBraceJovanovich,Inc.Passage2isadaptedfromJohnBoardman,“TheParthenonFrieze—AnotherView.“©1977byJohnBoardman.BothpassagesdiscusstheParthenonFrieze,abandofsculpturethatonceencircledallfourwallsoftheParthenon,atempletothegoddessAthena.Thenaosistheinnersanctuaryofthetemple.
22. TheauthorofPassage1referencesaquotefromHeraclitus(lines29–35)primarilytoA) reinforcethesenseofthepassageoftimepresentinthefrieze.B) suggestthatopposingqualitiesofthecarvingpresentasenseofoverallbalance.C) provethatthestyleofthefriezeischaracteristicallyGreek.D) emphasizethecontrastbetweenthemenintheprocessionandthegoddessAthenaat
itsend.
23. WhichofthefollowingbestdescribesthestructureofPassage1?A) Apurposeforthefriezeisproposed,andthenadescriptionisgiven.B) Aninterpretationofthefriezeisquestionedandanewsolutionisoffered.C) Thefriezeisdescribedindetail,withemphasisonitsuniquequalities.
D) Ahistoricaloverviewisgiventhathelpsexplainthelayoutofthefrieze.
24. Asusedinline44,“unparalleled”mostnearlymeansA) crooked.B) normal.C) unsurpassed.D) unprecedented.
25. ThefirsttwoparagraphsofPassage2primarilyservetoA) rejecttheideathatthefriezedepictsthePanathenaicprocession.B) argueagainsttheideathatthefriezerepresentsthepassageoftime.C) suggestthatthefriezerepresentstheheroesofMarathon.D) outlineproblemsinthetraditionalinterpretationofthefrieze.
26. Asusedinline59,“mortal”mostnearlymeansA) human.B) deadly.C) terrible.D) common.
27. Inthecontextofthepassage,theauthor’suseofthephrase“thereIgo”(lines57–58)isprimarilymeanttoconveytheideathatA) figuresinthefriezewerenotmeanttobeportraitsofindividualcitizens.B) thefriezecannotbearepresentationofahumanevent.C) thecitizensofAthensdidnotparticipateinthePanathenaicprocession.D) thesubjectofthefriezeshouldbeobvioustomodernviewers.
28. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines46–49(“Andhere…theprocession”)B) Lines54–55(“Theflagrant…explanation”)C) Lines62–64(“Moreover…background”)D) Lines66–69(“Wemust…Athens”)
29. TheauthorofPassage2wouldmostlikelyarguethatthe“youths”(line21)describedinPassage1areA) citizensofAthensfromaroundthetimetheParthenonwasbuilt.
B) AthenianmenwhodiedinbattleatMarathon.C) peopleofMarathonwhowereworshippedasheroesinAthens.D) purelydivineparticipantsinthecelebrationofafestivalofAthena.
30. Passage2differsfromPassage1inthatPassage1A) focusesondeterminingthesubjectofthefrieze.B) givesadetaileddescriptionofthefiguresinthefrieze.C) considershowGreekcitizensmighthaveviewedthefrieze.D) entirelyrejectsthetraditionalinterpretationofthefrieze.
31. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines4–10(“Thoughitssubject…Parthenon”)B) Lines13–14(“Thisisthe…reliefs”)C) Lines15–17(“ThePanathenaicfrieze…time”)D) Lines19–25(“Inthepart…turn”)
Questions32–42arebasedonthefollowingpassage.
Thefollowingisanexcerptfrom“AStrangeTaleofaNewSpeciesofLizard”byCarlZimmerinTheNewYorkTimes.OriginallypublishedDecember14,2014.
32. Theauthormentions“sterilemules”(line21)primarilyinordertoA) delineateoneoftheonlyinstancesofanoccurrence.B) contradicttheopinionpresentedinthepassage.C) provideevidencethatsupportsscientists’beliefs.D) reiteratethatthelizardisanunusualcreature.
33. Asusedinline24,“striking”mostnearlymeansA) beautiful.B) conspicuous.C) aggressive.D) remarkable.
34. ThepassagesuggeststhattherelationshipbetweenDr.NeavesandDr.Baumannisbestcharacterizedaswhichofthefollowing?A) AscientificefforttounderstandparthenogenesisB) AcompetitiverivalrytobreedAspidoscelisexsanguisfirstC) AjointlabortodisprovethetheoriesofStowersD) Afriendshipbasedonasharedinterestinwhiptaillizards
35. Thethirdparagraph(lines12–17)moststronglysuggeststhatevolutionA) canhappenonlyoverthousandsofgenerations.B) dependsontheseparationofindividualsofonespecies.C) customarilytakesmanyyearstooccur.D) isolatespopulationssotheycan’tinterbreed.
36. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines12–13(“Theevolution…affair”)B) Lines13–15(“Typically…themselves”)C) Lines15–17(“Over…interbreed”)D) Lines21–23(“Inrecent…species”)
37. Asusedinline53,“hightime”mostnearlymeansA) afestival.B) anhourlate.C) anopportunemoment.D) aloftyideal.
38. Accordingtothepassage,parthenogenesisinwhiptaillizardsischaracterizedbyeachofthefollowingEXCEPTA) femaleindividualsthatcanduplicatechromosomeswithoutmales.B) stemcellsfromthemaleAspidoscelisinornata.C) clonesthataredifferentfromtheparentalspecies.D) offspringwithtwosetsofchromosomes.
39. ThepassagesuggeststhatwhiptaillizardsA) havetwoidenticalsetsofchromosomes.B) werefirstdiscoveredinthe1960s.C) requireamaleandafemaletobreed.D) createonlyfemaleclones.
40. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines32–33(“Theeggs…parthenogenesis”)B) Lines44–45(“Thefemale…species”)C) Lines61–62(“In…chromosomes”)D) Lines66–68(“When…chromosomes”)
41. Whichofthefollowing,iftrue,wouldmostweakentheauthor’sargumentinlines8–11?A) Scientistsdon’talwaysconsideranimalbreedscreatedinlabstobenewspecies.B) Evolutionisacomplexprocessthatcan’tbemanipulatedbyhumans.C) Thetwoanimalsusedintheprocessarenotconsidereddifferentspeciesbysome
scientists.D) Researchershaveproventhatalllizardshavetheabilitytoclonethemselves,but
theyonlycloneincaptivity.
42. Asusedinline43,thesentence“Somehow,thistriggersaswitchtoparthenogenesis,”suggeststhatA) scientistsarestilllookingfortheswitchthatcausescloning.B) hybridizationisacomplex,butmanageableprocess.C) scientistsareunclearastohowfemalewhiptailscanclonethemselves.D) nooneknowswhyfemalewhiptailschoosecloningovermating.
Questions43–52arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromDavidP.Hill,RoyA.Bailey,JamesW.HendleyII,PeterH.Stauffer,MaeMarcaida,“California’sRestlessGiant:TheLongValleyCaldera.”©2014byU.S.GeologicalSurvey.
LongValleyCalderacumulativeearthquakesbetween1983and2015,USGS.Theverticalbarsonthegraphsabovecorrespondwiththeleft-sidey-axisandrepresentthenumberofearthquakesperweek.Thethickergraylineindicatesthecumulativenumberofearthquakesandcorrespondswiththeright-sidey-axis.
43. Asusedinline10,“depression”mostnearlymeansA) dejection.B) decrease.C) crater.D) trouble.
44. Theauthorsusethephrase“asrecentlyas600yearsago”(line22)primarilytoA) suggestthattherewillbeanothereruptionthiscentury.B) conveyasenseofthemagnitudeofgeologictime.C) communicateirony,because600yearsagoisnotrecent.D) indicatethattheword‘recently’isarelativeterm.
45. Asusedinline38,“temblor”mostnearlymeansA) drum.B) earthquake.C) eruption.D) caldera.
46. WhatisthereasongeologistshaveincreasedtheirmonitoringoftheLongValleyCaldera?A) Ithasbeenmorethan150yearssincethelasteruption.B) Eruptionshappenfrequentlyinvolcanicchainsofsuchsize.C) Theareaisexperiencinggeologicactivityindicativeofanimpendingeruption.D) Theswellingofthecalderamaydamagethesensitivegeodeticequipment.
47. Whichchoiceprovidethebestevidencefortheanswertothepreviousquestion?A) Lines19–24(“Thevolcanic…mid-1800s”)B) Lines38–39(“Thattemblor…California”)C) Lines58–60(“Today,…caldera”)D) Lines70–72(“Suchemissions…eruptions”)
48. Inthecontextofthepassageasawhole,whatistheprimarypurposeofthelastparagraph?A) TosuggestthatgeologistsbelievedangerfromaneruptionisnotimminentB) ToexplainhowquicklygeologicunrestcanturnintoacatastrophiceruptionC) TowarnofthedireimpactofanothereruptionlikeMountSt.HelensD) Toemphasizetheimpactoftheearthquakesdiscussedearlierinthepassage
49. ItcanbeinferredfromthepassagethatMammothMountainA) eruptedmostrecentlyaround600yearsago.B) isanactivevolcanothattheUSGSismonitoringforearlysignsoferuption.C) showssignsthatthelargervolcanicsystemtowhichitbelongsisstillactive.D) wasformed760,000yearsagobypyroclasticflowsfromavolcaniceruption.
50. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–5(“About760,000…surface”)B) Lines19–24(“Thevolcanicsystem…mid-1800s”)C) Lines25–27(“Althoughno…frequently”)D) Lines75–77(“However,symptoms…Caldera”)
51. WhichofthefollowingsituationsismostanalogoustotherecentswellingoftheLongValleyCaldera?A) Manysmalltremorsalongaparticularfaultprecedealarge,magnitude8earthquake.B) Ascientistdiscoversanewspeciesofinsectbychancewhileobservingsnakesin
theAmazonrainforest.C) Badroadconditionscauseacollisionbetweentwocars,andpoorvisibility
contributestoamulti-carpile-up.D) Adoctorisunabletogiveadefinitivediagnosistoapatientafterassessing
symptomstypicalofaparticulardisease.
52. Whichofthefollowingclaimsissupportedbyinformationinthegraph?A) LongValleyCalderahadexperiencedmorethan120,000cumulativeearthquakesby
2015.B) LongValleyCalderaexperiencedroughly30,000earthquakesperweekin1990.C) By2012,LongValleyCalderahadexperienced1.0cumulativeearthquakes.D) By1988,LongValleyCalderahadexperiencedover2,500cumulativeearthquakes.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
WritingandLanguageTest35MINUTES,44QUESTIONS
TurntoSection2ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassagebelowisaccompaniedbyanumberofquestions.Forsomequestions,youwillconsiderhowthepassagemightberevisedtoimprovetheexpressionofideas.Forotherquestions,youwillconsiderhowthepassagemightbeeditedtocorrecterrorsinsentencestructure,usage,orpunctuation.Apassageoraquestionmaybeaccompaniedbyoneormoregraphics(suchasatableorgraph)thatyouwillconsiderasyoumakerevisingandeditingdecisions.
Somequestionswilldirectyoutoanunderlinedportionofapassage.Otherquestionswilldirectyoutoalocationinapassageoraskyoutothinkaboutthepassageasawhole.
Afterreadingeachpassage,choosetheanswertoeachquestionthatmosteffectivelyimprovesthequalityofwritinginthepassageorthatmakesthepassageconformtotheconventionsofstandardwrittenEnglish.Manyquestionsincludea“NOCHANGE”option.Choosethatoptionifyouthinkthebestchoiceistoleavetherelevantportionofthepassageasitis.
Questions1–11arebasedonthefollowingpassageandsupplementarymaterial.
ParkRangers,Naturally
OfthemanyparksthatarepartoftheAmericanheritage,theNationalPark 1 Service(NPS)iseasilythemostmajestic.FromthemomentofthefirstEuropeansettlementsinthefifteenthandsixteenthcenturies,visitorsandresidentsalikehavemarveledatthenaturalbeautyanddiversityof 2 theAmericanlandscape’sattractiveness.Aspartofacommitmenttopreservingthesenationaltreasuresagainsttheforwardmovementofindustrialization,theNationalParkServicewasfoundedin1916duringthepresidencyofWoodrowWilson.
1. WhichofthefollowingalternativestotheunderlinedportionwouldNOTbeacceptable?A) Service,NPS,B) ServiceNPSC) Service—NPS—D) Service,abbreviatedNPS,
2.A) NOCHANGEB) thepulchritudinousAmericanlandscape.C) theprettyAmericanlandscape.D) theAmericanlandscape.
Today,thereareover400parksintheservice,andtheseparksarerunandoverseenbytheDepartmentoftheInterior.Theday-to-dayoperations, 3 includingmaintenanceandtours,aretheworkofparkrangers.Theseparkrangersareresponsiblefortheupkeepofthe 4 parks,theirmainresponsibilityistomaintainthebalancebetweenthewildlifeandplantspeciesandthehumanvisitorsthatcometotheparkseveryday.
3. Thewriterwantstoincludeadetailthatwillclarifythephrase“day-to-dayoperations.”Whichofthefollowingwouldbestfulfillthisgoal?A) NOCHANGEB) andsomethataremorelong-term,C) oftenrepetitivetasks,D) notthepoliticaldecisionmaking,
4.A) NOCHANGEB) parkstheirC) parks—their
D) parks,their—
5 Withoutparkrangers,theparkswouldbeoverrunwithpollution.Somearescientistswhorevelintheecologicalaspectsofmaintainingtheparts.Someareeducators 6 helpingvisitorstounderstandtheuniqueaspectsandhistoricalsignificanceoftheparks.Stillotherscomefromlawenforcementandfirefighting,giventhattheirpostsareoftenveryfarindeedfromthemunicipalbodiesthattypicallyprovide 7 them.
5. Whichofthefollowingwouldbestintroducethetopicofthisparagraph?A) NOCHANGEB) Parkrangerscancomefromallwalksoflife.C) ManymillionsvisittheNationalParkseveryyear.D) Themostsuccessfulparkrangersusuallyhavesomebackgroundinecology.
6.A) NOCHANGEB) thatarehelpingC) whoarehelpingD) whohelp
7.A) NOCHANGEB) theseservices.C) those.D) it.
Therearenearly4,000parkrangersinservicewiththeNPStoday. 8 Visitorsareontherise,poisingthatnumberforgrowth. 9 Althoughparkvisitationnumberspeakedin1987,thegeneraltrendhasbeenasteadyrise.Thenumberscontinuetobehigh,withover270millionvisitorsin2013.Itseemsthataseconomicconditionsinthecountryasuncertain,moreandmorepeopleturntoparksforeconomical,educational,andenlighteningalternativestothemorecostlytouristactivitiesandtrips.Now,too,thatclimatesciencehas 10 foretolddifficulttimes,theNPSisseentobeprotectingthelastvestigesofourgreenworldbeforeitslipsaway.
VisitorstoAmerica’sNationalParks,1979–2009(inmillions)
8.A) NOCHANGEB) Visitationnumbersarepoisedontheriseforsignificantgrowth.C) Thatnumberispoisedtogrow,asvisitationnumbersareontherise.D) Poisedontherise,visitationnumbersaregrowing.
9. Whichofthefollowinggivesaccurateinformationbasedonthegraph?A) NOCHANGEB) Parkvisitationpeakedinthemid-1980sandhastaperedoffsincethen.C) Parkvisitationreachedrecordhighsin2009.D) Parkvisitationhasriseninalinearprogressionsincethelate1970s.
10. WhichofthefollowingalternativestotheunderlinedportionwouldbeLEASTacceptable?A) predictedB) statedC) anticipatedD) forecast
11 Thepark-rangerworkforceissodiverse,thereareactuallyafewcommonattributesamongparkrangers.Parkrangersneedatleastatwo-yeardegreeandsomeexperienceworkinginparks.Manyseasonalparkworkersandvolunteersgoontobecomeparkrangers.Ultimately,attainingworkasaparkrangerislessaboutaskill-setthanaparticularmindset.Parkrangersmusthonorandreverethenatural
world:theyspendtheirentirecareerslearningaboutandlivingintheplacestheywork.Parkrangershavespecialjobs,soitnaturallytakesagroupofspecialpeopletodothosejobs.
11.A) NOCHANGEB) Truly,thepark-rangerC) Becausethepark-rangerD) Althoughthepark-ranger
Questions12–22arebasedonthefollowingpassageandsupplementarymaterial.
TheFerryGodfather
[1]FormuchoftheearlypartofAmericanhistory,PennsylvaniaandVirginia,twomajorearlycoloniesandstates,sharedaborder.[2]ThispartofVirginiabecamethemodernstateofWestVirginiaonJune20,1863.[3]ThencametheCivilWar.[4]Amidthefurorofsecessionandconflict,PresidentAbrahamLincolngrantedaspecialprovisionforthatpartofVirginiathatwasloyaltotheUnion. 12
12. Forthesakeofthelogicandcoherenceofthisparagraph,sentence2shouldbeplacedA) whereitisnow.B) beforesentence1.C) aftersentence3.D) aftersentence4.
Althoughthisregionisnotinthenewsquitesooftentoday,inAmerica’searlyhistoryonepartofitwasonthetipofeveryone’stongue.ThetownofHarpersFerryplayedacrucialroleinpre-CivilWarera.GeorgeWashingtonproposedthattheUnitedStatesstationoneof 13 theirtwomajorarmoriesthere,andby1799,HarpersFerrybecame 14 oneofthemajorindustrialtowns,intheUnitedStates.Itspositionabout60milesfromWashington,D.C.,andBaltimoreputitcloseenoughtomajorcities,butitsplace 15 inthehillsatthemeetingofthePotomacandShenandoahRiversmadeitdifficulttoaccessandeasytodefend.
13.A) NOCHANGEB) they’reC) itsD) it’s
14.
A) NOCHANGEB) one,ofthemajorindustrialtowns,intheUnitedStates.C) one,ofthemajorindustrialtownsintheUnitedStates.D) oneofthemajorindustrialtownsintheUnitedStates.
15. Whichofthefollowinggivesaccurateinformationbasedonthemap?A) NOCHANGEB) approximately20milesnortheastofthetownofBolivarC) acrosstheShenandoahRiverfromMarylandD) atthefootoftheAdirondackMountains
BecauseitwassituatedontheborderlinebetweentheUnionandtheConfederacy,andbecauseitsarmorywasfulloftheweaponsbeingmanufacturedtofighttheCivilWar, 16 theConfederacytookitfourtimesandtheUniondidalso,andbothsidessawitasapivotalstrategicbase.
16.A) NOCHANGEB) thewarsawHarpersFerrychangehandseighttimes,C) HarpersFerrychangedhandseighttimesduringthewar,D) eightwasthenumberoftimesHarpersFerrychangedhands,
Inthepopularimaginationtoday,HarpersFerryisstillseenasacrucial 17 placeofgreatimportanceduringtheCivilWarbutmainlyforeventsthatoccurredtherebeforethewarhadevenstarted.In1859,radicalabolitionistJohnBrownledaraidonHarpersFerry,seekingtofreeslavesandbeginaguerillacampaigntofreeslavesalloverthecountry.WhileBrown’sraidwasultimatelyadismalfailureandBrownwasexecutedfortreason, 18 hisraidbegananationalconversation.
17.A) NOCHANGEB) placeC) placethatwasimportantD) placewhereagreatdealhappened
18. ThewriterwantstoincludeanideaherethatshowsthatBrown’sraidstillhadmajorimportance.Whichofthefollowingtrueideaswouldbestfulfillthisgoal?A) NOCHANGEB) HermanMelville’spoemaboutJohnBrownisverywell-known.C) theraidwasbasedonsomeearlierwell-knownslaverevolts.
D) hecouldnothavechosenamorecentrallocation.
AbolitionistsintheNorthsawhimasaheroandafreedomfighterwhilethoseintheSouthsawhimasa19 filthyterrorist. 20 TheCivilWarandthenation’smovementtowardsitusedJohnBrown’snameasbothsides’rallyingcry.
19.A) NOCHANGEB) heroicC) jankyD) vile
20.A) NOCHANGEB) Brown’snamebecamearallyingcryforbothsidesasthenationmovedtoward
CivilWar.C) Brown’scrywastherallythatbothsidesnamedastheCivilWarmovedinonthe
nation.D) bothsidesusedBrown’snameasthenation’sCivilWarwasmovingtowardit.
Today,HarpersFerryisasleepytowninthemountainsofWestVirginia.Muchofitsheritageremains 21 intact.Historicaltoursruneveryday.Aboveall,HarpersFerryisalivingreminderthatthecrucialeventsinhistoryarenotlimitedtothebigplacesandthemajorplayers.Withoutthecatalyzingeffectofthissmall 22 town:Americanhistoryasweknowitmighthavebeenmuchdifferent.
21.A) NOCHANGEB) intact,historicalC) intacthistoricalD) intact;andhistorical
22.A) NOCHANGEB) town;AmericanC) town.AmericanD) town,American
Questions23–33arebasedonthefollowingpassage.
StefanZweig’sReturn
StefanZweig’snamehasbeenshowingupalotlately.Inadditiontoa 23 largeamountofrecentlyrepublishedworks,WesAndersoncitesZweigasthemajorinfluenceonAnderson’srecentfilmTheGrandBudapestHotel(2014).ItseemsthatZweighassuddenlybecome 24 revelantagainafternearly75yearsofobscurity.Whythissuddeninterest?Whatcanheofferthatourcultureseemstoneed?
23. WhichofthefollowingalternativestotheunderlinedportionwouldbeLEASTacceptable?A) bevyB) massC) multitudeD) volume
24.A) NOCHANGEB) relevantC) irrelevantD) irrevelant
StefanZweigwasbornin1881. 25 HisparentswerepartoftheJewishculturaleliteinViennaatthetime.Stefanwasaffordedeverypossibleluxuryandprivilege.By1904,ZweighadearnedadoctoraldegreefromtheUniversityofVienna,andheformedtheconnectionsthatwouldallowhisentryintothe26 city’sculturalelite.Zweigwentontopublishanearinfinitudeofworksoffiction,drama,journalism,andbiography,andenjoyedaperiodofmajorcelebrityinthe1920sand1930s. 27
25. Theauthorwouldliketocombinethetwosentencesreproducedbelow:
HisparentswerepartoftheJewishculturaleliteinViennaatthetime.Stefanwasaffordedeverypossibleluxuryandprivilege.
Whichofthefollowinggivesthebestcombinationofthetwosentences?A) HisparentswerepartoftheJewishculturaleliteinViennaatthetime;Stefanwas
affordedeverypossibleluxuryandprivilege.B) Zweigwasaffordedeverypossibleluxuryandprivilegebecausehisparentswere
partoftheJewishculturaleliteinViennaatthetime.C) BorntoparentswhowerepartofVienna’sJewishculturalelite,Stefanwasafforded
everypossibleluxuryandprivilege.D) HisparentswerepartoftheJewishculturaleliteinViennaatthetime,andsoStefan
benefitedfromtheirelitenesswithluxury.
26.A) NOCHANGEB) citiesC) citie’sD) cities’
27. Thewriterisconsideringdeletingthephrase“offiction,drama,journalism,andbiography”andplacingacommaafterthewordworks.Shouldthephrasebekeptordeleted?A) Kept,becauseitshowsthatZweighadnoproblemfindingworkafterheleftVienna.B) Kept,becauseitdemonstratestherangeofZweig’stalents.C) Deleted,becauseitisimplausiblethatasinglewritercouldworkwellinsomany
forms.D) Deleted,becauseitpresentsinformationgiveninnumerousplacesthroughoutthe
essay.
Still,Zweig’srelationshipwithhishomelandwasalwaystenuous.WhilehedidsupporttheGermansideinWorldWarI,ZweigremainedacommittedpacifistandparticipatedonlyintheArchivesoftheMinistryofWar.Bythesecondwar, 28 however,Zweig’spacifismwasnolongerlookedonwithsuchunderstanding.ZweigandhiswifefledNaziGermanyin1939andspenttheirremainingyearsintheAmericas.Onlyafewshortyearsaftertheirescape,ZweigandhiswifetooktheirownlivesoutofdespairoverwhathadbecomeofEurope.Zweig’sancestralhome, 29 which,you’llrecall,wasinVienna,insistedontearingitselfapart,andJewishmenlikehimselfwerebeingslaughteredbythemillions.
28.A) NOCHANGEB) indeed,C) ontheonehand,D) although,
29. WhichofthefollowingchoiceswouldbestemphasizethepersonalstakethatZweighadintheconflictinEurope?A) NOCHANGEB) nottheAmericastowhichhehadmoved,C) inwhichhehadsuchpride,D) thelandofGoetheandBeethoven,
Formanyyears,culturalcriticssawZweig’sworkasahistoricalcuriosity.HisdecisiontofleeEuropewasseenasanactofquaintpacifism,andhisultimatedecisiontoendhisownlifewasseenastheactofaprivilegedmanfor 30 whicheverydayrealitiesweresimplytoomuchtobear.Muchmorepopularinthepost-WWIIeraweremoretraditionally“masculine”figures,whonotonlywenttowarbuttreatedwriting,painting,andfilmmaking 31 likecompetitivesports.
30.A) NOCHANGEB) whoC) whoseD) whom
31. Whichofthefollowingconclusionstothissentencewouldbestsupporttheideapresentedatthebeginninginthesentence?A) NOCHANGEB) withapacifistbent.C) likepropergentlemen.D) astheprovinceofveterans.
Today,however,Zweig’ssensibilitymakesagooddealmoresense.LikeZweig,manyofuswerealiveandawarebeforethegreatcatastrophesof 32 hisownage,andourlongingfora“simplertime”isnotpurenostalgia.Weknowthatthingscannotbeastheyoncewere,butwe 33 havesensedtheinjusticeintheworldbeingsocomplicated,andinthepowerjustafewpeoplehavetotakeitallawayfromus.
32.A) NOCHANGEB) theirC) herD) our
33.A) NOCHANGEB) aresensingC) senseD) sensed
Questions34–44arebasedonthefollowingpassage.
ForFigs?TheChimpsAren’tChumps
Sometimesasyoufallasleep,you’rethinkingaboutwhattoeatforbreakfastthenextmorning.“WhenIgetup,I’llgotothefridge.I’llhaveanegg, 34 apieceoftoast,andafewstripsofbaconwhileI’mmakingcoffee.”Eventhoughyoumayknowwhereyourfoodiscomingfrom,youplanbreakfastasawaytoplantheday.
34.A) NOCHANGEB) apieceoftoast,andafewstripsofbacon,C) apiece,oftoast,andafewstrips,ofbacon,D) apieceoftoastandafewstripsofbacon
Ourspeciesmayhavebeendoingthiskindofbreakfastplanninglongbeforerefrigerators,longbeforeourspecieswasevenourspecies.AteamofresearchersrecentlyfollowedgroupsofchimpanzeesthroughthreeperiodsoffruitscarcityinWestAfrica. 35 Forachimpanzee,everydayduringafruit-poorseasoncanbelikeBlackFriday,whereallthe“shoppers”wantthesamehotitem.
35. Atthispoint,theauthorwantstoaddasentencethataccuratelysummarizesthescientists’researchinawaythatisconsistentwithotherinformationinthepassage.Whichsentencewouldmosteffectivelyachievethatgoal?A) Theywantedtoseewhetherthechimpswouldprefernew,high-yieldfruitslikefigs
totheirtraditionaldietofbananas.B) Theywantedtodiscoverwherechimpsspentthetimebetweenwakingandsleep.C) Theywantedtoknowhowthechimpsacquiredhighlysought-afterfruits,likefigs,
whenthetreesthatbearthesefruitsaredepletedsoquickly.D) Theywantedtouncoverthesecretsofhumanevolutionandhowchimpswould
operateinaretailenvironment.
36 WhydoeseveryonefreakoutduringBlackFridaywhenthedealsaren’teventhatgood?Ifyouwanttobesuretogetthenew,say,plasmaTV,whatdoyouhavetodo?Campoutinfrontofthestore!Well,that’sexactlywhattheresearchersfoundthechimpanzeestodowiththecovetedfruits.Infruit-poorseasons, 37 thenomadicchimpanzeessetuptheircampsiteswithinstrikingdistanceoftheripefruits.Whenthefruitswere 38 “_________,”orquicktodisappear,thefemalechimpanzeessetuptheirsleepingnestsmorepointedlyinthedirectionofthefruit 39 thanthefruitwasplentiful.Moreover,inordertoensurethatthefruitsupplywouldnotbe 40 gobbledbythetimethechimpsgotthere,theywokeupearly,oftenbeforesunrise,whentheforestswerestilldark.
36. Whichofthefollowingwouldprovidethebesttransitionfromthepreviousparagraphandintroductiontothisparagraph?
A) NOCHANGEB) ThesimilaritytoBlackFridayshoppersgoesevenabitfurtherthanthis.C) Foramonkey,everydayoftheyearislikeBlackFriday,butwithoutThanksgiving.D) BlackFridayisthedayaftertheAmericanThanksgiving,anditisoften
characterizedbyheavyretailtraffic.
37.A) NOCHANGEB) thenomadicchimpanzeesetsuptheirC) thenomadicchimpanzeesetsupitsD) thenomadicchimpanzeessetupits
38. Whichofthefollowingprovidesthemostprecisewordgiventhedefinitionthatimmediatelyfollows?A) livelyB) desiccatedC) ephemeralD) eternal
39.A) NOCHANGEB) thentheC) thaniftheD) thanwhenthe
40.A) NOCHANGEB) depletedC) chompedD) ate
Thefindingsaboutthechimp 41 hasledscientiststoreopenanumberofheatedquestions.Thefirsthastodowithanimals’existenceoutsidethepresentmoment:howmuchdotheyremember,andhowmuchdotheyplan?Inotherwords,is“consciousness”reallyonly 42 theprovinceofhumans?Theothersetofquestionshastodowiththelinesofevolution.Ithasbeenfirmlyestablishedthatchimpanzeesareourevolutionaryancestors,butnowwehavetowonderifwe’veinheritedevenmore 43 thanwethoughtfromtheminitially.Havethelivesofchimpanzeesconditionedthesmall,day-to-daypatternsof
ourownlives?
Whilesuchquestionsmayseempurelyacademicandconceptual,theyactuallyhaveagooddealtodowithourlivedexperience.Welearnmoreandmoreaboutwhatwesharewithotheranimals—andwitheachdiscovery,welearnanewwaytorelatetotheworldaroundus.
41.A) NOCHANGEB) haveleadC) haveledD) haslead
42.A) NOCHANGEB) theprovidenceofhumans?C) theprovenanceofhumans?D) providentialforhumans?
43.A) NOCHANGEB) fromthemthanweinitiallythought.C) theninitiallythought.D) thanwehadbeenthinkingfromtheminitially.
Question 44 asksaboutthepreviouspassageasawhole.
Thinkaboutthepreviouspassageasawholeasyouanswerquestion44.
44. Supposetheauthor’sgoalhadbeentopresentanargumentthatsuggestsBlackFridayshoppingisananimalisticbehavior.Wouldtheinformationinthisessaysupportthatargument?A) Yes,thisessayestablishesaparallelbetweenhumansandchimpanzeesandexplores
itindetail.B) Yes,thisessaysuggeststhatchimpshaveadaptedBlackFridaybehavioreasily.C) No,thisessaysuggeststhatchimpanzeesaremoreadvancedthanmostBlackFriday
shoppers.D) No,thisessayismoreconcernedwithdescribingabehaviorofchimpanzeesthanin
passingjudgmentonhumans.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–NoCalculator25MINUTES,20QUESTIONS
TurntoSection3ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–15,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions16–20,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion16onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorisnotpermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Iftwotimesanumberisequaltothatnumberminus4,whatisthenumber?A) −7B) −6C) −4D) −3
2. Thenumberofsoilsamples,s,thatSonalneedsforanexperimentmustbegreaterthan6butlessthanorequalto13.WhichofthefollowingrepresentsanacceptablenumberofsoilsamplesforSonal’sexperiment?A) 6<s<13B) 6≤s<13C) 6<s≤13D) 6≤s≤13
3.
Inthefigureabove,thegraphofy=f(x)isshown.Whichofthefollowingcouldbetheequationoff(x)?
A) f(x)=− x+3
B) f(x)=− x−3
C) f(x)= x−3
D) f(x)= x+3
4. Ifx+y=0,whichofthefollowingmustbeequivalenttox−y?A) −2y
B)
C) xD) x2
5. Whichofthefollowingisequivalentto2x2−6x−8?A) 2(x−4)(x+1)B) 3(x+4)(x−1)C) 2(x−3)(x+2)D) 3(x−4)(x−2)
6. RyanandAllisonbuildaramptohelptheirelderlycat,Simms,walkuptotheirbed.Theyneedtheramptomakea35°anglewiththeirbedroomfloor.Howlongmusttherampbetoreachthetopoftheirbedthatisexactlythreefeetofftheground?
A)
B)
C)
D)
7. If3a+2b=24and4a+5b=53,whatisthevalueofa+b?A) 2B) 7C) 9D) 11
8. Giventheequationy=3x2+4,whatisthefunctionofthecoefficientof3?A) Itmovesthegraphofy=3x2+4threeunitshigherthanthegraphofy=x2+4.B) Itmovesthegraphofy=3x2+4threeunitslowerthanthegraphofy=x2+4.C) Itmakesthegraphofy=3x2+4widerthanthegraphofy=x2+4.D) Itmakesthegraphofy=3x2+4narrowerthanthegraphofy=x2+4.
9. Stevenneedstobuytthemeparkticketsforhimselfandhisfamily.Eachticketcosts$80,andthenumberofticketsheneedstobuycanbemodeledbytheexpressiont2−4t−90=6whent>0.WhatisthetotalcostofthethemeparkticketsthatStevenpurchased?A) $640B) $800C) $960D) $1,120
10.
2c+3d=17
6c+5d=39
Inthesystemoflinearequationsabove,whatisthevalueof4c−4d?A) −4B) 1C) 4D) 13
11. Ifx2+2xy+y2=64andy−x=12,whichofthefollowingcouldbethevalueofx?A) −10B) −4C) 2D) 10
12. Samanthaofferstwodifferentpackagesofyogaclassesatheryogastudio.Sheofferstwohotyogasessionsandthreezerogravityyogasessionsatatotalcostof$400.Shealsooffersfourhotyogasessionsandtwozerogravitysessionsatapriceof$440.Samanthawantstoofferalargerpackageforlong-timeclientsinwhichthecostmustexceed$800.IfSamanthadoesnotwishtoincludemorethan13sessionsforthelong-timeclientpackage,willshebeabletocreatethispackageforherclients?
A) No,becausetheclosestpackagethatshecanofferconsistsofthreehotyogaandthreezerogravityyogasessions.
B) No,becausetheclosestpackagethatshecanofferconsistsoffourhotyogaandfourzerogravityyogasessions.
C) Yes,becauseshecanofferfivehotyogaandfivezerogravityyogasessions.D) Yes,becauseshecanoffersixhotyogaandsixzerogravityyogasessions.
13. Cuthbertisconductingachemistryexperimentthatcallsforanumberofchemicalstobemixedinvariousquantities.Theoneamountofwhichheisunsureisgramsofpotassium,p.IfCuthbertiscertainthat(3p2+14p+24)−2(p2+7p+20)=0,whatisonepossiblevalueof3p+6,theexactnumberofgramsofpotassiumthatCuthbertwouldliketouseforthisexperiment?A) 20B) 18C) 12D) 10
14. Whatisthevalueof(2+8i)(1−4i)−(3−2i)(6+4i)?(Note:i= )A) 8B) 26C) 34D) 50
15. If2 =x−3,whichofthefollowingisthesolutionsetforx?A) {−1,9}B) {1,−9}C) {9}D) {1,9}
DIRECTIONS
Forquestions16–20,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.
3. Noquestionhasanegativeanswer.
4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpreted
as ,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
16. AgroupofstudentsatOmegaHighSchoolareusingstaplesandpopsiclestickstobuildascalemodeloftheGreatWallofChinaaspartofaprojectdetailingChina’smilitaryhistory.Thenumberofstaplesthestudentswillneedisthreetimesthenumberofpopsiclestickstheywillneed.Ifthestudentsdeterminetheyneed84staplesforthisparticularproject,howmanypopsiclestickswilltheyneed?
17. Astandardparabolainthex,y-coordinateplaneintersectsthex-axisat(5,0)and(−5,0).Whatisthevalueofthex-coordinateofthisparabola’slineofsymmetry?
18. DanielleisacivilengineerforDastisDynamicConstruction,Inc.Shemustcreateblueprintsforawheelchairaccessiblerampleadinguptotheentranceofamallthatsheandhergrouparebuilding.Therampmustbeexactly100metersinlengthandmakea20°anglewiththelevelground.Whatisthehorizontaldistance,inmeters,fromthestartoftheramptothepointlevelwiththestartoftherampimmediatelybelowtheentranceofthemall,roundedtothenearestmeter?(Disregardunitswheninputtingyouranswer.)
(Note:sin20°≈0.324,cos20°≈0.939,tan20°≈0.364)
19. Iftwiceanumberisequaltothatnumberminusfive,whatisthreetimesthatnumberplusseventeenminusthatnumber?
20. Giventhattheequation3x2+2x−8=0hastwodistinctsolutions,whatisthevalueofthesmallersolutionsubtractedfromthelargersolution?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–Calculator55MINUTES,38QUESTIONS
TurntoSection4ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–30,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions31–38,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion31onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorispermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.
Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. If3y=y+2,whatisthevalueof2y?A) 1B) 2C) 3D) 4
2. Merryjoinedanonlinecommunitythatchargesamonthlyfeeof$15.Aone-timeenrollmentfeeof$50waschargedwhenshejoined.WhichofthefollowingrepresentsthetotalamountoffeesthatMerryhaspaidtothecommunityorganizersaftermmonths,indollars?A) 15m+50B) 15+50mC) 15m−50D) (15+50)m
3. RobhashisfavoriteguitartunedupandreadytobringtoaperformancebyhiscoverbandatalocalvenueSaturday.Hedecidesatthelastminutetobringxadditionalguitars,justincasehisfavoriteguitarhasanissue.IfthetotalnumberofguitarsthatRobertbringstotheperformancecanbemodeledasx+1,whatdoesthe“+1”accountforintheexpression?A) ItaccountsforanadditionalguitarthatRobreturnstohishouseandpicksupinthe
middleoftheperformance.B) Itaccountsforhisfavoriteguitar,whichRobwasbringingfromthebeginning.C) ItaccountsforthenumberofadditionalguitarsthatRobdecidedtobring.D) Itaccountsforanadditionalnon-guitarmusicalinstrumentthatRobdecidedtobring.
4. Agroupof24studentswaspolledastowhethertheyenjoybiologyclass,chemistryclass,both,orneither.Theresultsareshowninthetablebelow:
Giventheabovedata,whichofthefollowingconclusionsistrue?A) Theratioofthosewhoenjoybiologyclasstothosewhoenjoychemistryclassis
7:8.B) Theratioofthosewhoenjoychemistryclasstothosewhodon’tenjoychemistry
classis9:4.
C) Theratioofthosewhoenjoybiologyclasstothosewhodon’tenjoychemistryclassis7:2.
D) Theratioofthosewhodon’tenjoybiologyclasstothosewhoenjoychemistryclassis5:9.
5. Dr.Goldberg,anoteddietician,mixesdifferentsolutionsaspartofherresearchintosugarsubstitutes.Byweight,shemixes40%ofasampleofsubstituteAand70%ofasampleofsubstituteBtocreatesubstituteC.IfDr.Goldberginitiallyhad60gramsofsubstituteAand110gramsofsubstituteB,thenwhatwouldbetheweight,ingrams,ofsubstituteC?A) 24B) 77C) 101D) 170
6. Whichofthefollowingisequivalenttotheexpressionx4−x3−x2?A) x(x2−x−1)B) x(x−x2−x3)C) x(x3−x2)D) x2(x2−x−1)
7. OfficerBlakedriveshissquadcar1mileperminutewhilepatrollinglocalhighwaysduringhisshift.Ifhehasdriven480milesbytheendofhisshift,howmanytotalhoursdidhedrivehiscarattheaboverate?A) 8B) 12C) 16D) 20
8. Intheinequality37≤−2x+1,whatistheappropriateorderofstepsneededtosolvetheinequalityforx?A) Add1tobothsides,dividebothsidesby2,andfliptheinequalitysignto≥.B) Subtract1frombothsides,dividebothsidesby−2,andfliptheinequalitysignto≥.C) Add1tobothsides,dividebothsidesby−2,andkeeptheoriginalinequalitysign.D) Subtract1frombothsides,dividebothsidesby2,andkeeptheoriginalinequality
sign.
9. Whatisthevalueof(2x2+4x+8)−(2x2−4x+7)?A) 4x2+8x+15
B) 2x2+x+1C) 8x+1D) 8x+15
10. Aspartofaprojectforhiscartographyelective,Adamclimbsseveralhillstocreateareliefmapforthewoodssurroundinghishouse.Herecordstheverticalheightsofthefivehillsheclimbedat55feet,42feet,38feet,50feet,and48feet.Forhisproject,Adammustconverthismeasurementstoinches.If1foot=12inches,whatisthemeasurement,ininches,ofthetallesthillAdamwillhaveonhismap?A) 660B) 600C) 576D) 456
11.
Inthefigureabove,ify=40andLN=8,whichofthefollowingmostcloselyapproximatesthelengthofMN?A) 0.10B) 9.53C) 10.44D) 12.45
12. McCoyMaxSpeed,Inc.makescustomskateboardsforitscustomers.Twowoodenskateboardsandthreecompositeskateboardscost$650.Threewoodenskateboardsandonecompositeskateboardcost$450.HowmuchwouldMcCoyMaxSpeedchargeacustomerwhopurchasesfivewoodenskateboardsandfourcompositeskateboards?A) $500
B) $600C) $1,000D) $1,100
13. ThechartbelowshowsdataaboutthenumberofemployeesatCudaCola,apopularbeveragecompany.
Assumingtheemployeetotalgrowsatthesamerateeachyear,andmaleandfemalepercentagescontinuetodecreaseandincreaseby5%,respectively,approximatelyhowmanymaleemployeeswillworkatCudaColain2015?A) 1,515B) 1,398C) 1,282D) 1,165
14. JohnCroxley,themayorofBlackRock,NY,iscountingthenumberofrestaurantsthathaveopenedinhistownpermonthforthelastsevenmonths.HecompilesthesevennumbersintoSetF,whichcontainstheelements4,5,11,13,16,18,andx.Ifboththemedianandaverage(arithmeticmean)ofSetFequal11,whatmustbethevalueofx,theunknownnumberofrestaurantsthatopenedinMayorCroxley’stownlastmonth?A) 9B) 10C) 11D) 12
15.
17s+20t=59
30s+40t=110
Inthesystemofequationsabove,whatisthevalueoftintermsofs?
A)
B)
C)
D)
16.
Giventhescatterplotgraphabove,tenstudentsatWeltonAcademywerepolledatrandomabouttheirusageoftheschool’snewphysics-centeredsocialmediaapp,E=MCShared.Theappwasdevelopedtoencouragestudentstodiscussphysicscurriculaandconceptsinwaysthatmirroredsocialmediatrendsin2013.Studentswereaskedhowmanytimestheyloggedintotheappeachdayaswellashowmanypoststheyactuallymadeusingtheapp.Withthegivendata,whatconclusionscanbedrawnaboutthisgroupofstudents?A) Themajorityofstudentspolledloggedinmoretimesperdaythantheyposted.B) Themajorityofstudentspolledpostedmoretimesperdaythantheyloggedin.C) Themajorityofstudentspolledloggedinandpostedanequalnumberoftimes.D) Norelationshipcanbedrawnbetweenloginsperdayandpostsperday.
17.
Twographs,f(x)andh(x),areshownabove.Iff(x)=3x+4andf(x)andh(x)areperpendicular,whichofthefollowingcouldbetheequationofh(x)?
A) h(x)= x+9
B) h(x)=− x+9
C) h(x)=3x+9D) h(x)=−3x+9
18. ThenumberofeggsthatFarmerJoneshasinhischickencoopwillgrowexponentiallyasFarmerJonesbuysmorechickenstoincreaseproduction.ThenumberofeggsFarmerJoneshasinthecoopcanbemodeledbytheequationy=3xbeginningonDay1,wherexisgivenbyx=1,andyisthenumberofeggscurrentlyinthecoop.Ifthecoopcansupport
only4,000eggs,andFarmerJonesemptiesthecoopeveryday,onwhichdaywillthechickensproducetoomanyeggsforthecooptosupport?A) Day6B) Day7C) Day8D) Day9
19. Ifa= andaisanonzerointeger,whichofthefollowingisequivalenttoa?
A) 4aB) 4
C)
D) 2
20. Threedifferentchefsworktogethertopreparemealsfor280dinnerguests.Eachworksatadifferentspeed,andtheircombinedoutputthroughoutthenightismodeledbytheequation8x+4x+2x=280.Ifxisapositiveinteger,whichofthefollowingcould8xrepresentintheequation?A) Thetotalmealoutputbytheslowestchef,whomade40meals.B) Thetotalmealoutputbythefastestchef,whomade160meals.C) Thetotalmealoutputbythefastestchef,whomade80meals.D) Thedifferencebetweentheoutputbetweentheslowestandfastestchef,which
wouldbe120meals.
21.
Thegraph,y=f(x),shownabovemodelstheperformanceofacertaincrop,wherexisthenutrientssubtractedoraddedtothesoilandyisthegainorlossofpiecesoffruitaddedtothetotalharvest.Amorepowerfulfertilizerthatisusedcausesthegraphy=f(x)tobereflectedovertheliney=x.Whichofthefollowingbestdescribesthebehaviorofthecropwiththenewfertilizer?A) Foreverythreenutrientsaddedtothesoil,thecroplosestwoadditionalfruitsfor
thetotalharvest.B) Foreverytwonutrientsaddedtothesoil,thecroplosestwoadditionalfruitsforthe
totalharvest.C) Foreverythreenutrientsaddedtothesoil,thecropaddstwoadditionalfruitstothe
totalharvest.D) Foreverytwonutrientsaddedtothesoil,thecropaddsthreeadditionalfruitstothe
totalharvest.
22. GeorgeandJoebothinterviewthesame20fellowstudentsregardingtheirinterestintheirschool’snewModelUNClub.GeorgeaskedthestudentstorespondwithInterested,SortofInterested,andNotInterested.Joeaskedthestudentstoratetheirinterestonascaleof1to5.Theresultsofthepollsarebelow.
George’sPoll
Joe’sPoll
Afterreviewingthedata,theModelUNadvisorsdeterminethatJoeneglectedtoincludewhethera1or5wasthebestratinginhisreport.Whatadditionalpieceofinformationwouldmosthelptheadvisordeterminewhethera1or5wasthebestrating?A) RequestingthatGeorgeredohispollwiththesameratingsystemasJoe’spollB) RequestingthatJoeredohispollwiththesameratingsystemasGeorge’spollC) Pollingallofthestudentswhosaid“Interested”inGeorge’sPollandaskingthemto
choosebetween“ExtremelyInterested”and“VeryInterested”D) Pollingallofthestudentswhogavea“1”ratinginJoe’spollandaskthemifthey
areinterestedinModelUN
23. Eachwinter,CaptainDan’sSkiLodgerentsbothpairsofskisandsnowboardstoitsguestsforaflatdailyrateperpairofskisandaflatdailyratepersnowboard.Fivepairsofskisandtwosnowboardswillcostafamily$370.Threepairsofskisandfoursnowboardswillcostafamily$390.Duringaparticularlyslowseason,CaptainDanannouncesa10%discountonallskisandsnowboards.Whatwouldbethecostofrentingtwopairsofskisandtwosnowboardsiftheywererentedduringthisdiscountperiod?A) $99B) $110C) $198D) $220
24. If8x+8y=18andx2−y2=− ,whatisthevalueof2x−2y?
A) −
B) −
C)
D)
25. Shaunisdevelopingaweightlossregimen,whichincludesbothaworkoutplanandacalorie-restrictionplan.Shaunwantstoworkoutfornolessthan30minutesandnomorethan60minutesadayandconsumenolessthan2,000andnomorethan2,500calories.Ifeachminute,m,ofhisworkouttimeburns50calories,whichofthefollowinginequalitiesrepresentsthenumberofminutes,m,thatShauncanworkouteachdaytoburnoffasmanycaloriesasheconsumes?A) 30≤m≤60B) 30≤m≤50C) 40≤m≤50D) 40≤m≤50
26. Aprofessionalbaseballteamwishestoaverage45,500ticketpurchasespergamefortheentire162-gameseason.Throughthefirst60gamesoftheseason,theteamhasaveraged43,000ticketpurchasespergame.Whichofthefollowingmostcloselyapproximateshowmanyticketpurchasespergametheteammustaveragefortheremainderoftheseasoninordertohititsoverallgoalofanaverageof45,500ticketpurchasespergamefortheseason?A) 46,970B) 47,880C) 48,000D) 48,220
27. Acertainpolynomial,P,hasadegreeof2.PolynomialPhaszerosof2and−3,anda>0whenthefunctionofpolynomialPiswrittenintheformofy=ax2+bx+c.Giventhisinformation,whichofthefollowingcouldbethegraphofpolynomialP?A)
28. CircleO(notshown)isdividedintothreesectors.PointsP,Q,andRareonthecircumferenceofthecircle.SectorPORhasanareaof8π,andsectorROQhasanareaof6π.IftheradiusofcircleOis4,whatisthemeasureofthecentralangleofsectorQOP,indegrees?A) 45B) 90C) 135D) 180
29. MedicalresidentsatLakewoodHospitalarechoosingtheirindividualspecialties.Amongthem,40%choosecardiology,16%chooseoncology,34%chooseendocrinology,andtheremainingx%choosehematology.Oncethedoctorspicktheirfirstspecialty,theyaretheneachaskedtochooseasecondspecialtyfromthepreviousfouroptionsincasetheiroriginalspecialtyisalreadyfilled.Theymaynotpicktheiroriginalspecialtyagain.20%ofthosewhooriginallypickedcardiologychooseoncologyastheirsecondchoice.Ifnootherfieldchoosesoncologyastheirsecondchoice,andthehospitalboasts200medicalresidents,thenwhatisthetotalnumberofresidentswhonamedoncologyaseithertheirfirstorsecondchoice,intermsofx?A) 8x−128B) 8x−144C) x2+24x−188D) x2−24x+188
30. Mr.Lastorka’sscienceclassisrunningexperimentswithanenergy-efficientmodelelectriccar.Astheinitialrateofenergydeliveredtothecar,measuredinwatts,increases,thenumberofmillimetersmovedbythecarfromitsstartingpositionincreasesexponentially.Theresultsofseveraltrialrunsareshownonthescatterplotgraphbelow.
Basedonthedata,thestudentsinMr.Lastorka’sclassdeterminetheexactequationinvolvingWatts,x,andtotaldistancefromstart,y.Theycallthefunctiony=f(x).Mr.Lastorkatheninstructshisclasstoreflecty=f(x)overthex-axis.Hechallengeseachstudenttodeterminethenewfunctionandwhatitwouldmeanfromaphysicsperspective.Fourstudentpairsgavetheiranswersbelow.Whoiscorrect,andforwhatreasons?A) CharlesandShannon,whoidentifythenewequationasy=−2xandexplainthatthe
newgraphindicatesthatthecarisstillmovingforwardatthesamerateasbefore.B) MichaelandLauren,whoidentifythenewequationasy=−2xandexplainthatthe
newgraphindicatesthecarisnowmovinginreverseatthesamerateasbefore.C) MatthewandKaren,whoidentifythenewequationasy=2−xandexplainthatthe
newgraphindicatesthatthecarisnowmovingforwardmorerapidlythanbefore.D) AndyandJoanie,whoidentifythenewequationasy=2−xandexplainthatthenew
graphindicatesthatthecarisnolongermovinginanydirection.
DIRECTIONS
Forquestions31–38,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.
3. Noquestionhasanegativeanswer.
4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpretedas
,notas3 .)
6. DecimalAnswers: If you obtain a decimal answer withmore digits than the grid can accommodate, it may be eitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
31. Whatnumberdividedbytwoisequaltothatsamenumberminus15?
32. ThenumberofhoursRobertspendsinhisgameroomisproportionaltothenumberofhourshespendsplayingCallofDestinyIV:ModernBattlefield.IfheplaysCallofDestinyIVfor6hours,hewillspend8hoursinhisgameroom.HowmanyhourswillRobertspendinhisgameroomifheplaysCallofDestinyIVforonly3hours?
33. TwelveSmooth-GlidepensandeightEasy-Writepencilscostexactly$16.00atOfficeWorld.SixSmooth-GlidepensandtenEasy-Writepencilscost$11.00atthesamelocation.HowmuchwillnineSmooth-GlidepensandnineEasy-WritepencilscostatOfficeWorld?(Disregardthedollarsignwhengriddingyouranswer.)
34. Intheequation3x2−16x=−20,whatisonepossiblevalueofx?
35. Inacertainancientfarmingcommunity,anthropologistsdeterminethatnewdwellingswereconstructedmonthlyasmodeledbythefunctionf(x)=2x+100,wherexisthecurrentmonthoftheyearandf(x)isthenumberofdwellingsconstructedbytheendofthatmonth.Additionally,theydeterminethatthepopulationgrewexponentiallyeachmonth,thankstothediscoveryofmorefertilelandforfarming.Thisgrowthismodeledbytheequationg(x)=3x,whereg(x)representsthecurrentpopulationattheendofagivenmonth.Whatisthesmallestintegervalueofx,with1representingtheendofJanuaryand12representingtheendofDecember,atwhichthepopulationsurpassesthenumberofdwellingsbuilt?
36. Inaschool-widecompetitionheldatSaulC.TighMemorialHighSchool,Olympiadteamsarechallengedtocomeupwithdifferentcircuitsinvolvingbothrealandimaginarycurrents.Imaginarycurrentsexistinspotswheretheelectricalenergyencounterszeroresistance,suchasthroughacoilorwire.Realcurrentsexistonlywheretheelectricalenergyheadedthroughthecircuitencountersresistance,suchaswhenalightbulb
“resists”thecurrentandtakesupsomeoftheenergycarriedthroughoutthecircuit.
ThemembersofTeamCharliedevelopacircuitinwhichthetotalcurrent,realandimaginary,canbemeasuredat50+12iamps.TheythenaddthecurrenttogetherwiththecurrentproducedbyTeamDelta’scircuit,40−9iamps.Finally,theydecidetomultiplytheresultingcurrent,inamps,byTeamEpsilon’stotalcurrent,60−2iamps.Whatisthefinalcurrent,inamps,aftertheentireprocessiscompleted?
Questions37and38refertothefollowinginformation.
Thechartbelowshowsthepopulationdistributionforthe2,400occupantsofthecityofCentreHill.
37. Ifthereareanequalnumberofadultsandchildren,andadultfemalesoutnumberadultmalesby200,whatisthesumofthewomenlivinguptownandthechildrenlivinginthesuburbsofCentreHill?
38. CentreHillplanstoannextheareaaroundanearbylake.ThisnewpartofCentreHillwillbecalled,appropriately,TheAnnex.TheAnnexwilladdtothecurrentpopulationofCentreHill.ThepercentofadultmaleslivinginUptownwilldecreaseto6%afterincorporatingTheAnnexintoCentreHill.IftheinformationfromPart1holdstruefortheoriginalfourdistrictsofthecityofCentreHill,thenhowmanyadultmalesliveinTheAnnex?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
SATEssay
ESSAYBOOK
DIRECTIONS
Theessaygivesyouanopportunitytoshowhoweffectivelyyoucanreadandcomprehendapassageandwriteanessayanalyzingthepassage.Inyouressayyoushoulddemonstratethatyouhavereadthepassagecarefully,presentaclearandlogicalanalysis,anduselanguageprecisely.
Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteinprintsothatwhatyouarewritingislegibletothosereaders.
Youhave50minutestoreadthepassageandwriteanessayinresponsetothepromptprovidedinsidethisbooklet.
REMINDER
— Donotwriteyouressayinthisbooklet.Onlywhatyouwriteonthelinedpagesofyouranswerbookletwillbeevaluated.
— Anoff-topicessaywillnotbeevaluated.
Asyoureadthepassagebelow,considerhowtheauthoruses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
“RobertRedford:ProtectOurWildHorses”byRobertRedford,publishedinUSAToday,November3,2014.
1 HorsesandIhavehadasharedexistence,personalandprofessional,foraslongasIcanremember.AndwhileIcarryastrongpassionforallhorses,mytenacioussupportforthepreservationofhabitatforwildlifeandtheAmericanmustangsderivesfromtheirsymbolicrepresentationofournationalheritageandfreedom.
2 AnyinfringementontheirlegallyprotectedrighttolivefreelyisanassaultonAmerica’sprinciples.Thevariedandsubjectiveinterpretationoflawsintendedtoprotecttheseanimalsonourpubliclands,continuestoleavewildhorsesunderattack.
3 Recent“stand-offs”betweenranchersandthefederalgovernmentarereminiscentofoldwesterns.ButthisAmericantragedydoesnothaveaheroridingintosavetheday,andwildhorseshavebecomethevictiminthecontroversiesoverourpubliclandresources.
4 In1971,asaresultofconcernforAmerica’sdwindlingwildhorsepopulations,theUSCongresspassedtheWildFreeRoamingHorseandBurroAct.TheactmandatedthattheBureauofLandManagement(BLM),protectfreeroamingwildhorsesandburros,underamultipleusemanagementpolicy,ondesignatedareasofourpubliclands.
5 TheBLMmanages245millionacresofourpubliclands,withlivestockgrazingpermitson155millionacres.Wildhorsesaredesignatedtoshareamere26.9millionacres.Thatmeansonly17percentofBLM-managedpubliclandismadeavailabletowildhorses.Wildhorsepopulationsvarybetween32,000and50,000,whilelivestockgrazingallocationsaccommodatenumbersinthemillions.Yes,inthemillions.
6 Advocatesareonlyaskingthatthehorsesbetreatedfairly.Wildhorsesareconsistentlytargetedastheprimarycauseofnegativeimpacttograzinglandsresultingfromdecadesofpropagandathatignoresmath,scienceandsolutionsthatcanbeimplementedtoday.
7 Ranchersholdnearly18,000grazingleasepermitsonBLMlandalone.GrazingcostsonBLMlandgofor$1.35percowandcalfpair,wellbelowthemarketrateof$16.ThispricedisparityderivedfromBLM’scurrentpermitpolicyestablishesanunevenplayingfieldongrazingeconomies.Understandably,ranchershaveavestedinterestinmaintainingthestatusquo.
8 Althoughlessthan3percentofAmerica’sbeefisproducedonfederalland,thissubsidizedgrazingprogramcoststhetaxpayermorethan$123milliondollarsayear,andmorethan$500millionwhenindirectcostsareaccountedfor.
9 Thelong-termeconomicsuccessofpubliclandsliesinmaintainingabio-diverseecosystemwithinitsboundaries.However,understandingtheneedforapreservationbalanceinthrivingagriculturalcommunitiesoftenbecomessidelined.
10 TheBLMneedstocomplywithitsoriginal“multipleuse”principleinmanagingwildhorsesandburros.InlightoftheinequitableshareoflivestockonBLMland,theongoingpersecutionofwildhorsesandthosethatvaluethemisunacceptableandthreatenstheveryspiritoftheAmericanWest.IurgeCongresstostandupformuchneededreformoftheBLM’swildhorseandburroprogramandlivestockgrazingonfederallands.
11 Nowisnotthetimetorepudiateenvironmentalbalance,butratheritisthetimeforallofustoworktogether—politician,advocate,rancher,scientist,andcitizen.OnlybydoingthiswilltheUnitedStatesmoveforwardandbealeaderinenvironmentalissuesandensuresustainabilitytoourdelicateecosystem.
WriteanessayinwhichyouexplainhowRobertRedfordbuildsanargumenttoconvinceCongresstodomoretoprotectwildhorses.Inyouressay,analyzehowRedfordusesoneormoreofthefeatureslistedabove(orfeaturesofyourownchoice) to strengthen the logic and persuasiveness of his argument. Be sure that your analysis focuses on themostrelevantaspectsofthepassage.
Your essay should not explain whether you agree with Redford’s claims, but rather explain how the author builds anargumenttopersuadehisaudience.
PRACTICETEST3ANSWERKEY
Section1:Reading
1. A2. B3. B4. D5. C6. A7. D8. C9. B10. C11. C12. B13. D14. B15. B16. D17. C18. A19. B20. B21. D22. B23. A24. D25. D26. A27. B28. D29. B30. B31. D32. C33. D
34. A35. C36. A37. C38. B39. D40. A41. D42. C43. C44. B45. B46. C47. D48. A49. C50. D51. D52. A
Section2:Writing&Language
1. B2. D3. A4. C5. B6. D7. B8. C9. A10. B11. D12. D13. C14. D15. A16. C17. B
18. A19. D20. B21. A22. D23. D24. B25. C26. A27. B28. A29. C30. D31. A32. D33. C34. A35. C36. B37. A38. C39. D40. B41. C42. A43. B44. D
Section3:Math(NoCalculator)
1. C2. C3. D4. A5. A6. D7. D8. D9. C
10. C11. A12. D13. B14. A15. C16. 2817. 018. 9419. 7
20.
Section4:Math(Calculator)
1. B2. A3. B4. D5. C6. D7. A8. B9. C10. A11. B12. D13. D14. B15. C16. A17. B18. C19. D20. B21. D22. D23. C24. A
PRACTICETEST3EXPLANATIONS
Section1:Reading1. A Although Jane resistsMr. Rochester, the first sentence of the passage indicates that her
conscience and emotions are actually favorably inclined towardMr.Rochester.Becauseshehaspositivefeelingstowardhim,(A)isanaccuratedescriptionofherattitude.WhileMr. Rochester perceives Jane to be uncaring, (B) is incorrect because the narrationindicatesthatshedoescarebutresistsherownfeelings.Similarly,(C)isincorrectbecausethefirstsentencetellsusshehaspositivefeelingsforRochester.BecauseJaneactscalmly,ignoringher emotions, she cannot accurately be described as reckless. Therefore, (D) isalsoincorrect,and(A)isthecorrectanswer.
2. B Becausequestions2and3aregeneralpairedquestions,considerquestion2andthetextualevidencegiveninquestion3atthesametime.Question2asksforthereasonJanerefusedRochester’s advances.Consider the lines referenced in question 3’s answer choices andwhether they support any of the answers in question 2. Choices (A), (C), and (D) ofquestion 3 do not support any of the answer choices in question 2, so they can beeliminated.Choice(B)ofquestion3(IwillholdtotheprinciplesreceivedbymewhenIwassane,andnotmad—asIamnow)providessupportonlyfor(B)inquestion2,so(B)mustbetheanswertobothquestion2andquestion3.TheseanswersmakesensebecausetheyindicatethatJaneresistsRochesterbecauseshewishestoholdtoherprinciples.
3. B See theexplanationforquestion2.Asnotedabove, (B)ofquestion3(Iwillhold to theprinciplesreceivedbymewhenIwassane,andnotmad—asIamnow)providessupportonly for (B) inquestion2, so (B)mustbe theanswer tobothquestion2andquestion3.Theseanswersmake sensebecause they indicate that Jane resistsRochesterbecause shewishestoholdtoherprinciples.
4. D There isnoevidence that Jane is literally insane.Rather, she is speakingmetaphoricallyabout theconflictbetweenher reasonandherdesires.Therefore, (A) iswrong.BecauseJanesaysthelaw(nothermentalstate)hasbeengivenbyGod,(B)isincorrect.Janesaysthatherinsanitytemptshertodisregardtheworthofherprinciples,anditisherprinciplesthatarepreventingherfromgiving in toMr.Rochester,soher insanity is temptingher togive in to Rochester. Therefore, (C) is wrong; her insanity does not urge her to rejectRochester,butrathertoaccepthisadvances.Choice(D)iscorrectbecauseherfeelingofinsanity is directly related to her emotions, as evidenced by the phrasewith my veinsrunningfire,andmyheartbeatingfasterthanIcancountitsthrobs,whichJaneprovidestoexplainwhyshefeelsinsane.
5. C Becausewrought describesMr. Rochester’s fury, and the passage says that his fury hasreacheditshighest,wroughtmustmeansomethinglike“increased.”Becausehammeredhasnothingtodowithincreasingfury,(A)isincorrect.Choice(B)alsodoesnothaveanythingto do with “increased,” so eliminate it. Because excited could mean “increased” when
applied to someone’s emotions, (C) accurately describes the passage’s use ofwrought.Sincewrung means squeezed and twisted, (D) does not describe the passage’s use ofwrought.Thecorrectansweris(C).
6. A Choice(A)iscorrectbecauseMr.RochesterdescribesJane’ssoulasstrongandherbodyasweakinparagraph5.Whileparagraph1statesthatRochesterlovesJane,andparagraph4 states that he is angry with her for refusing his advances, Rochester is angry for theentiretyofparagraph5.Therefore,itdoesnotcontrasthislovewithhisanger,and(B)isincorrect.ThoughRochesterspeaksofacage,heneveractuallymentionsabird;eliminate(C).Similarly,RochesteronlyreferstoJane’spurity.BecausehenevercallsJaneimpure,(D)isnotcorrect.
7. D Rochester is speaking metaphorically, not about a literal convict, so (A) is incorrect.BecauseheistalkingaboutJane,nothimself,(B)cannotbecorrect.WhenRochesterreferstobreakingtheprisonandJane’sbody,youcantellthattheinmate’sprisonreferstoJane’sbody, not the ideals of the time.Therefore, (C) is incorrect. The inmate refers to Jane’ssoul,so(D)accuratelydescribesRochester’suseofinmateandisthecorrectanswer.
8. C Think about the evidence in the passage that helped you answer the previous question:RochesterisusingthewordinmatetorefertoJane’ssoultrappedinherbody.Because(A)mentionsneithersoulnorbody,(A)isincorrect.Choice(B)refersonlytoJane’sbody,soitcannot be correct. Choice (C)mentions both Jane’s spirit and body (her brittle frame),providing good support for the answer to the previous question. Choice (D) makes nomentionofeithersoulorbody,soitisincorrect.Thecorrectansweris(C).
9. B BecauseJaneishavingahardertimeresistingRochesternowthatheissad,worsemeanssomething close to harder. Because less desirable,of lower quality, and unskillful allmean things other than harder, you can eliminate (A), (C), and (D). Because hardermatchesmore difficult, (B) accurately describes the passage’s use ofworse and is thecorrectanswer.
10. C PathosreferstoJane’semotions,sotheparagraphdepictsJaneovercomingheremotions.Therefore, (A) cannot be correct. Jane makes no allusion to social conventions, whichmakes (B) incorrect. However, because the paragraph depicts Jane overcoming heremotions, (C) isagooddescriptionof Jane’svalues.SinceJanebattles toovercomeherfeelings,(D)isnotanaccuratedescriptionofhervalues.Choice(C)istheanswer.
11. C Clinton’sspeechspeaksoutagainstgenderinequalityallovertheworldandadvocatesinfavor of these injustices being amended. Choice (C) best reflects this idea. AlthoughClintoncriticizeshowwomenaretreatedworldwide,shedoesnotcounteranyarguments,so eliminate (A). She does not take a scholarly approach to analyze women’s place insociety,soeliminate(B).Clintonisnotmediatingbetweentwoparties,soeliminate(D).
12. B Althoughwomenplaydifferent roles in society,manyof these roles arenot appreciated.Choice(B)mostaccuratelyreflectsthismeaning.Choices(A),(C),and(D)havemeaningsthatarerelatedtothewordvaluedbutarenotusedinthecontextoftheword’suseinthe
passage.
13. D Clintondiscussestheimportanceofconferencesincompellingpeopletoconsiderimportantissues.ShethenmentionstheconferenceinNairobiashelpingtobringtolightthecrisisofdomesticviolence.Therefore, (D) is thecorrectanswer.Thepassagedoesnotclaimthatthe crisis of domestic violencewas not solved, so eliminate (A). The passage does notdiscussanyonequestioningthereasonforholdingthecurrentconference,soeliminate(B).AlthoughClintonmentionsthefactthattheexperiencesofwomentendtogounnoticed,thisisnotherreasonformentioningtheconferenceinNairobi.Eliminate(C).
14. B Thinkabouttheevidenceinthepassagethathelpedyouanswerthepreviousquestion:Itisconferences like this that compel governments and peoples everywhere to listen, look,andfacetheworld’smostpressingproblems.ShethenmentionstheconferenceinNairobiashelpingtobringto light thecrisisofdomesticviolence.Choice(B)provides themostsupport forwhyClintonmentions theconference inNairobi.ThecurrentconferencewasnotheldbecauseoftheconferenceinNairobi,soeliminate(A).Womenbeingtheprimarycaretakers of the world is not the reason for mentioning the conference in Nairobi, soeliminate(C).WomendyingfrompreventablediseasesisnotthereasonformentioningtheconferenceinNairobi,soeliminate(D).
15. B Clintondiscusseshowsomewomenareabletoattendaconferencethatspeaksoutagainstthe inequalities against women, while others are not able to do so. Choice (B) mostaccurately reflects this idea.Clinton does not differentiate between peoplewhowork inschools and hospitals, so eliminate (A). Clinton does not mention employed women,unemployedwomen,orwomenwhocanorcannotvote,soeliminate(C)and(D).
16. D Choices (A), (B), and (C) are each discussed in paragraph 4, so eliminate them. Thepassagedoesnotdiscusswomensufferingfromwidespreadunemployment, so (D) is thecorrectanswer.
17. C Inparagraph4,Clintondiscusseswomenwhohaveavoicestandingupforwomenwhoareunable tostandupfor themselves.Choice(C)mostaccuratelyreflects this idea.Choices(A),(B),and(D)havemeaningsthatarerelatedtothewordspeakbutarenotusedinthesamecontextasthiswordisusedinthepassage.
18. A Inparagraph8,Clintonargues thatwomen’s rights are alsohuman rights,whichmatches(A).Women’sattendanceattheconferenceisnotdiscussedinthisparagraph,soeliminate(B).Clintondoesnotclaimthatwomen’srightshaveaspecialnature,justthattheserightsarethesameashumanrights,soeliminate(C).Clintondoesnotsuggestthatwenolongerneed to focus on women’s problems; this is the opposite of what is discussed in thepassage,soeliminate(D).
19. B Thinkabout theevidence in thepassage thathelpedyouanswer thepreviousquestion: Inparagraph8,Clintonarguesthatwomen’srightsarealsohumanrights.Choice(B)providesthemostsupportfortherhetoricaleffectofthephrasediscussedinthepreviousquestion.Although Clinton discusses the respect and protection of women’s rights, this is not the
phrase that best supports the rhetorical effect of the discussed phrase, so eliminate (A).Givingexamplesofthespecificrightsinquestiondoesnotprovidethebestsupportfortherhetoricaleffectofthediscussedphrase,soeliminate(C).Theattendanceofwomenattheconferenceisnotrelatedtothediscussedphrase,soeliminate(D).
20. B Inparagraph2,Clintondiscussestheexperiencesofwomenthroughouttheworld:Yetmuchof theworkwedo isnotvalued—notbyeconomists,notbyhistorians,notbypopularculture,notbygovernmentleaders.Choice(B)mostaccuratelyreflectsthisidea.Clintondoesnotstatethattheseleadersarepurposelyworkingagainst theprosperityofwomen,soeliminate(A).Choice(C)iscontradictedbywhat thepassagestates,soeliminatethischoice.Althoughtheseleadersmaynotvaluetheworkofwomen,thepassagedoesnotstatethattheseleadershavemadeitunacceptabletodiscusswomen’srights,soeliminate(D).
21. D The graphic shows poverty rates inAmerica divided by gender and age.Across all agegroups,womenexperiencehigherratesofpovertythantheirmalecounterparts.Thisfallsinline with the passage’s assertion that women comprise 70 percent of the world’s poor.Therefore,(D)iscorrect.Choice(A)isincorrectbecause,whilethegraphicshowsahighgenderdisparityamong those65andolder, it refersonly toAmericanpoverty rates.Thegraphicactuallystatesthat15.4percentofAmericanwomen18to65areimpoverished,notthattheymakeupthatpercentageoftheworld’spoor.Therefore,(B)isincorrect.Andthereisnomentionofhowmanychildrenareimpoverishedworldwideineitherthegraphicorthepassage,so(C)isincorrect.
22. B Thenext-to-lastsentenceofthepassagestatesthatSeenthroughouttheprocessionisthatbalanceofthemonumentallysimpleandtheactual,andgoesontolistseveralmoretypesof balance, thatHeraclitus, the philosopher,wrote of in the sixth centuryB.C. This issupportfor(B).Whiletheauthordoesdiscusstherepresentationofthepassageoftimeinthefrieze,thisideaisnotconnectedtoHeraclitus,so(A)canbeeliminated.ThementionofHeraclitusalsodoesnotsupporttheideathatthefriezeischaracteristicallyGreek,so(C)is incorrect.Choice (D) is tempting, if the entiretyof the sentencementioningHeraclitusisn’t included; however, the balance mentioned isn’t between mortals and the goddessAthena.
23. A InthefirstparagraphofPassage1,theauthorproposeshisideaofwhatthefriezeprobablyrepresents.Inthesecondparagraph,hedescribesthefrieze.Thismatches(A).Choice(B)mayseemcloseatfirstbecausetheauthordoesindicatethatthesubjectofthefriezeisstilla matter of scholarly dispute. However, he does not question someone else’sinterpretation,so(B)isincorrect.Choice(C)fallsintothecategoryof“toonarrow”:Theauthordoesdescribethefrieze,butonlyinparagraph2.Choice(C)doesn’ttakeparagraph1intoaccount.Sincenohistoricaloverviewisgiven,(D)isalsoincorrect.
24. D By using the word unparalleled, the author is saying that it is unusual to see arepresentationofafestivalinclassicalGreekartthatshowsdeitiesinattendance.Choices(A),(B),and(C)donotmatchthemeaningof“unusual,”and(D)does.Therefore,(D)istheanswer.
25. D Passage2beginswiththefirstparagraphdescribingwaysthattheparticularpieceofartinquestionisunusualintheworldofclassicalGreekart:Itshowsdeitiesattendingafestival,includingAthena,andtheyareignoringthepeplos.Thisrepresentsaflagrantbreachwithtradition thatrequiresexplanation.Paragraph2continueswithanexplanationofwhat itcannotrepresent.SincetheauthordoesnotsaythatthefriezecannotdepictthePanathenaicprocession,(A)isincorrect.Theauthoralsodoesnotdiscussthepassageoftime,so(B)isincorrect.WhiletheauthorgoesontodescribetheheroesofMarathon, thequestionisaskingaboutthepurposeofthefirsttwoparagraphs,so(C)isatemptingtrapanswerbutmustbeeliminated.Choice(D)comestheclosesttowhattheauthorisdoinginthefirsttwoparagraphs,describingproblemsinthetraditionalinterpretationofthefrieze.
26. A Paragraph2beginsbydiscussingwhataclassicalAthenian,orresidentofAthens,wouldnothavethoughtashelookedatthefrieze,thatis,thatitwasarepresentationofhimself.Inthesecondsentence,mortalcouldbereplacedbyclassicalAthenian,because thesubjectmustbesomethinggreaterthanaresidentofAthens.Therefore,(B),(C),and(D)donotfit,and(A)isthecorrectanswer.
27. B Paragraph2beginsbydiscussingwhataclassicalAthenian,orresidentofAthens,wouldnothavethoughtashelookedatthefrieze:“thereIgo”orevenmorevaguely“therewego.”Thenextsentencetellsusthatthesubjectofthefriezemustbemorethanmortal,ormorethanabouttheclassicalAthenianlookingatit.Puttingthesetogether,youcansurmisethatwhentheauthorsaysthattheclassicalAthenianwouldn’tsay“thereIgo,”hemeansthatthefriezeisnotabouttheclassicalAthenian.Paragraph3confirmsthisideabysayingwemust rule out…that it is a contemporary or generic statement of the Panathenaicprocessionconductedbythecitizens….Sincetherewasneveradiscussionofthefiguresthemselvesandwhethertheyrepresentedindividualcitizens,(A)isincorrect.Choice(B)doesmatchprettyclosely,sokeepit.Choice(C)hasmoretodowithwhoparticipatedintheprocessionratherthanthesubjectofthefrieze,soeliminate(C).Choice(D)goestoofarbecausetheauthorneversaysthatthesubjectofthefriezeshouldbeobvioustomodernviewers.Choice(B)isthecorrectanswer.
28. D Think about the evidence in the passage that helped you answer the previous question:Supportfor(B)inquestion7comesfromparagraph2andparagraph3,so(A)and(B)canbeeliminated.Whileitmaybetruethattheexplanationmusthavebeenapparent to theclassicalAthenianwhoknewthisbackground,thisdoesnotsupporttheideathatthefriezecannot represent a human event, so eliminate (C). Choice (D) directly supports (B) inquestion27andisthereforethecorrectanswer.
29. B The author of Passage 2 proposes that the frieze shows the fighters of Marathoncelebrating theprime festivalof thegoddessAthena…asa thanksgiving forheraidatMarathon and afterwards. This ties into (B), Athenian men who died in battle atMarathon.Thereisnoindicationthattheauthorbelievestheyouthswerefromaroundthetime the Parthenon was built, so eliminate (A). Choice (C) is too broad because itincludes all people of Marathon who were worshipped as heroes, whereas the authorspecifies the fighters ofMarathon, so eliminate (C).Choice (D) contradicts the author’sdescriptionthatthefriezeisarepresentationofthefighters,notpurelydivineparticipants,
soeliminateit.Choice(B)istheanswer.
30. B Passage1doesnotfocusondeterminingthesubjectofthefrieze—that’sonlyinthefirstparagraph.Eliminate(A).Passage2considershowGreekcitizensmighthaveviewedthefrieze,butPassage1doesnot.Eliminate(C).Passage1alsodoesnotentirelyreject thetraditionalperspective,soeliminate(D).Passage1doesgiveadetaileddescriptionofthefiguresinthesecondparagraph,so(B)isthecorrectanswer.
31. D Think about the evidence in the passage that helped you answer the previous question:Passage1givesadetaileddescriptionofthefiguresinthefriezeinthesecondparagraph.Only(D)referenceslinesthatgiveadetaileddescriptionoffiguresinthefrieze,so(D)isthecorrectanswer.
32. C Choice(A)isincorrectbecausethemulesarenotunusual.Theyareanexamplefamiliartomany people to help readers understand what the author is describing. Choice (B) isincorrectbecausethemulesarenotpartofacounterargument.Choice(D)ispartiallytrueinthatsterilemulesarepartofthelargerargumentthatthewhiptailsareunusual;however,thespecificpurposeofmentioningthesterilemulesatthatpointinthepassageistogiveanexampleofwhyscientistsbelievethathybridsaresterile.Thus,(C)iscorrect.
33. D The lizardsareunusual to thepointofbeingremarkable, so (D) iscorrect.Theyarenotespeciallybeautiful,(A),orconspicuous,(B).Choice(C)isatrapbecauseaggressiveisrelatedtostrikingbutnotcontextuallycorrectinthisinstance.
34. A The scientists do seem to be friends, as stated in (D), but the best description of theirrelationshipinthisarticleisasateamofscientistsworkingonparthenogenesis,so(A)iscorrect.Theyarenotrivals,so(B)isincorrect.StowersisaninstitutewhereDr.Neavesserved as president, so they were not trying to disprove theories from Stowers, whichmakes(C)incorrect.
35. C Choices(A)and(B)aretooextreme,sotheyareincorrect.Choice(D)referstosomethingthatoftenhappensinevolution,butevolutionitselfdoesn’tisolatepopulations.Choice(C)mirrorswhatissaidinthepassageandisthecorrectanswer.
36. A Think about the evidence in the passage that helped you answer the previous question.Choice(A)iscorrect,sincethelineTheevolutionofanewanimalspecies isusuallyadrawn-out affair supports the idea that evolution usually takes many years to happen.Choices(B),(C),and(D)donotsupportthisandarethereforeincorrect.
37. C The Doctor thought it was a good time to move forward due to the new technologyavailable,soitwasanopportunemoment,(C).Thepassageimpliesthatit’stakenalongtime,butanhourlate,(B),istooshortatime.It’snotafestival,so(A)isincorrect,norisitaloftyideal,making(D)incorrect.
38. B Choices(A),(C),and(D)arementionedinthepassageandareaspectsofparthenogenesis.Choice (B) ismentioned, but only the female lizards can clone themselves, so any cells
fromamalewhiptailwouldbeuselessforparthenogenesis.Therefore,(B)istheanswer.
39. D Choice (A) is the opposite ofwhat the passage says, so it’s incorrect. The lizards havedifferentsetsofchromosomes.Thewhiptailsweren’tdiscoveredinthe1960s;theirgeneticmakeupwas found to be strange, so (B) iswrong.The lizards don’t require amale andfemale,(C),buttheclonescomeonlyfromfemalewhiptails,sotheclonesmustbefemale.Thus,(D)iscorrect.
40. A Think about the evidence in the passage that helped you answer the previous question:Choice(A)clarifiesthattheclonescomeonlyfromfemalewhiptails,sotheclonesmustbefemale.Choices(B),(C),and(D)donotsupportthisandarethereforeincorrect.
41. D Choices (A) and (C) aren’t definitive enough and (B) is too general, making them allincorrect. Choice (D) addresses the author’s argument that mating animals in captivitydefiesideasabouthowspeciesevolve.Iflizardsneverclonethemselvesinthewild,thenspeciesoutsideofthelabdon’tevolvethroughcloning.Thus,(D)iscorrect.
42. C The word somehow implies that scientists still don’t understand how female whiptailsclonethemselves,so(C)iscorrect.Choice(A)isincorrectbecauseitusesthewordswitchinanincorrectandmisleadingway,while(B)istoovagueanddoesn’tanswerthequestion.Choice(D)addresseswhythewhiptailsclone,butthesentenceisreferringtohowtheydoit,so(D)isincorrect.
43. C LookearlierinthesentenceforthephrasetheEarth’ssurfacesankmorethan1mile.Gothrough the answer choices to find the one that matches this description. Choice (C) iscorrectbecauseacraterisa“large,bowl-shapedcavityintheearth.”Eliminate(A),(B),and(D),asnoneofthemmatchthisphysicaldescription.
44. B Thesecondparagraphprimarilydiscussestheextensivetimerangeofvolcaniceruptions,startingasfarbackas400,000yearsagoandasrecentlyas600yearsago.UsePOEtofind the answer choice that matches this information. There is no evidence of anothereruptionthiscenturybasedonthepassage,soeliminate(A).Choice(B)worksbecauseitshowsthelargerangeoftimeingeologicterms.Choice(C)almostworks,buttheauthorisnot just trying tobe ironic.The information isnot relevant to theparagraph,soeliminate(C). Choice (D) is incorrect because a relative term doesn’t fit; recently isn’t beingcomparedtoanyothervariables.Choice(B)istheanswer.
45. B Thepronoun thatprecedes temblor, so itmust refer to something earlier in theprevioussentence. The first sentence discusses a magnitude 5.4 earthquake struck 6 milessoutheastofthecaldera,so(B)iscorrectbecausethetemblorendedtwodecadesoflowquakeactivity.
46. C Thethirdsentenceinparagraph7statesthatthegeologistsstudiedtreesthatweredyingonMammoth Mountain from carbon dioxide, and that this would often precede volcaniceruptions.Thisinformationsuggeststhepossibilityofavolcaniceruption.Choice(C)isagoodmatchforthisinformation.Thereisnoevidencetosupport(A)and(B),soeliminate
them.There is nomention ofgeodeticequipment in this paragraph, so eliminate (D) aswell.Choice(C)istheanswer.
47. D Thinkabouttheevidenceinthepassagethathelpedyouanswerthepreviousquestion:Thegeologistsaremonitoringthecalderatotrytopredictafutureeruption.UsePOEtofindthebest reference from the passage to the previous question. Eliminate (A) because thatsentence refers to eruptions from centuries ago.Choice (B) does not reference geologistactivity at all, so get rid of it.Eliminate (C) because it discusses the equipment, not thegeologists.Choice(D)worksbecauseitdetailsstudiesfromtheUSGSregardingformsofevidencethatoftenprecedevolcaniceruptions.
48. A Thefinalsentenceinthelastparagraphstatesthatgeologiststhinkthatthechancesofaneruptionintheareainanygivenyeararequitesmall.Thiscontradictstheinformationin(B)and(C),soeliminatethem.Earthquakesareonlyasmallpartoftheoverallpassage,soeliminate(D)becauseitistoolimited.Choice(A)iscorrect.
49. C UsePOE to find the answer choice that is best supportedby thepassage.Choice (A) isincorrectsinceitwasboththeInyoCratersandMonoCratersthaterupted600yearsago.Choice (B) almost works, but the passage never suggests that Mammoth Mountain isactually active, as opposed to the larger chain—the Long Valley Caldera—it’s part of.Choice (C) is agood fitbecause the seventhparagraphstates thatsymptomsof volcanicunrest may persist for decades or centuries at large calderas, such as Long ValleyCaldera. The information in (D) is mentioned in the first paragraph, but there is noevidencethatreferstoMammothMountain,soeliminateit.Choice(C)iscorrect.
50. D Thinkabouttheevidenceinthepassagethathelpedyouanswerthepreviousquestion:Theseventh paragraph states that symptoms of volcanic unrest may persist for decades orcenturiesatlargecalderas,suchasLongValleyCaldera.Thissentenceisreferencedby(D),while theotherchoicesdonot relate to thecorrectanswer to thepreviousquestion.Therefore,(D)istheanswer.
51. D Thelastfewsentencesoftheseventhparagraphstatethatsymptomsofvolcanicunrestmaypersistfordecadesorcenturiesatlargecalderas,suchasLongValleyCaldera.Studiesindicatethatonlyaboutoneinsixsuchepisodesofunrestatlargecalderasworldwideactually culminates in an eruption. The swelling of the LongValleyCaldera is part ofthesesymptoms,sothisbasicallysaysthatthereisnodefinitiveoutcomethatresultsfromthem.Choice(D)isagoodanalogyforthisinformationandthereforethecorrectanswer.
52. A 2015 isat the far rightendof thegraph,atwhichpoint the line indicating thenumberofcumulativeearthquakeshitsabovethe1.2line.However,eachnumberontherighty-axisneedstobemultipliedby105,sothenumberofcumulativeearthquakesisactuallygreaterthan120,000.Therefore, (A) is the correct answer.Choice (B) is incorrect for the samereason; earthquakes per week are tracked on the right axis, not the left. Choice (C) isincorrect because 1.2 needs to be multiplied by 105. Choice (D) is incorrect becausecumulativeearthquakesaretrackedontherighty-axis,nottheleft.
Section2:WritingandLanguage
ParkRangers,Naturally1. B ThisquestionasksfortheanswerchoicethatwouldNOTbeacceptable,sotheunderlined
portioniscorrectasitstands.Choice(B)isthecorrectresponsebecausetheotheranswerchoicesmatch theunderlinedportion—theysetoff theabbreviationNPS from itsofficialnameofNationalParkServices.
2. D Use POE here, since there doesn’t seem to be a common thread being tested on thisquestion. Eliminate (B) and (C) because pulchritudinous andpretty basically mean thesame thing,making these choices interchangeable and impossible to choosebetween.Goback to the passage and notice that it already uses the phrasemarveled at the naturalbeauty,sousinganotherwordtodescribeitsbeautyagainwouldberedundant.Therefore,eliminate(A).Choice(D)isthemostconciseresponse,andthereforethecorrectanswer.
3. A Noticethequestion!You’reaskedforachoicethatwillincludedetailtoclarifyday-to-dayoperations.Lookatthenextsentence,whichdescribestheactivitiesoftheparkrangers.Itstatesthat theyareinchargeof thepark’supkeepandmaintain thebalancebetween thewildlife and plant species and the human visitors. Both of these correspond with theunderlined portion ofmaintenance and tours. Nothing is stated about the length of thetasks,whetherornottheyarerepetitive,orthepoliticalaspectsofthem,soeliminate(B),(C),and(D).Choice(A)providesthedetailthequestionasksforandisthecorrectanswer.
4. C Theideabeforethepunctuation,Theseparkrangersareresponsiblefortheupkeepoftheparks, is a complete idea, as is the clause, theirmain responsibility is tomaintain thebalancebetweenthewildlifeandplantspeciesandthehumanvisitorsthatcometotheparkseveryday, thatfollowsit.Therefore,acommaalonecannotseparatetwocompleteideas,soeliminate (A)and(D).Eliminate (B)aswell,becausepunctuation isneeded toseparate two complete ideas. Choice (C) is the correct answer because a dash (HALF-STOPpunctuation)canbeusedtoseparatethesecompleteideas.
5. B Theparagraphdescribestheparkrangersasscientists,educators,andprofessionalswithbackgrounds in law enforcement and firefighting. Look for the answer choice that isconsistentwiththistypeofdiversity.Eliminate(A)becausepollutionisnottalkedaboutintheparagraph,aswellas(C)becausetheparagraphisnotinterestedinthevisitorstothepark.Ecology is too limited for (D), so eliminate it. You’re leftwith (B),which is thecorrectanswer.
6. D Look to theprevious sentence,whichdescribes someof thepark rangers, andnotice thephraseSomearescientistswhorevel.Since thenextsentence isalsodescribingtheparkrangers, itneeds tobeconsistentandparallelwith theprevioussentence,so itshouldbeSomeareeducatorswhohelp.Choice(D)isthecorrectresponse.
7. B Noticethat theanswerchoicesarepronouns,so lookat thecurrentsentencetodeterminewhat thepronoun them refers to; thismightbeunclearbecausebothpostsandmunicipal
services are used in the sentence.Eliminate (A) and (C),which are ambiguous, and (D)becauseit’ssingularandambiguous.Choice(B)istheclearest,mostprecisechoiceandisthereforecorrect.
8. C UsePOEtofindtheclearestandmostconciseresponse.Choice(A)isawkwardbecausevisitorsareontherisedoesn’tnecessarilyrefertotheirnumbers,soeliminateit.Choice(B) is incorrect, as poised on the rise is an idiom error and should be poised to rise.Choice(D)isawkward,unclear,andredundant,aspoisedontheriseseemstobereferringtothenumbers,whicharealsodescribedasgrowing.Choice(C)istheanswer.
9. A Check the underlined portion of this sentence, which states that the visitation numberspeaked in1987,andcompare itwith thechart.This information is true,as is thesecondphrase,thegeneraltrendhasbeenonasteadyrise,sokeep(A).Eliminate(B)because1987isn’treallythemid-1980sandhasnottaperedoff.Choice(C)issimplyincorrect,and(D)canbeeliminatedbecausethegrowthhasbeensomewhaterraticandnotlinear.Choice(A)iscorrect.
10. B The question asks for the LEAST acceptable response to the underlined portion, so theunderlined word is correct. Use POE to eliminate answer choices that are similar inmeaningtoforetold.Choice(B)istheoddmanoutbecausestatedjustmeans“toexpressor declare,” whereas the other choicesmean “to predict.” Therefore, (B) is the correctanswer.
11. D Theideabeforethepunctuation,Thepark-rangerworkforce issodiverse, isacompleteidea,as is theclause that follows it, thereareactuallya fewcommonattributesamongparkrangers.Acommacannotseparatetwocompleteideas,soeliminate(A).Lookat(C)and (D), since the transitionwordsbecause andalthough are exact opposites, and thenrefer back to the sentence to see if the two ideas are complimentary or contrasting. Thewordsusedinthesentencearediverseandafewcommon,sopickthetransitionwordthatindicatesacontrast.Choice(D)istheanswer.
TheFerryGodfather12. D Sentence2beginswiththephrasethispart.Becauseapronounisused,gobackandfind
thenoun it refers to.Sentence4 states thatLincolngranteda specialprovision for thatpartofVirginia,sothepronoun this refers to thepartofVirginia.Therefore,sentence2shouldgoaftersentence4,and(D)isthecorrectanswer.
13. C Theanswerchoicesheresuggestthatthisquestionistestingpronouns.Gobackearlierinthesentencetofindwhatthepronounrefersto.It’stheUnitedStates,whichisacollectivenoun and therefore singular. Eliminate (A) and (B). Eliminate (D) as well because acontractionisnotnecessaryhere.Choice(C)isthecorrectanswer.
14. D This question is testing comma usage, so check to see if the comma is separating twocompleteideasorifit’snecessarytobreakuptheincompleteideas.Neitherappearstobethecase,andthissentencedoesnotneedabreak.Choice(D)iscorrect.
15. A UsePOE to determinewhether the information in themap is consistentwith the answerchoices. Choice (A) seems like a good choice because Harpers Ferry is directly at themeeting point of theShenandoah andPotomacRivers, so keep it. Eliminate (B) becausethere is not enough information to support the 20-mile northeast approximation fromBolivartoHarpersFerry.Choice(C)isalsounsupportedbecauseHarpersFerryisacrossthe Shenandoah from Virginia, not Maryland, so eliminate (C). Choice (D) is incorrectbecause theAdirondackMountains are not evenon themap (they are actually in upstateNewYork).Choice(A)iscorrect.
16. C Use POE for this question, as there doesn’t seem to be a specific rule being tested.Eliminate(A)becauseitisanambiguouspronounthatcouldrefertoeitherthearmoryortheCivilWar.Choice(B)isincorrectbecausewarshouldnotbethesubjectofthisphraseasthoughitsawHarpersFerryliterallychangehands.Samegoesfor(D),aseightshouldnotbethesubjectofthephrase.Choice(C)makesitclearthatitwasHarpersFerry thatchangedhands,makingitthemostpreciseanswerchoiceandthecorrectanswer.
17. B Ifyoulookattheanswerchoices,youmaynoticethatthereisn’tahugedifferencebetweenthem;watchoutforredundancyandtrytobeconcise.Thesentenceusesthewordcrucialalready,soeliminate(A),(C),and(D),whichmeanthesamethingascrucial.Theansweris(B).
18. A Notice thequestion!UsePOE to findananswer choice that is consistentwith themajorimportance ofBrown’s raid.Anational discussion started because of the raid, so keep(A). Choice (B) suggests the raid’s importance, butHermanMelville is not mentionedanywhereelseinthepassage,soeliminate(B).Eliminate(C)and(D)becauseneitherdealswiththeimpactoftheraidafterthefact.Choice(A)istheanswer.
19. D Thecorrectanswertothisquestionneedstocontrastthepositivetermsofheroandfreedomfighter, so eliminate (B), which is also positive. Eliminate (A) because, taken literally,filthymeans“unclean”anddoesn’treallycontrasthero.Choice(C)isslang,andthereforeincorrect. Choice (D) works because vile is consistent with terrorist and contrasts thepositivetoneofhero.
20. B Use POE to find the clearest and most concise answer choice. Eliminate (A) and (D)becausebothuse the ambiguouspronoun it.Choice (C) is incorrect because it’s unclearhowBrown’s rally was named. Thiswould change the overallmeaning of the sentence.Choice(B)istheclearestandmostconcise,andthereforethecorrectanswer.
21. A The underlined portion uses a period, so check for complete and incomplete ideas. Theperiodhereseparatestwocompleteideas,sotheperiodisSTOPpunctuationthatisbeingusedcorrectly.Eliminate(D)becausethetransitionandisusedafterthesemicolon,turningthecompleteideaintoanincompleteone.Choice(A)iscorrect.
22. D TheunderlinedportionusesHALF-STOPpunctuation(acolon)toseparatethetwoideas,so the first idea must be complete in order for the colon to work. The first idea isincomplete,soeliminate(A).Alsoeliminate(B)and(C),asSTOPpunctuationcanbeused
onlybetweentwocompleteideas.Choice(D)istheanswer.
StefanZweig’sReturn23. D Noticethequestion!WhenaquestionasksfortheLEASTacceptablealternative,youcan
assumethattheunderlinedportion,largeamount,iscorrect.Choices(A),(B),and(C)caneach be defined as a significant quantity of something, whereas (D) is associated withspace,makingittheLEASTacceptableanswerandthereforethecorrectanswer.
24. B In the followingsentence, theauthorwondersabout thesudden interest inZweig’sworkafteritsobscurity,soanacceptablealternativetotheunderlinedwordwouldbesomethingsimilartoimportant.Relevantisthebestmatch,so(B)isthecorrectanswer.
25. C Noticethequestion!Thebestwaytocombinethesetwosentenceswouldbetoturnitintoone concise sentence. Choice (A) can be eliminated because the only difference is thesemicolon,whichbasicallyservesthesamepurposeasaperiod.Choice(D)isawkwardbecause eliteness is an improper form of the word elite. Therefore, (C) is the answerbecauseit’sgrammaticallycorrectandconcise.
26. A This question is testing theuseof apostrophes, and since thephrasecity’s cultural eliteindicatespossession,checktoseewhetherornotthenounissingularorplural.Sincecityissingular,thenthe’siscorrect,and(A)isthecorrectanswer.
27. B ThepassagestatesthatZweigpublishedanearinfinitudeofworksandthengoesontolistwhattheworksare.Therefore,theexamplesofthoseworksarenecessarytothesentence.Eliminate (C) and (D).Alsoget ridof (A) since the examples arenot forother typesofworkZweigcouldget.Choice(B)isthecorrectanswer.
28. A TheparagraphopensbydescribingZweig’srelationshipwithViennaastenuousand thengoesontodescribehimasacommittedpacifist.Thenextsentencestatesthathispacifismwasnolongerlookedonwithsuchunderstanding,whichmeansthattheconjunctionmustshowacontrast.Eliminate (B)and(C).Choice(A) iscorrectbecausehowever shows aclearshifttoanewidea.
29. C The answer to this question needs to address Zweig’s personal stake in the Europeanconflict, so eliminate (A) and (D), as neither choice addresses Zweig himself. Alsoeliminate (B)because thepassagenever states that hemoved toAmerica.Choice (C) iscorrectbecauseitstatesZweighassuchprideinhishomecountryofVienna.
30. D Basedontheanswerchoices,thisquestionistestingpronounuses.Sincethepronouninthesentence refers to theprivilegedman, eliminate (A);which cannot be used to refer to aperson. The correct answer will be an object pronoun, so eliminate (B) because it’s asubjectpronoun,and(C)becauseit’spossessive.Choice(D)istheanswer.
31. A Notice that the question asks for the choice that best supports the idea presented at thebeginning of the sentence, which emphasizes more “masculine” figures. Competitivesports might be something that is traditionally considered “masculine.” Therefore, the
sentenceseemstomakesenseasis,and(A)isthecorrectanswer.Theotherchoicescanbeeliminatedbecausenoneofthemrefertomasculinebehaviororactivities.
32. D Based on the answer choices, this question is testing pronouns. Be careful, however,because the underlined portion is not addressingZweig, but rathermany of us. You caneliminate(A)and(C)becausethosearesingularpronounsandthereforeinconsistent.Thenextphrasestatesourlonging,sotheuseofourin(D)createsconsistency.
33. C Checkouttheanswerchoices,whichshowthatverbtenseistheconceptbeingtestedhere.LookattheearlierpartofthesentencethatstatesWeknowthatthingscannotbeandselectthechoicethatisconsistentwiththeverbknow.Choice(C)isconsistentandthereforethecorrectresponse.
ForFigs?TheChimpsAren’tChumps34. A Based on the answer choices, the question is testing comma usage. In a list of items, a
commamustbeusedaftereachiteminthelistandbeforeand,soeliminate(D).Also,(B)and (C)useunnecessary commas afterbacon and strips, and there is no reason to slowdowntheflowofideasinthissentence.Choice(A)iscorrect.
35. C Notice the question and use POE. Although the passage is ultimately concerned withchimpanzees seeking fruit, there is no information that suggests the banana was itstraditionaldiet. Eliminate (A). The chimpanzeeswaking and sleeping habits are neverdiscussed in the passage, so get rid of (B). Choice (C) works because the followingparagraphdiscusseshowthenomadicchimpanzeessetuptheircampsiteswithinstrikingdistanceoftheripefruits.Therefore,keep(C)becauseit’sconsistentwiththisparagraph.Humanevolution isn’tdiscussedanywhere in thepassage, soeliminate (D).Thecorrectansweris(C).
36. B Notice thequestion!Look for thechoice that servesasa transitionand introduction.Thepreviousparagraphendswithforachimpanzee,everydayduringafruit-poorseasoncanbelikeBlackFridaywhereallthe“shoppers”wantthesamehotitem.UsePOEtofindthechoicethatcorrelateswiththisstatement.Eliminate(A)becausethevalueofthedealsis irrelevant. Eliminate (C) and (D) because Thanksgiving isn’t necessary for thecomparison between how chimpanzees get food and Black Friday. Choice (B) is theanswer.
37. A Look out for the pronoun changes in the answer choices, specifically its and their. Thesubjectofthesentenceischimpanzees,apluralnoun.Eliminate(C)and(D)becauseitsissingular.Eliminate(B)becausetheverbsetsissingularandisnotconsistentwiththepluralsubjectchimpanzees.Choice(A)iscorrect.
38. C Thedefinitioninthesentenceisquicktodisappear,sousePOEtofindthewordthatmostdirectlymatchesthemeaning.Eliminate(B)and(D)becausedesiccatedmeansto“dryup”and eternal would be the opposite of quick to disappear.Ephemeral means “brief” or“fleeting,”soit’sagoodmatch,making(C)thecorrectanswer.
39. D Thewordthan,acomparisonword,isusedseveraltimesintheanswerchoices.Figureoutwhatisbeingcomparedandeliminateanswerchoicesthatdon’tmatch.Thesentencebeginswithwhenthefruitswere,sotheanswerisgoingtohavetocomparetoatimeperiod.Only(D)doesthis,soit’sthecorrectanswer.
40. B Use POE to find aword that is consistentwith the paragraph,which is a lack of food.Gobbled,chomped,andateallrefertotheconsumptionoffood,butnotnecessarilyalackof food, so eliminate (A), (C), and (D).Depletedwould fit because itmeans to “useupcompletely.”Choice(B)iscorrect.
41. C Theanswerchoicessplitbetweentheverbshaveandhas,sofindthesubjectandpicktheverbthatisconsistent.Thesubjectinthiscaseisfindings,whichisplural,soeliminate(A)and (D), sincehas is singular.Eliminate (B) because theverb lead is present tense, buthaveispresentperfectandasimplepasttenseverbisneeded.Theansweris(C).
42. A Thisquestion is testingdiction,sofind theword that isconsistentwith thecontextof thesentence.Province,(A),means“typeoflearning,”whichwouldfitwellwiththeprevioussentence,sokeepit.Providencemeans“goodwillfromahigherpower,”soitdoesn’tfit;eliminate(B).Choice(C)canbeeliminatedbecauseprovenancemeans“origin.”Finally,eliminate(D)sinceprovidentialmeans“lucky.”Choice(A)istheanswer.
43. B The answer choices don’t seem to indicate that a clear grammatical rule is being testedhere, so use POE. Choice (A) seems to change the intended meaning, since the adverbinitiallycomesafterwhatit’ssupposedtobemodifyinginsteadofbefore,whichitshould;eliminate(A).Choice(D)makesthesamemistake,soeliminateitaswell.Choice(B)ismuchclearerandmoreconcise,soholdontoit.Choice(C)usesthen,whichisthewrongwordchoice(itindicatestime)andshouldthereforebeeliminated.Choice(B)iscorrect.
44. D Thisquestionaskswhetherthisessaysuccessfullyrelatestheactivitiesofchimpanzees toBlackFridayshoppers.Humansarediscussedverybrieflyinthispassage,sotheanswerto the question is no. Eliminate (A) and (B). Eliminate (C) aswell sinceBlack Fridayshoppersandchimpanzeesareneverdirectlycompared.Thecorrectansweris(D).
Section3:Math(NoCalculator)1. C Translatethequestionintoanequation.Letxequalthenumber,andthen2x=x−4.Solving
forx,youfindthatx=−4.Thisis(C).
2. C Sonalneedsssoilsamples.Ifaccordingtothequestion,hemusthavemorethan6samples,thens>6.Alsoaccordingtothequestion,hemayhavenomorethan13samples,sos≤13.Combiningthesetwoexpressions,youfindthat6<s≤13.Thisis(C).
3. D Thegraphoff(x)hasay-interceptaty=3.Becauseofthis,youknowthatwheny=3,x=0. f(x) must then satisfy the condition that f(0) = 3. This is true only for (A) and (B).Alternatively,byrecognizingthateachequationisintheslope-interceptform:f(x)=y=mx+b,whereb is they-intercept,we can reach the same conclusion.Next, notice that the
slopeofthelineispositive.Thatis,asthevalueofxincreases,sotoodoesy.Returningtotheslope-interceptform,mgivestheslopeoftheline.Only(D)hasapositivecoefficient(m).Choice(D),then,isthecorrectfunction.
4. A Ifx+y=0,thenx=−y.Usingthisrelationshipandsubstitutingintotheexpressionx−y,youfindthatx−y=−y−y=−2y.Thisis(A).
5. A Thisquestionrequiresfactoringtheexpression2x2−6x−8.Beginbyfactoring2fromtheexpression:2(x2−3x−4).Thisexpression is further factorable,giving2(x−4)(x + 1),whichis(A).
6. D Thequestiondescribesarampthatformsatriangle,thelengthofwhichisthehypotenuseofthetriangle.Theheightoftheramp(3feet)isthelengthofthesideofthetriangleopposite
the 35° angle. In general for some angle θ, sinθ = . In the question, this
corresponds tosin35°= = lengthoframp= .This is
(D).
7. D Thisquestion requiresevaluatingbothequations todetermine thevaluesofaandb. Youcanbeginbysolvingeitherofthetwoequationsforaorb,andthensubstitutingthesolutionintotheotherequation.Butnotethatthequestionasksforthevalueofa+b,sochecktoseeifthere’safasterway:Canyoustackandadd(orsubtract)theequations?Ifyoustackandadd the equations, you get 7a + 7b = 77. Now divide both sides of the equation by 7,resultingina+b=11.Thisis(D).
8. D Whenafunctionf(x)istransformedintoafunctionoftheformf(ax),whereaisaconstant,ifa>0,thefunctionwillbecompressedhorizontallybyafactorofa.Here,y=x2+4canbe represented as the parent function, and y = 3x2 + 4 as the transformed functioncompressed horizontally versus the parent function, and thus narrower, by a factor of 3.Thisis(D).Ifyou’renotsure,trypluggingvaluesintoeachequationtoconstructaroughgraphofeachequationandcomparethem.
9. C Rearrangingandfactoringtheexpressionprovidedinthequestion,youhavet2−4t−90=6 t2−4t−96=0 (t−12)(t+8)=0.Therefore,t−12=0andt+8=0.tmustthenequal 12 or −8. If t represents the number of tickets Steven buys, then only t = 12 isconsistentwiththecontextofthequestion.Ifeachticketcosts$80,Stevenmusthavespent$80×12=$960.Thisis(C).
10. C Findvaluesofcanddbysolvingthesystemofequationsinordertodeterminethevalueof4c−4d.Thereareseveralwaystogoaboutthis.Onewayistomultiplythetermsoftheequation2c+3d=17by−3toget−6c−9d=−51.Ifyoustackandaddthisequationwiththesecondequation,theresultis−4d=−12,whichsolvestod=3.Plugthisvaluefordintotheequation6c+5d=39toget6c+15=39,so6c=24andc=4.Therefore,4c−4d=4(4)−4(3)=16−12=4.Thisis(C).
11. A Factoringthe leftsideof theequationx2+2xy+y2=64gives (x+y)2=64.Taking thesquarerootofbothsidesoftheequation,youfindthatx+y=8or−8.Theotherequationprovidesthaty−x=12,soy=x+12.Substitutethisvalueofy into thefirstequation:eitherx+(x+12)=8,so2x+12=8,2x=−4,andx=−2,orelseorx+(x+12)=−8,so2x+12=−8,so2x=−20,andx=−10.Therefore,xcouldbeeither−2or−10,andonly−10isanoptionintheanswers,so(A)iscorrect.
12. D TranslatefromEnglishtomathusingBite-SizedPieces.Makethepriceofahotyogalessonhandthepriceofazerogravityyogasessionz.Ifsheoffers2hotyogaand3zerogravityyogasessionsfor$400,then2h+3z=400.Similarly,if4hotyogaand2zerogravityyogasessionsare$440,then4h+2z=440.Now,besuretoReadtheFullQuestion:YouwanttoknowwhetherSamanthacancreateapackagethat’sgreaterthan$800buthasfewerthan13sessions.Ifyoustackthetwoequationsandthenaddthemtogether,youget6h+5z=880.Inotherwords,shecanoffer6hotyogaand5zerogravityyogasessions(11totalsessions)for$880.Thissatisfiesherrequirements,soyouknowtheansweris“Yes”;eliminate(A)and(B).For(C),becauseyoudon’tknowthepriceofeachlessonindividually,youdon’tknowyetwhether5hotyogaand5zerogravityyogasessionswillbeover$800;leave(C)for now. For (D), if 6 hot yoga and 5 zero gravity yoga sessionswere over $800, thenaddingazerogravityyogasessionwillstillbeover$800.Givenwhatyoualreadyknow,(D)mustbetrue;choose(D).
13. B Beginbysimplifyingthegivenequation:(3p2+14p+24)−2(p2+7p+20)=3p2+14p+24−2p2−14p−40=p2−16=0.Factoringtheleftsideofthesimplifiedequation,youfindthat(p−4)(p+4)=16.Solvingforp,youfindthatp=±4.Thevalueof3p+6mustthenbeeither3(−4)+6=−6or3(4)+6=18.Thelattervalueis(B).
14. A Takingnotethati= ,theexpression(2+8i)(1−4i)−(3−2i)(6+4i)becomes(2+8
)(1−4 )−(3−2 )(6+4 ).Expanding,thisbecomes2−8 +8 −
32( )2−(18+12 −12 −8( )2)=2−32( )2−18+8( )2=8( )2
−32( )2−16.Thisfurthersimplifiesto−8+32−16=8.Thisis(A).
15. C PlugIntheAnswers!Theanswerchoicesaren’tinanyparticularorder,andsomenumbersappear more than once, so you don’t need to start in the middle. Instead, start with 9becauseitisinthreeofthefourchoices.Ifx=9,then2 =9−3. =3,sotheleftsideoftheequationis2×3=6,andtherightsideoftheequationis9−3=6.Thisworks,so9ispartofthesolutionset;eliminate(B)becauseitdoesn’tinclude9.Next,tryx=1:2=1−3,whichsolvesto2=−2.Thisisn’ttrue,so1isnotpartofthesolutionset;eliminate(D). Lastly, try x = −1: 2 = −1 − 3. You cannot take the square root of a negativenumber,sothisdoesn’twork.Eliminate(A)andchoose(C).
16. 28 Let s equal the number of staples required by the students and let p be the number ofpopsiclesticksrequired.If thenumberofstaplesthestudentswillneedisthreetimesthenumberofpopsiclestickstheywillneed,thens=3p.Ifthestudentsneed84staplesforthis
project,thens=84.Substitute84forstoget84=3p.Dividebothsidesby3toget28=p.Thestudentswillneed28popsiclesticks.
17. 0 Ifaparabolaintersectsthex-axisatthepoints(5,0)and(−5,0),itmustbesymmetricaboutthex-axisandcenteredatx=0.Thex-coordinateofitsverticalaxisofsymmetrymustthenbe0.
18. 94 The question describes a 100-meter ramp that forms a triangle. The length of this ramp
correspondstothehypotenuseofatriangle.Theheightoftherampisthelengthoftheside
of the triangle opposite the 20° angle; the horizontal distance from the start of the ramp
immediatelybelowtheentranceof themall is thesideof the triangleadjacent to the20°
angle.Thefunctionthatrelatesadjacentandhypotenuseiscosine:cosθ= .Inthis
problem, cos 20° = , where x is the horizontal distance. Solve bymultiplying both
sides by 100: cos 20° = x. Next, replace cos 20° with the value given in the problem,
0.939:100(0.939)=x.Multiply100by0.939togetx=93.9,whichroundsto94.
19. 7 Letxequalthenumber.Then,2x=x−5 x=−5.Threetimesthatnumberplusseventeenminusthatnumberis3(−5)+17−(−5)=7.
20. 3x2+2x−8=(x+2)(3x−4)=0.Solvingx+2=0and3x−4=0forx,youfindthatthe
twosolutionsforxare−2and .Thequestionasksyoutosubtractthevalueofthesmaller
solutionfromthelargersolution.Thisdifferenceis −(−2)= + = .
Section4:Math(Calculator)1. B To solve this question, simply subtract y from both sides of the equation to get 2y = 2,
whichis(B).
2. A Wheneverthequestionincludesvariables,PlugIn.Ifm=2,thenMerrywouldpaytheone-timeenrollmentfeeplus2months’worthofmonthlyfees,whichis50+15(2)=80.Plugin2formintheanswerchoicestoseewhichanswerequalsthetargetnumberof80.In(A),15(2)+50=80.Thisisthetargetnumber,soleavethisanswer,butbesuretochecktheotherchoicesjustincase.In(B),15+50(2)=115.In(C),15(2)−50=−20,andin(D),(15+50)(2)=130.Sincenoneof theotheranswerchoicesequals thetargetnumber, thecorrectansweris(A).
3. B SincethequestionstatesthatRobisplanningtobringhisfavoriteguitarplusxadditionalguitars, he will have a total of x + 1 guitars. The question states that the variable x
representsthenumberofadditionalguitars,sothenumber1mustrepresentRob’sfavoriteguitar,whichis(B).
4. D ThebestwaytoapproachthisquestionisthroughPOE.Accordingtothedatainthetable,theratioofthosewhoenjoybiologytothosewhoenjoychemistryis14to18,whichcanbereducedtoaratioof7to9;eliminate(A).Theratioofthosewhoenjoychemistrytothosewhodon’tenjoychemistryis18to6,whichcanbereducedtoaratioof3to1;eliminate(B).Theratioof thosewhoenjoybiologyto thosewhodon’tenjoychemistry is14to6,whichcanbereducedtoaratioof7to3;eliminate(C).Theratioofthosewhodon’tenjoybiologytothosewhoenjoychemistryis10to18,whichcanbereducedtoaratioof5to9;thismatches(D).
5. C Dr.Goldbergtakes40%ofsubstituteA,whichconsistsof60grams.Mathematically,this
canbeexpressedasor (60)or (0.4)(60)=24grams.She takes70%ofsubstituteB,
whichconsistsof110grams.Mathematically,thiscanbeexpressedasor (110)or(0.7)
(110)=77grams.SubstituteCwillthereforeconsistof24grams+77grams=101grams,
whichis(C).
6. D Tosolvethisquestion,simplyfactoroutthelargestvaluethatfitswithineachofthetermsintheexpressionprovided.Inthiscase,x4,x3,andx2arealldivisiblebyx2,sothatiswhatyouwillwanttofactorout.Doingsowillleaveyouwithx2(x2−x−1),whichis(D).
7. A SinceOfficerBlakedrives480milesatarateof1mileperminute,histotaldrivetimewas480minutes.Thequestionasks forOfficerBlake’sdriving time inhours, soyouneed toconvertthoseminutesintohours.Sincethereare60minutesin1hour,youcandivide480minutesby60todeterminethatOfficerBlakedrovefor8hours,whichis(A).
8. B Thegoalhereistoisolatex.Sincetheright-handsideoftheequationis−2x+1,youwillwant tosubtract1frombothsides,soeliminate(A)and(C).Togetxby itself,youwillwant todivideby−2, not 2, so eliminate (D) and choose (B).Remember thatwhenyoumultiplyordivideacrossaninequalitysignusinganegativenumber,youneedtoflip theinequalitysignintheoppositedirection,asreflectedin(B).
9. C Tosolvethisquestion,rearrangetheexpressions(2x2+4x+8)and(2x2−4x+7)inordertoplacethesimilartermsnexttoeachother.Doingsowillgiveyou2x2−2x2+4x−(−4x)+ 8 − 7 (remember to distribute the negative sign for each of the terms in the secondexpression).Simplifyingthisnewexpressionwillyield0+8x+1,or8x+1,(C).Anotherwaytoapproachthisquestionwouldbetopluginasimplenumberforx,suchasx=2,andmatchyourtargetvaluewiththevaluesintheanswerchoices.
10. A ThetallesthillthatAdammeasuresis55feethigh.Since1footisequivalentto12inches,simplymultiply55×12=660inches,(A).
11. B TrianglelegsLNandMNareoppositeandadjacent,respectively, to y.Therefore, from
SOHCAHTOA,youneed touse the tangent trigonometric function.Plugging in thevalues
thatthequestiongivesyouintotheequationfortangent,yougettan40°= .Now,use
yourcalculatortodeterminethatthelengthofMNmostcloselyapproximates9.53,whichis
(B).
12. D Ifyourepresentthewoodenskateboardswithawandthecompositeskateboardswithac,youcanwritetwoequationsbasedontheinformationgiveninthequestion:2w+3c=650and 3w + c = 450. It is possible to isolate one of the variables and solve these twoequationsbysubstitution,butinthiscaseitiseasiersimplytostacktheequationsontopofeachotherandaddthemtogetherasfollows:
Since the question asks for the price of five wooden skateboards and four compositeskateboards,theansweris(D).
13. D Thequestionstatesthatthenumberofemployeesincreasesatthesamerateperyear,soyou
candeterminethisnumerical increasebysubtractingoneyear’s totalfromthenextyear’s
total.Subtractingthe2013totalfromthe2014totalgives2,110−1,890=220.Tofindthe
totalin2015,add220tothe2014total:2,110+220=2,330.Thequestionalsostatesthat
themalepercentagescontinuetodecreaseatthesamerate,which,basedonthedatainthe
table,is5%peryear.Thepercentmalein2014was55%,sothepercentmalein2015will
be50%.50%of2,330canbeexpressedasor (2330)or(0.5)(2330)=1,165,whichis
(D).
14. B Theformulafordetermininganaveragecanbeexpressedby .Plugthe
valuesprovided into the equationas follows:11= , or11=
.Multiplybothsidesby7toget77=67+x.Subtract67frombothsidestogetx=
10,whichis(B).
15. C Thereareavarietyofwaystoapproachthisquestion.Youcouldsolveoneequationforsortandsubstituteitintotheotherequation,butlooktoseeifyoucandoitmoresimplybystackingandadding(orsubtracting)theequations.Ifyoudoublethefirstequationtoget34s+40t=118,youcanthenstackandsubtracttheequationstoeliminatetandsolvefors,asfollows:
So,4s=8andtherefores=2.Nowplug in2 for thevalueofs inoneof theequations:30(2)+40t=110,so40t=110−60,so40t=50andt= =1.25.Next,plugs=2into
theanswerchoicestodeterminewhichonematchesyourtargetof1.25:(C), = =
=1.25.
16. A ThebestwaytoapproachthisquestionisthroughPOE.Choice(A)statesthatthemajorityofstudentspolledloggedinmoretimesthantheyposted.Thevaluesalongthex-axisofthegraphare,formostofthedatapoints,higherthanthevaluesalongthey-axisofthegraph,andthus(A)istrueaccordingtothedataprovided.Thissamedatacontradicts(B)and(C).Youcaneliminate(D)becausethedatadoes,infact,allowyoutodrawaconclusionabouttherelationshipbetweenthevariables.
17. B Don’tgettoothrownoffbythegraph.Allyouneedtoknowtosolvethisquestionisthatperpendicular lineshaveslopes thatare thenegative reciprocalsofeachother.Since thestandardequationforalineisy=mx+b,theslopeofthef(x)lineis3.Theslopeoftheh(x)linemustthereforebe− .Theonlyanswerchoicethatmatchesis(B).
18. C ThebestwaytodealwiththisquestionistoPlugIntheAnswers(PITA),startingwith(A).Ifx=6,theny=36=729.Thisislessthan4,000,soeliminate(A)andmovetothenextanswerchoice.Ifx=7,theny=37=2,187.Thisisstilllessthan4,000,soeliminate(B).Ifx=8,theny=38=6,561.Thisisgreaterthan4,000,so(C)mustbethecorrectanswer.
19. D The first step here is to simplify the equation and solve fora. Start bymultiplying bothsidesby16toget16a=4a2.Dividebothsidesby4toget4a=a2.Dividebothsidesbyatoget4=a.Thisisnowyourtargetanswer.Pluga=4intothevaluesofaintheanswerchoicestodeterminewhichonematches4.Choice(D)istheanswer,since2 =2 =2(2)=4.
20. B Sincework=rate×time,the280intheequationmustrepresentthetotalnumberofmeals(i.e.,the“work”).Allthreechefsareworkingtogether,sotheyworkforthesameamountoftime,andxmustrepresent that time.Thecoefficients8,4,and2must thereforerepresentthechefs’respectiverates,orhowmanymealseachpreparesinasetamountoftime.Since8isthegreatestofthesethreecoefficients,8xmustbethemealoutputof thefastestchef,either(B)or(C).Nowyouneedtosolvetheequation:8x+4x+2x=280.Combiningliketermsgivesyou14x=280.Dividebothsidesby14todeterminethatx=20.Thisnumberrepresentstheamountoftimethatthechefsworked,sotheactualnumberofmealspreparedbythefastestchefwouldbe8×20=160meals,whichis(B).
21. D Startbyfindingtheslopeofthelineprovidedonthegraphusingthepoints(0,−4)and(6,
0) and the point-slope formula: = = . When this line is reflected
acrosstheliney=x,thex-andy-valuesswitch,sothenewslopewouldbethereciprocal
of the original slope. Since the original slope was , the new slope will be . The
numeratorherereflectsthegainorlossofpiecesoffruitintheharvest,andthedenominator
reflects thenutrients subtractedor added.Thismeans that for every twonutrients added,
therewillbeaharvestgainofthreepiecesoffruit,whichis(D).
22. D TheissuethatneedsclarificationhereiswhetherthestudentspolledbyJoethoughtthatascoreof1orascoreof5wasgood.Since(A)and(C)dealwithGeorge’spoll,theywoulddonothingtohelpclarifythisambiguity.Choice(B)mighthelpustofigureoutwhichofthestudentsJoepolledwereinterestedintheModelUNClub;itwouldnothelptodeterminewhether1or5wasthebestrating.Choice(D)iscorrect.
23. C Inorder todetermine thenormalcost forrentingskisandsnowboards,youneed towritetwo equations and then manipulate and solve those equations. If you call skis x andsnowboardsy,your twoequationswillbe5x+2y=370and3x+4y=390.Lookforawaytostackandaddtheequationstoeliminateoneofthevariables.Forinstance,multiplythefirstequationby2toget10x+4y=740,andthenstackandsubtracttheequations,asfollows:
So,7x=350andx=50,sothepriceofapairofskisis$50.Plugthisnumberbackintoeitherequationtofindthecostofasnowboard:10(50)+4y=740,so4y=740−500and4y=240.Therefore,y=60,thecostofasnowboard.So,thecostoftwopairsofskisand
twosnowboardswouldnormallybe2(50)+2(60)=100+120=220.Finally,rememberthatpricesarediscountedby10%,somultiply thepriceof$220by10%toget$22,andsubtract$22fromtheprice.Thefinalcostoftwopairsofskisandtwosnowboardsis220−22=198,whichis(C).
24. A Startbysimplifying8x+8y=18bydividingeachtermby8:x+y= or:x+y= .The
secondequationprovidedinthequestioncanbefactored:x2−y2isthesameas(x+y)(x−
y),sothesecondequationcanalsobewritten(x+y)(x−y)=− .Sinceyouknowthatx+
y= ,youcanrewritethesecondequationas (x−y)=− .Multiplybothsidesby :x−
y= orx−y=− .Sincethequestionasksforthevalueof2x−2y,simplymultiply
everythingby2:2(x−y)=2=2 =− ,whichis(A).
25. D Ifeachminuteofhisworkout timeburns50calories,andhewants toconsumeno fewer
than2,000calories,Shaunmustworkoutforaminimumof =40minutes.Ifhewants
toconsumenomorethan2,500calories,Shaunmustworkoutforamaximumof =
50minutes.Sincethequestionasksfortheinequalitythatrepresentsthenumberofminutes
for which Shaun will burn off as many calories as he consumes, (D) is correct, as it
includesboththeminimum(40minutes)andmaximum(50minutes)amountoftimethathe
canworkout.Choice(C)isincorrectbecausetheanswershouldinclude50(hecanwork
outfora“maximum”of50minutes,sohecouldworkoutfor50minutes),butthelessthan
sign(“<”)excludes50.
26. A Thereare162gamesintheseason,sotheteamneedsatotalof162×45,500=7,371,000ticketpurchasestohaveameanof45,500ticketpurchasespergamefortheseason.The60games with an average total ticket purchase of 43,000 gives a total of 2,580,000 ticketpurchases,leaving4,791,000ticketpurchasesleftfortheteamtoreachitsgoal.Dividing4,791,000by102makes(A)theclosestvaluetotheaverageof46,971ticketpurchasespergametheteamneedstomake.
27. B ThebestwaytodealwiththisquestionisthroughPOE.Ifthepolynomialhaszeroesof2and−3, then thatmeansyouhave twopoints: (2,0)and (−3,0)—eliminate (A)and (C).Sinceitisgiveninthequestionthata>0whentheparabolaisintheformy=ax2+bx+c,theparabolamustbepointedupwards—eliminate(D)andchoose(B).
28. A Sincetheradiusofthecircleis4,theareaoftheentirecircleisπr2=π(42)=16π.Sector
PORhasanareaof8πandsectorROQhasanareaof6π,sotheremainingsector(QOP)
hasanareaof16π−8π−6π=2π.Youcansetupaproportiontodeterminetheassociated
angle using the following formula: = . Using the numbers you now
have, your calculationwill look like this: or = .Multiply
bothsidesoftheequationby360todeterminethatthesectorangleis45°,whichis(A).
29. D 16%ofthe200medicalresidentsnamedoncologyastheirfirstchoice: (200)or(0.16)
(200) = 32 residents. 40% of the 200medical residents named cardiology as their first
choice: (200)or(0.4)(200)=80residents.Ofthese80residents,20%choseoncology
astheirsecondchoice: (80)or(0.2)(80)=16residents.Thetotalnumberofresidents
who named oncology as either their first or second choicewas therefore 32 + 16 = 48
residents.Tofindthevalueofx,youneedtosubtractthepercentagesgiveninthequestion
fromthetotal,100%:100−40−16−34=x=10%.Now,plugx=10intotheanswer
choices in order to determine which onematches your target of 48 residents. Only (D)
works:x2−24x+188=100−24(10)+188=100−240+188=48.
30. B Iftheoriginalgraphisreflectedacrossthex-axis,thex-valueswillremainthesamebutthey-values will switch signs. Since the y-axis represents distance from start, negative y-values means that the car is now going in reverse. The only answer that matches thisinformationis(B).
31. 30 Translate English to math. “What number divided by two is equal to that same number
minus15?”canbewrittenasanequation,withxrepresentingthemissingnumber: =x−
15.Add15tobothsidesoftheequationtoget +15=x.Subtract frombothsidestoget
15= .Multiplybothsidesby2togetx=30.
32. 4 Whendealingwithvaluesthataredirectlyproportional,youcanusetheequation = .
Forthisquestion,youcancallthenumberofhoursspentplayingCallofDestinyxandthe
numberofhoursspentinthegameroomy.Yourequationwillthenlooklikethis: = .
Cross-multiplytoget6y2=3(8)or6y2=24.Dividebothsidesoftheequationby6toget
y2=4.
33. 13.5 StartbytranslatingEnglishtomath.MakesthepriceofSmooth-GlidepensandethepriceofEasy-Writepencils.If12pensand8pencilscost$16,then12s+8e=16.Similarly,if6pensand10pencilscost$11,then6s+10e=11.RemembertoReadtheFullQuestion!Thequestionwantsthepriceof9pensand9pencils.Ifyoustacktheequationsandadd,youget18s+18e=27.Thisisexactlydoublethenumberofpensandpencilsyouwant,sodividetheentireequationby2toget9s+9e=13.5.
34. 2or
Thereareafewdifferentwaystoapproachthisquestion.Sincethecalculatorispermitted
onthissectionofthetest,youcanputtheequationintothestandardax2+bx+c=0form
andplugthatequationintothe“y=”buttononyourgraphingcalculator.Theequation,once
rearranged, is 3x2 − 16x + 20 = 0.You can trace the graph or use the “calc” feature to
calculatethezeroes,whicharethesameasthevaluesofx.Doingsowillyieldvaluesofx
= 2 and x = 3.33. Alternatively, you can factor the equation the long way or use the
quadratic formula, . In this equation,a=3,b =−16, andc = 20. Plugging
those values into the equation, you get = = .
Therefore,thesolutionsare = = and = =2.Eithervalue( or2)
isavalidanswer.
35. 5 Sinceyouarelookingforthevalueofxforwhichthepopulationsurpassedthenumberofdwellings,youcansetupaninequality:3x>2x+100.Now,simplypluginvaluesforxstartingwithx=1untiltheleft-handsideoftheinequalityislargerthantheright-handside.Usingthevaluesx=1,x=2,x=3,andx=4,youwillfindthattheleft-handsideoftheinequality is less than the right-handside.Usingx=5,35=243, and2(5)+100=110,makingtheleft-handoftheinequalitygreaterthantheright-handside.Therefore,theansweris5.
36. 5,406 The first step here is to addTeamCharlie’s andTeamDelta’s total currents together asfollows:
Next,useFOILtomultiplythisvaluebythetotalcurrentfromTeamEpsilon:(90+3i)(60−2i)=5,400−90(2i)+60(3i)−2i(3i)=5,400−180i+180i−6i2=5,400−6i2.Sincei2=−1,thisisequivalentto5,400−6(−1)=5,400+6=5,406.Ifyouhaveacalculatorthatis able to deal with imaginary numbers, you can simply type the expressions into yourcalculator,whichwillsolveeverythingforyou.
37. 860 Thequestionstates that thereare2,400total inhabitantsofCentreHill,so if thereareanequalnumberofadultsandchildren,thenthereare1,200ofeach.Sincethereare200moreadultfemalesthanadultmales,youcansetuptwoequations:f+m=1,200andf=m+200.Youcanrewritethesecondequationbysubtractingmfrombothsides:f−m=200.Next,stackandaddthetwoequationsasfollows:
Divideboth sidesof theequationby2 todetermine that f = 700.Thenumberofwomen
living uptown is therefore 8% of 700: (700) or (0.08)(700) = 56. The number of
children living in the suburbs is 67%of1,200: (1,200)or (0.67)(1,200)=804.The
sumofthesetwofiguresis56+804=860.
38. 250 Usingyourinformationfromquestion37,youcandeterminethatthetotalnumberofadult
malespriortotheadditionoftheannexis1,200−700=500.Theoriginalpercentageof
adultmaleslivingUptownis9%of500: (500)or(0.09)(500)=45.Sincethequestion
statesthatthepercentageofadultmaleslivingUptowndecreasesto6%,youcanconclude
that the45adultmales livingUptownafter theannexationconstitute6%ofthetotaladult
malepopulation:45= (x)or45=(0.06)x.Dividebothsidesoftheequationby0.06to
determinethatx=750.Sincetheoriginalnumberofadultmaleswas500,750−500=250
additionaladultmalesliveinTheAnnex.
ReadingTest65MINUTES,52QUESTIONS
TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassageorpairofpassagesbelowisfollowedbyanumberofquestions.Afterreadingeachpassageorpair,choosethebestanswertoeachquestionbasedonwhatisstatedorimpliedinthepassageorpassagesandinanyaccompanyinggraphics(suchasatableorgraph).
Questions1–10arebasedonthefollowingpassage.
Thepassagethatfollowsisadaptedfroma1907novelthatfollowstheactionsofanEnglishbaronetwho,usingasecretidentity,leadsagroupofwealthyEnglishmenindaringrescuesofmembersoftheFrencharistocracyduringtheReignofTerror.
1. ThepassageasawholeisprimarilyconcernedwithA) consideringthereasonsbehindasetofexploits.B) examiningthecausesofarevolution.C) comparingtheself-confidenceoftwodifferentmen.D) questioningtheruthlessnessofagovernment.
2. Basedontheinformationinthepassage,itcanbeinferredthatthewhentheComtesseescaped,thepeopleinthenearbycrowddidnotapproachhercartbecauseA) thecartwasmovingtooquickly.B) theyfearedarrestanddeathbyguillotine.C) thewomandrivingthecartwasknowntobeviolent.D) theywereafraidofcontractingadisease.
3. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines51–55(“Andthis…guillotine”)B) Lines65–70(“Thencame…children”)C) Lines70–72(“thecovered…handle”)D) Lines75–78(“She…plague”)
4. Asusedinline14,“designated”mostnearlymeansA) budgeted.B) chosen.
C) classed.D) illustrated.
5. Incontext,thephrase“pulltheharefrombetweentheteethofthehound”(lines32–33)referschieflytoA) dangerousEnglishhuntingcustoms.B) planstoavengethedeathsofinnocentEnglishmen.C) deliveringmembersoftheFrencharistocracyfromharm.D) thecrueltyofFrenchnoblestowardrevolutionaries.
6. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines37–40(“Faith…go”)B) Lines46–48(“Theirnationality…them”)C) Lines48–51(“Anyone…nationality”)D) Lines61–64(“Ithad…perhaps”)
7. Inlines41–46,theComtesseisbestdescribedasA) critical.B) anxious.C) relieved.D) perplexed.
8. Asusedinline52,“bearded”mostnearlymeansA) camouflaged.B) braved.C) embellished.D) masked.
9. Lines73–78provideacontrastbetweenA) tranquilityandturmoil.B) traditionalismandmodernity.C) freedomandignorance.D) austerityandhysteria.
10. Theuseofitalicsinline86primarilyservestoemphasizeaperceiveddistinctionbetween
A) thereasonsbehindoneman’sactionsandthosebehindhiscompanions’actions.B) theeffectivenessoftwodifferentmethodsofcarryingoutthesameplan.C) honest,noblemotivationsforrescueandrescueformonetarygain.D) adesireforadventureandadesireforpublicadmirationandpraise.
Questions11–21arebasedonthefollowingpassageandsupplementarymaterial.
ThispassageisadaptedfromDanielJ.Boorstin,TheCreators:AHistoryofHeroesoftheImagination.©1992byDanielJ.Boorstin.
Rome,BathsofDiocletian
11. Whichofthefollowingbestexpressesthemainideaofthepassage?A) PublicbathsinRomansocietyprovidednotonlysanitaryfacilitiesbutalsosocial
andculturalgatheringplaces.B) Romanarchitecturerejectedtheexterior-basedGreektraditionsinfavoroflarge,
public,interiorspaces.C) ThelargecurvedspacesthatconcretemadepossibleinRomanarchitecturewere
moreappropriateforcivicthanforreligiousfunctions.D) AcombinationofcivicneedandinnovationinbuildingmaterialsledRomansto
greatarchitecturalinnovation.
12. Inthefirstparagraph(lines1–14),whatisthemostlikelyreasontheauthormentionsGreektemplearchitecture?A) ToshowhowRomanarchitecturalinnovationsimprovedupontheearlierGreek
traditionsB) TolocatethenewtrendsinarchitecturedevelopedbytheRomanswithin
architecturalhistoryC) ToprovethatRomanarchitectsweremorecreativeintheirimaginingofinterior
spacethanGreekarchitectsD) ToarguethatthenewinteriorspacescreatedbyRomanswerebettersuitedto
religiousarchitecturethanGreektempleswere
13. Asusedinline7,“omnipresent”mostnearlymeansA) large.B) pervasive.C) eternal.D) imposing.
14. TheauthorimpliesthatwhichofthefollowingwascriticaltoRomanarchitecturaldevelopments?A) Theneedforlarge,interiorspaceswhereurbanculturecouldbeexpressedB) TheconvenienceofpublicbathstopeopleofallsocialstrataC) ThedevelopmentovertimeofconstructiontechniquesusingconcreteD) Therapidexpansionofbathsintocommunityandculturalcenters
15. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines5–6(“They…spaces”)B) Lines15–18(“This…error”)C) Lines22–27(“While…mystery”)D) Lines42–47(“Others…thousand”)
16. Whatistheprimarypurposeofthethirdparagraph(lines19–27)inrelationtothestructureofthepassageasawhole?A) TointroduceaneedthatgaverisetoinnovationsdescribedelsewhereinthepassageB) Toreinforceacontrastmentionedinthefirstparagraphandprovideadditional
detailC) ToemphasizethemysteriousnatureoftheinnovationsdiscussedinthepassageD) Todismissanearlierthesisinfavoroftheonedescribedinthefollowing
paragraphs
17. Asusedinline31,“anticipated”mostnearlymeansA) foreshadowed.B) expected.C) prevented.D) enjoyed.
18. ItcanbeinferredfromthedescriptionofpublicbathsinthelastparagraphthatA) avisittothebathmightbequitedifferentfromavisittoamodernbath.
B) theyweremuchlikemoderngyms;patronswouldfirstexercise,thenbathe.C) Romansbelievedinthebenefitsofexposingoneselftoavarietyoftemperatures.D) theconvenienceofhavingsomanyactivitiesinonelocationisunparalleledin
history.
19. TheauthorbelievesthatthemostexemplaryRomanbathsprovidedA) avenueforarchitecturalexperimentation.B) importantsanitaryfacilitiesforcitizens.C) fineartsenrichmenttothepublic.D) communitygatheringspaces.
20. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines15–18(“Thisgrand…error”)B) Lines21–22(“Andthenew…cities”)C) Lines32–34(“Grandpublic…provinces”)D) Lines64–66(“Thebaths…art”)
21. Whichofthefollowingissupportedbyinformationinboththepassageandthediagram?A) Romanbathsusuallyincludedfrigidariums.B) Thepalestraewerelocatedonoppositesidesofthebuilding.C) Commercialcontractorsalwaysbuiltpublicbathsinarectangularshape.D) Thenatatiowasoftenusedforwrestlingandhoop-rolling.
Questions22–31arebasedonthefollowingpassage.
ThispassageisadaptedfromaspeechdeliveredbyRafaelPalmaofthePhilippinesonNovember22,1919,asasenatorforthecountry’sfourthdistrict.Inthepassage,Palmadiscussesthereasonsthatwomenshouldbeallowedtovote.Palma’sspeechwasdeliveredinthecontextofthefirstsessionofthefifthFilipinolegislature,whichwaspreparingtovoteonthequestionoffemalesuffrage.
22. Inthisspeech,therolethatPalmaplayscanbestbedescribedasthatofA) ananalystdiscussingtheadvantagesofeachsideofanissue.B) atraditionalistcautioningagainstthedangersofreform.C) anidealistarguingforasocialchange.D) apoliticianrousingsupportforhisparty.
23. Basedontheinformationinlines1–7,itcanbeinferredthatatthetimethatPalmagavehisspeechwomenwere
A) Palma’sprimarysupporters.B) notallowedtospeakbeforetheFilipinolegislature.C) notrepresentedbyanyotherFilipinoleaders.D) notviewedwithsympathybythemembersoftheFilipinolegislature.
24. Asusedinline30,“check”mostnearlymeansA) certify.B) inspect.C) advise.D) stop.
25. BasedontheinformationpresentedinPalma’sspeech,itcanbeinferredthatsomeofthosewhoopposethebilltogivewomentherighttovoteA) believethattryingtogivewomentherighttovotewouldbeequivalenttotryingto
checkthesunandmoonintheircourse.B) areprejudicedagainstthecausesofmodernmenandwomenanddonotsupport
liberaldemocracy.C) claimthatdoingsowillbedamagingtohomelifeandmaydisruptlong-established
traditions.D) assertthatanysuddenchangestothecountry’scivicinstitutionsmightpermanently
paralyzethecountry.
26. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines25–29(“Femalesuffrage…common”)B) Lines46–51(“Aswasto…years”)C) Lines64–67(“Ithasseen…liberty”)D) Lines79–88(“Inview…society”)
27. Theprincipalrhetoricaleffectofthephrase“paralyzation,retrogression,disorganization,ordestruction”inlines57–58istoA) highlightwithincreasingforcehowchangesinidealsandinstitutionscandamagea
society.B) emphasizethenumberofwaysinwhichpastchangeshavenotnegativelyaffected
thePhilippines.C) showthatthePhilippinesbecamedisabled,afterwhichitreverseditssocial
progress,becamedisorganized,andwasnearlydestroyed.D) suggestfourmethodsbywhichthelegislaturecouldhalttheprogressofradical
socialupheavals.
28. Palmarefersto“greatsocialupheavals”inordertoA) useananalogytoshowthatallowingwomentovotewouldnotpermanentlyweaken
thenation.B) arguethatgivingwomenmorerightswouldcausethenationtocrumbleinlessthana
generation.C) demonstratethatthetheories,beliefs,andcodesofethicsofthepeoplesofthe
Philippinesareunchangeable.D) contrasttheoldinstitutionsofthecountry,whichupheldliberaldemocracy,withthe
newinstitutions,whichsupportmoreradicalideas.
29. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines7–12(“Thecause…strong”)B) Lines40–46(“Itisan…cost”)C) Lines67–74(“despiteall…existence”)D) Lines85–88(“Idonot…society”)
30. Asusedinthepassage,“marked”inline81mostnearlymeansA) fixed.B) targeted.C) significant.D) underlined.
31. Inthefinalparagraphofthepassage(lines79–88),Palma’sattitudetowardthosewhoopposefemalesuffragecanbestbedescribedasA) perplexedandmournful.B) academicandunbiased.C) deferentialandhopeful.D) bewilderedanddissenting.
Questions32–41arebasedonthefollowingpassageandsupplementarymaterial.
Thispassageisadaptedfrom“YellowstoneWolfProject:AnnualReport,2012.”
YellowstoneNationalParknorthernrangeelk-wolfpopulations,1995–2010.
32. Thepassagesuggeststhatwhichofthefollowingpreviousbeliefsaboutwolfpacksmaybeinaccurate?A) Thesizesofelkpopulationsandwolfpopulationsarerelatedtooneanother.B) Wolvesarepartofthenaturallyfunctioningecosystem.C) Predatorcontroleffortscanbeextremelyeffective.D) Wolfpacksaretoodangeroustobeleftalive.
33. Asusedinline14,“native”mostnearlymeansA) inborn.B) constitutional.C) indigenous.D) canine.
34. Asusedinline28,“harvested”mostnearlymeansA) gathered.B) killed.C) acquired.D) grown.
35. Whichofthefollowing,iftrue,wouldmostweakentheauthor’sargumentinlines30–32?A) PredationstudiesonDeltaandBechlerpacksdonebyaseparateresearchgroup
showtheirdiettoconsistalmostentirelyofelk.B) Northernpacksthatoccasionallyroamintothepark’sinteriorhavemorestable
populationsthanothernorthernpacks.C) In2013apackofcoyotesinfectedwithmangemigratedintotheparkandwolf
populationssoondeclined.D) Studiesofbisonpopulationsareincompleteandareknowntoover-estimatethe
numberofbisonlivinginYNP.
36. Thefifthparagraph(lines57–85)moststronglysuggestswhichofthefollowingaboutthepredationdatagatheredin2012?A) Thewolvesareprimarilyresponsibleforthedropsintheelkpopulation.B) Thepredationdataisincomplete.C) Mostofthepackswereobservedbygroundteams.D) Researchersdocumentedcharacteristicsofonlywolfprey.
37. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines59–63(“Wolfpacks…mid-December”)B) Lines63–68(“TheBlacktail…session”)C) Lines71–73(“TheDelta…located”)D) Lines78–85(“During…sites”)
38. Thepassagesuggeststhattherelationshipbetweenelkandwolfpopulationsisbestcharacterizedaswhichofthefollowing?A) Thesizeofthenorthernwolfpacksisthemajorlimitingfactoronelkpopulations.B) Thesuperiorhuntingtacticsthatwolvespossessareoneofmanyfactorsthataffect
elkpopulations.C) Thesizesofwolfandelkpopulationsaffectoneanother.D) Thesizeoftheelkpopulationisthemajorlimitingfactoronthewolfpacks.
39. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines25–27(“Wolfnumbers…YNP”)B) Lines51–52(“Wolfpacks…2012”)C) Lines57–59(“Wolf-prey…sites”)D) Lines90–94(“Inaddition…severity”)
40. Theauthorreferencesweather(lines94–96)primarilyinordertoA) illustrateonepossiblelogisticaldifficultyintrackingwolvesinYNP.B) provideareasonfortheimprovedqualityofelkfood.C) argueforthedesignofanewpredationstudyinYNP.
D) provideadditionalinformationrelevanttothedeclineofelk.
41. WhichclaimaboutwolfandelkpopulationsstudiedbytheNationalParkServiceissupportedbythegraph?A) Currently,elkpopulationsout-numberwolfpopulationsinYNP.B) SincewolfreintroductioninYNP,elkpopulationshaveonlydecreased.C) Wolfpopulationsarehighestwhenelkpopulationsarelowest.D) Currently,elkpopulationsandwolfpopulationsareaboutthesame.
Questions42–52arebasedonthefollowingpassages.
ThisfirstpassageisadaptedfromanarticlefromImperialCollegeLondonpublishedin2010,andthesecondisadaptedfromanarticlefromReuterspublishedin2013.Bothdiscussthedifferentfactorsthatmayhavecontributedtotheextinctionofthedinosaurs.
42. InthefirstparagraphofPassage1,theauthorsuggeststhatmammalsA) weretheonlyspeciesthatsurvivedtheKTextinction.B) wereveryrareuntil65millionyearsago.C) werenotthedominantspeciesonEarthbeforetheasteroidhit.D) werewipedoutafteranasteroidhittheEarth.
43. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines1–4(“Apanel…ago”)B) Lines4–8(“Theextinction…Earth”)C) Lines9–12(“Thenew…Mexico”)D) Lines53–56(“TheKT…Earth”)
44. Asusedinline24,“spewed”mostnearlymeansA) conflagrated.B) disgorged.C) exhumed.D) siphoned.
45. BasedontheinformationinPassage1,itcanbereasonablyinferredthatA) fires,earthquakes,andtsunamiskilledmostofthedinosaurs.B) loweredtemperaturesdecimatedmanyspecies.C) theimpactoftheasteroidcausedvolcanoestoerupt.D) thereisnoconsensusonwhatcausedtheKTextinction.
46. Asusedinline44andline73,thephrases“finalnailinthecoffin,”and“nailinthatcoffin”inbothpassagesreferto
A) aprofounddeduction.B) adeadlyresult.C) agruesomemetaphor.D) aterminatingevent.
47. Theauthor’sreferencetothe“high-precisionradiometricdatingtechniques”inlines68–69primarilyservestoA) proposeanewtheory.B) validatethestudy’sdata.C) provetheconclusionright.D) countertheassumption.
48. Asusedinline97,“preclude”mostnearlymeansA) cause.B) limit.C) bar.D) tap.
49. TheauthorofPassage2mentionstektites(line83)primarilyinordertoA) exploreanothercausefortheKTextinction.B) diminishtheroleoftheasteroidinthedemiseofthedinosaurs.C) substantiatethatthevolcanoescausedthemostdamage.D) contrastwithvolcanicashinordertosupportthenewtheory.
50. Whichchoiceprovidesthebestevidencefortheanswertothepreviousquestion?A) Lines19–23(“Scientistshave…years”)B) Lines61–65(“Earth’sclimate…said”)C) Lines92–97(“Theprevious…relationship”)D) Lines106–108(“Hesays…struck”)
51. ThepassagesdifferinthatPassage1A) describesthesizeoftheasteroid,whilePassage2onlymentionsitsimpact.B) concludesthattheextinctionhappenedbeforetheasteroidhit,whilePassage2says
theextinctionhappenedaftertheasteroidhit.C) explainshowmammalswereaffectedbytheKTextinction,whilePassage2does
not.
D) contradictstheprevioustheoryconcerningtheKTextinction,whilePassage2supportsit.
52. IsthemainconclusionofthestudydescribedinPassage2consistentwiththepanel’sconclusion,asdescribedinPassage1?A) Yes,sincetheasteroidcausedearthquakesandvolcanoeruptionsthatshroudedthe
Earthindebris.B) Yes,sincetheasteroidisconsideredtheprimarycauseoftheKTextinctionbyboth
parties.C) No,sincethestudyinPassage2conveysdoubtaboutthetimingoftheasteroid
impact.D) No,sincePassage1concludesthattheasteroidimpactledtothegrowthofmammal
populations.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
WritingandLanguageTest35MINUTES,44QUESTIONS
TurntoSection2ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Eachpassagebelowisaccompaniedbyanumberofquestions.Forsomequestions,youwillconsiderhowthepassagemightberevisedtoimprovetheexpressionofideas.Forotherquestions,youwillconsiderhowthepassagemightbeeditedtocorrecterrorsinsentencestructure,usage,orpunctuation.Apassageoraquestionmaybeaccompaniedbyoneormoregraphics(suchasatableorgraph)thatyouwillconsiderasyoumakerevisingandeditingdecisions.
Somequestionswilldirectyoutoanunderlinedportionofapassage.Otherquestionswilldirectyoutoalocationinapassageoraskyoutothinkaboutthepassageasawhole.
Afterreadingeachpassage,choosetheanswertoeachquestionthatmosteffectivelyimprovesthequalityofwritinginthepassageorthatmakesthepassageconformtotheconventionsofstandardwrittenEnglish.Manyquestionsincludea“NOCHANGE”option.Choosethatoptionifyouthinkthebestchoiceistoleavetherelevantportionofthepassageasitis.
Questions1–11arebasedonthefollowingpassageandsupplementarymaterial.
SLP,OMG!
1 Whilealargenumberofpeoplebelievethatsocialmediaarefadsthatwillsoondieout,anewtrendshowsthatsuchabeliefmaybefalse.It’struethatmostyoungerpeoplewritetooneanother(viaTwitter,Facebook,ortext)morethan 2 speakingtooneanother(whousesaphonetotalkanymore?),butthespokenwordisasimportantasever.Thisimportanceisnowhereclearerthanintheriseofspeech-languagepathologists(SLPs).
1. Whichofthefollowingwouldbestintroducethemainsubjectofthisparagraph?A) NOCHANGEB) Althoughmanybelievethatsocietyismovingawayfromthespokenwordaltogether,C) Eventhoughsomebelievethatkidstodaycan’twriteorspell,D) Becauseanewbatchofresearchhasbeenperformedonthebelief,
2.A) NOCHANGEB) spokenC) theyspeakD) havespoken
TheBureauofLaborStatisticsprojectsthattheSLPprofessionwillgrowby19%between2012and2022.Alongsidethisgrowth,thenatureoftheprofessionischangingaswell:while 3 SLPsoverwhelminglyworkinhospitals,therehasbeenanotableriseinrecentyearsinprivate-practiceSLPs.
Thename“speech-languagepathologist”isactuallyabitofanunderstatement. 4 SomeSLPsdoworkwithcommunicationdisorders,stemmingfromspeechimpedimentstodisabilitiesrelatingtooral,written,orgraphicallanguage.AnSLPwhospecializesinspeechmayworkonarticulationorphonation,thoughsomeofthesespecialistswillalsoworkwithattentionand 5 memory.Inparticular,theyworkwiththecomponentsofthosepracticesthatdealwithlanguage.Somearemoreconcernedwiththemechanicalsideofspeech,addressing 6 theirrespiratoryaspects,particularlyasrelatedtovolume,breathiness,orrasp.
ImagemodifiedfromASHALeader.
3. Whichchoicegivesinformationconsistentwiththegraph?A) NOCHANGEB) currentlyabouthalfofallSLPsworkinschools,C) thereareonlyabout5,300SLPsatworkinschools,D) collegesanduniversitiesdevoteonlyabout3%oftheirbudgetstoSLPs,
4. Thewriterisconsideringreplacingthewordsanunderstatementwiththewordsamisnomer.Shouldthewritermakethechangeorkeepthesentenceasis?A) Makethechange,becausethewordmisnomerismorecommoninsocialscience.B) Makethechange,becausetheparagraphgoesontosaythat“speech-language
pathologist”isthewrongnamefortheprofession.C) Keepthesentenceasis,becauseunderstatementislongerandthereforemore
formal.D) Keepthesentenceasis,becausethenameisnotincorrect,merelyinsufficientto
representtherangeofduties.
5. Whichofthefollowinggivesthebestwaytocombinethesetwosentences?A) NOCHANGEB) memory;theyworkinparticularwiththecomponentsC) memory.Particularlythecomponents
D) memory,particularlythecomponents
6.A) NOCHANGEB) one’sC) itsD) it’s
AlthoughcommunicationdisordersareSLPs’mostcommontargets,somespecialistswillworkmorewithswallowingdisorders.Ifaninfantisstrugglingtofeed,forinstance,anSLPmightworkintandemwithamedicaldoctortocleartheesophagealfunctiontogetitbackinto 7 goodworkingorder.AnSLPcan 8 leadaregimenofswallowingtherapiesandadvisedietarychangesthatmightmakeswallowingmorecomfortable.
7.A) NOCHANGEB) shipshape.C) gravy.D) goodtimes.
8. Whichofthefollowingwouldbestmaintainthissentence’sfocusontheactionsanSLPmighttaketoaddressaswallowingdisorder?A) NOCHANGEB) handlemanypatientsatonceC) workinaschoolorhospitalD) keepdetailedpaperworkonapatient’sprogress
Inmostcases,aspeech-languagepathologistwillworkinterdisciplinarily,oftenwithotherSLPspecialistsormedicaldoctors.AlongwiththeincreasedinvolvementofSLPs,researchcontinues 9 toshowthatthemechanisms,ofthemouthandrespiratorysystem,arecentral,toanunderstanding,ofthebodyasawhole.Speech-languagepathologyalsooffersaninterestingintersectionofthesocialandmedical.Speechisafterallnotmerelyabiological 10 function,it’salsoamajormeansofsocialization,andtherangeofthingsthatmightrenderapatientspeechlessisvast.Althoughthedigitalagehaschangedmanyfacetsofourlives,theriseoftheSLPremindsusthattherearesomebasicsthatnomachinecanfixorreplacefor 11 itself.
9.A) NOCHANGEB) toshowthatthemechanisms,ofthemouthandrespiratory,systemarecentraltoan
understandingC) toshowthatthemechanismsofthemouthandrespiratorysystemarecentraltoan
understandingD) toshowthatthemechanismsofthemouthandrespiratorysystemarecentral,toan
understanding,
10.A) NOCHANGEB) function;it’sC) function,butit’sD) functionit’s
11.A) NOCHANGEB) it.C) them.D) us.
Questions12–22arebasedonthefollowingpassage.
TheOtherSteelCity
—1—
12 SetonthebanksofMonocacyCreek,theareathatisnowBethlehem,PA,wasinhabitedbyarich13 diversityofindigenouspeoples.[A]Bythetimeofthatcontact,theareawasprimarilyoneoftheAlgonquian-speakingLenapetribeanditsvariousdivisions. 14 Theytradedwithmanysettlersinthemid-Atlanticregion.
12. Whichofthefollowingbestintroducesthehistoricaltoneofthisessay?A) NOCHANGEB) Hometoover700,000people,C) LongbeforeEuropeancontact,D) About50milesnorthofPhiladelphia,
13. WhichofthefollowingalternativestotheunderlinedportionwouldbeLEASTacceptable?A) varietyB) arrangementC) assortmentD) multiplicity
14.A) NOCHANGEB) ItC) SomeD) Thesegroups
—2—
Whilemanygroupsinotherregionsweresystematicallyexterminatedandrelegatedtosmallerplotsofland,theLenape 15 wentontocontinuetobeacontributingfactortothelandscapeoftheearlyregion.EvenaftertheinitialEuropeansettlementonChristmas 16 Evein1741,theLenapetradingcontinued,thoughthewrittenhistoryprimarilyfollowstheprogressofwhitesettlers.
—3—
Thesesettlers,agroupofMoraviansledbyDavidNitschmanandCountNicolasvonZinzendorf,
calledtheregionBethlehem,afterthebirthplaceofJesusChrist.TheMoravianssetupmissionstoconverttheLenapeandnon-English-speakingChristianstothetenetsofMoravianism, 17 apracticewidelycriticizedforitsignoranceoflocaltraditions.[B]Althoughthegroupwasrelativelysmallanditsreligiousinfluencedidnotreachasfaras 18 othergroups,theMoravianshadalastingculturalinfluenceontheshapeoftheearlyUnitedStates.WiththeirstrongtiestoGermanyandmusicalbent,theannualMoravianBachfestivalwasoneofthefirstplacesforpeopletohearthemusicfromoverseasthatwouldbecomesointernationallyinfluential.[C]
15.A) NOCHANGEB) continuedgoingonC) wentonD) continued
16.A) NOCHANGEB) Evein1741theLenapetradingcontinuedC) Evein1741theLenapetradingcontinued,D) Eve,in1741,theLenapetradingcontinued,
17. WhichofthefollowingtruechoiceshelpstomaintainthefocusonthewaytheMoraviansettlershavebeencharacterizedthroughouttheessay?A) NOCHANGEB) usingdiplomacyratherthanforce.C) acornerstoneofEuropeancolonizingmissionsinAfricaandAsia.D) whichhelpedtobringEuropeanliteracyandeconomicstomanyoutsideofEurope.
18.A) NOCHANGEB) someotherC) thoseotherD) thatofsomeother
—4—
Inthetwentiethcentury,Bethlehembecameknownalloverfortheworldforsomethingmuchdifferent:steel.BethlehemSteelwasfoundedin1857amidtheindustrialrevolution,andbythe1940s,19 itsfactorywasprovidingsubstantialamountsofarmorandsteelfortroopsinWorldWarII,in
additiontoprovidingthemetalworkforbridgesandstructuresalloverthecountry.Theplantceasedoperationsin1995,butitsblastfurnaces,thoseremindersofpastindustrialglory, 20 remains.
—5—
Somecitiesmighthavebeenlaidlowbythedeathofamajorindustry,butBethlehemhasemergedseeminglyunscathed.Althoughlocalsknowitasthe“ChristmasCity,”forthemanydecorationsandactivitiesthereinDecember,Bethlehemisalsoasignificantculturecenterfortheregion,anditsformersteelmillhasbeenrepurposedtohostallvarietyofevents.[D]ThecontributionsofBethlehemhavechangedfromcenturytocentury,soitshouldbenosurprisethatthetwenty-firstcenturyshouldbringtothecitysomething 21 noone’severseenthelikeof.
19.A) NOCHANGEB) theirC) they’reD) it’s
20.A) NOCHANGEB) isremaining.C) remain.D) areremaining.
21. Whichofthefollowingwouldbestconcludetheessaybypreservingitsstyleandtone?A) NOCHANGEB) tosteelitsreputationasarealblast!C) ithasn’tseenbefore.D) everyoneprettymuchexpectsbynow.
Question 22 asksaboutthepreviouspassageasawhole.Thinkaboutthepreviouspassageasawholeasyouanswerquestion22.
22. Uponreviewingthisessayandconcludingthatsomeinformationhasbeenleftout,thewritercomposesthefollowingsentence:
Afterthesemanyyearsofeducation,BethlehembecameaMoravianstronghold,withtheMoravianAcademyandCollegestillanucleusofintellectuallifeintheregion.
ThebestplacementforthissentencewouldbeatpointA) [A]inparagraph1.B) [B]inparagraph3.C) [C]inparagraph3.D) [D]inparagraph5.
Questions23–33arebasedonthefollowingpassage.
LookItUp!
[1]Imagineyou’retextingsomeone,andthetwoofyougetintoaheateddebate.[2]Theycorrectyourspelling.[3]Finally,toproveyourpointonceandforall,youwriteavoluminous,paragraph-longtext,onlytoseethatyourinterlocutorhasresponded,“TL;DR.”[4]Now,youmightknowthatthismeans“toolong,didn’tread,”butwhatifyoudon’t? 23 [5]Well,UrbanDictionarycansavetheday.[6]JusttypethephraseintoGoogleandseewhatturns 24 down.[7]Dictionarieshaveawayofshowingupineveryfacetofourdigitallives.[8]Theytranslatepagesinforeignlanguages.[9]Theydefinewordsthatwethinkweknowandthosewe’veneverheardof.[10]Dictionariesareeverywhere. 25
23. Thewriterisconsideringdeletingthephrasewhatifyoudon’t?,andadjustingthepunctuationaccordingly.Shouldthisphrasebekeptordeleted?A) Kept,becauseitaddsvarietytoaparagraphfullofdeclarativesentences.B) Kept,becauseitposesaquestionthatisansweredinthefollowingsentence.C) Deleted,becauseitisarhetoricalquestiontowhichtheanswerisalreadyimplied.D) Deleted,becausenopartoftheparagraphgoesontoanswerit.
24.A) NOCHANGEB) in.C) back.D) up.
25. Thebestplacementforsentence2wouldbeA) whereitisnow.B) atthebeginningoftheparagraph.C) aftersentence5.D) aftersentence8.
Infact,dictionariesaresoprevalentthatit’seasytoforgetthatthey 26 havenotalwaysexisted.Theword“dictionary”wasinfactnotcoineduntilJohnofGarlandpublishedhisDictionariusin1220tohelpreaderswiththeirLatindiction. 27 Furthermore, 28 numerousdictionariesappearedthroughouttheMiddleAgesandtheEarlyModernperiod,thefirstnoteworthyEnglishdictionarycamefromSamuelJohnson,whoseDictionaryoftheEnglishLanguagewaspublishedfirstin1755.Johnson’sopusremainsthefirstmoderndictionary,containingconsistentspellings,variantdefinitions,textual 29usages,andalphabetical,arrangements.Johnson’sdictionarywasthelawofthelexiconuntil1884,whentheOxfordEnglishDictionary(OED)beganitsreign,whichcontinuestoday.
26.A) NOCHANGEB) werenotC) didnotD) didnothave
27. Thewriterisconsideringreplacingtheworddictionwithpronunciation.Shouldthewritermakethechangeorkeepthesentenceasis?A) Makethechange,becausepronunciationisthemorecommonlyusedword.B) Makethechange,becausedictionhasanimprecisemeaninginthesentence.C) Keepthesentenceasis,becausedictionhelpstoexplainthetermgivenearlierin
thesentence.D) Keepthesentenceasis,becausepronunciationmeanssomethingcontraryto
diction.
28.A) NOCHANGEB) indeed,numerousdictionariesC) anumberofdictionariesD) whilenumerousdictionaries
29.A) NOCHANGEB) usages,and,alphabeticalC) usages,andalphabeticalD) usagesandalphabetical,
Johnson’sAmericancounterpartwasNoahWebster,whopublishedhisfirstdictionaryin1806.Webster’sbest-known 30 workAnAmericanDictionaryoftheEnglishLanguage,waspublishedin1828.ThetextwasbasedinlargepartonJohnson’sdictionary,thoughitincluded12,000 31 wordsthathadnotappearedinpreviousdictionaries.Inaddition,WebsterwasaspellingreformerwhothoughtEnglishspellingswereoverlyornateandcomplex.Asaresult,whenAmericanswrite“color”and“gray”wheretheEnglishwrite 32 otherthings,AmericanshaveNoahWebstertothank.
33 Whatisinterestingaboutthesetwodictionaries,andaboutthehistoryofdictionariesingeneral,ishowclearlytheyshowthedifferentdirectionsthatlanguagecanbepulled.Ontheonehand,anewdictionaryshouldsolidifythelanguageinanewway—itshouldsettleolddisputesandgivedefinitivedefinitions.Ontheotherhand,eachdictionaryupdateshowsthatlanguageisfluidandthatnoprintedwordcancontainthevarietiesoflanguageasitisactuallyused.Afterall,theOEDmayhavetoldthe
worldthat“selfie”wasthewordoftheyearin2013,butdidn’ttheworldknowthatalready?
30.A) NOCHANGEB) work,AnAmericanDictionaryoftheEnglishLanguageC) work,AnAmericanDictionaryoftheEnglishLanguage,D) workAnAmericanDictionaryoftheEnglishLanguage
31. WhichofthefollowingtruestatementswouldbestemphasizetheuniqueachievementofWebster’sdictionary?A) NOCHANGEB) wordsthatdrewfromlanguagesvaryingfromOldEnglishtoSanskrit.C) words,whichisaheckofalotofwords.D) wordsfrommanysources,includingbooksandspeeches.
32.A) NOCHANGEB) “colour”and“grey,”C) differently,D) DELETEtheunderlinedportion,placingthecommaafterthewordwrite.
33.A) NOCHANGEB) Bothwhatisinterestingaboutthesetwodictionariesandwhatisinterestingabout
dictionariesingeneral,C) Aboutthehistoryofdictionariesingeneral,butinparticularaboutthesetwo,D) Thesetwodictionariesareinteresting,butsoisthehistoryofdictionariesin
general,
Questions34–44arebasedonthefollowingpassage.
Goodnight,sleeptight…
—1—
Theyarethehorrorofeverycity-dwellerandinternationaltraveler.Youcan’tseethem.Youonlyseetheiraftermath,usuallyintheformthatbecomesmoreuncomfortableastheday 34 ofanitchyweltgoeson.Bedbugsarethesilentfeeders:theycomeoutatnightanddisappearwiththelightofmorning.Theyhideintheunseenplacesinthemattressorinthecracksofthefloor.Likethemostannoyingvampiresintheworld, 35 humanbloodisthefoodofbedbugs.
—2—
Interestinbedbugsseemstobenearlyasoldaswrittenhistoryitself. 36 Theywerenotthenuisancethenthattheyhavesincebecome.Remember,previousagesbelievedinthemedicinalvalueofleechesandblood-letting,andbedbugswereseenashelpingtoextractthetoxinsthatcamefromsnakebitesorearinfections 37 byremovingthem.
34. ThebestplacementfortheunderlinedportionwouldbeA) whereitisnow.B) afterthewordaftermath(andbeforethecomma).C) afterthewordform.D) aftertheworduncomfortable.
35.A) NOCHANGEB) bedbugsfeedonhumanblood.C) atypicalmealforbedbugsisoneofhumanblood.D) humanbloodiswhatbedbugsneedtolive.
36. Thewriterwantstoinsertapieceofevidencethatwillsupporttheprevioussentence(“Bedbugs…itself”).Whichofthefollowingtruestatementswouldofferthatsupport?A) SomeGreekwritersmentionthemasearlyas400BCE.B) Writtenhistoryisthoughttohavebegunaroundthe4thcenturyBCE.C) Bedbugstypicallyliveforapproximately6-12months.D) IntheUnitedStates,bedbugsaretypicallyassociatedwiththeEastCoast.
37.
A) NOCHANGEB) byassistingintheirremoval.C) gettingthemoutofthere.D) DELETEtheunderlinedportion.
—3—
Bythetwentiethcentury,however,bedbugswereseentobethenuisancethat 38 theyare.Thiswasinpartdueto 39 thereprevalence:in1933,theUKMinistryofHealthreportedthatallthehousesinmanyareasofthecountryhadsomebed-buginfestation.MilitarybasesduringWorldWarIIhadsignificantproblemswithbed-buginfestationasthebugsappearedalloverEurope.
—4—
Withincreasedpublicawarenessandsomeadvancesinpesticides,bedbugswerenearlyeradicatedfromtheUnitedStatesinthe1940s,thoughtheyreemergedasanurbanmenaceinthe1980s. 40 Nooneisentirelyclearonthereason,thoughscientistshypothesizethattheresurgenceofbedbugsisduetoincreasedpesticide 41 resistantsandinternationaltravel.Thenuisanceisnowtreated 42 locally.Thoughthelifespanandlongdormancyofthebedbugshaveledmanytobelievethattheproblemmaybeapermanentone.
38.A) NOCHANGEB) itis.C) somecanbe.D) theyareknowntobe.
39.A) NOCHANGEB) they’reC) theirD) the
40. Withtheprecedingsentence,thewriterintendedtointroducethisparagraphinawaythatestablishedcontinuitywiththepreviousparagraph.Hasthewriterachievedthisgoal?A) Yes,becausethepreviousparagraphaddressestheresurgenceofbedbugsinthe
laterpartofthecentury.B) Yes,becausethepreviousparagraphsuggestsanearliermomentchronologically.C) No,becausethereisnomentionofthe1940sorthe1980sinthepreviousparagraph.
D) No,becausethisparagraphdoesn’tmentionanythingaboutmilitarybasesorwartimeincidences.
41.A) NOCHANGEB) resistanceC) resistivityD) resisting
42.A) NOCHANGEB) locally;thoughC) locally,andD) locally,though
—5—
Today,bedbugsarestillmainlyconsideredanuisance.Theycostrentersandownersmillionsofdollarseachyearinexterminatorfeesandinfestedfurniturereplacement.Butarecentstudyhasshownthatwemayhaveanewreasontoworryaboutthebugs.Now,someresearchhasshownthatbedbugscantransmitdisease,apracticeofwhichtheywerelongbelievedincapable.AstudydocumentedintheAmericanJournalofTropicalMedicineandHygieneshowedthatbedbugscouldtransmitChagasdiseasebetweenmice, 43 whichmanyobjectedtoasbeinginhumane.
—6—
Ifthesefindingsaretrue,thenbedbugsmaybeamoresignificantpublichealththreatthanwaspreviouslybelieved.Likemosquitoesinmalaria-riddencountries,bedbugsmayberedefinedasatruemenace,ratherthanjustanitchynuisance. 44
43. Whichofthefollowingtruechoiceswouldbestmaintainthefocusofthissentenceandparagraph?A) NOCHANGEB) whichareoftenusedinlaboratorytests.C) thoughnotinrats,whomtheyhaven’ttested.D) whichisreallystartling.
44. Thebestplacementforparagraph6wouldbeA) whereitisnow.
B) afterparagraph2.C) afterparagraph3.D) afterparagraph4.
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–NoCalculator25MINUTES,20QUESTIONS
TurntoSection3ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–15,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions16–20,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion16onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorisnotpermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Marcoisorderingsalt,whichisonlysoldin30-poundbags.Hecurrentlyhas75poundsofsalt,andheneedstohaveaminimumof200pounds.Whichofthefollowinginequalitiesshowsallpossiblevaluesforthenumberofbags,b,thatMarconeedstoordertomeethisminimumrequirement?A) b≥4B) b≥5C) b≥6D) b≥7
2. Awebsitehopestosignup100,000subscribers.Sofar,thewebsitehassignedupanaverageof500subscribersperdayforddays.Whichofthefollowingrepresentsthenumberofadditionalsubscribers,W,thewebsitemustsignuptoreachitsgoal?A) W=500dB) W=99,500dC) W=100,000–500dD) W=100,000+500d
3. Iffisafunctionandf(4)=5,whichofthefollowingCANNOTbethedefinitionoff?A) f(x)=x+1B) f(x)=2x–3C) f(x)=3x–2D) f(x)=4x–11
4. Whichofthefollowingisequivalenttotheexpression ?
A)
B)
C)
D) x–1
5. RégineismeasuringhowmanysolutionsfromBatchxandBatchyareacidic.Shemeasuredatotalof100solutionsfrombothbatches.40%ofthesolutionsfromBatchxand70%ofthesolutionsfromBatchywereacidic,foratotalof48acidicsolutions.
SolvingwhichofthefollowingsystemsofequationsyieldsthenumberofsolutionsinBatchxandBatchy?A) x+y=100
0.4x+0.7y=48B) x+y=48
0.4x+0.7y=100C) x+y=100×2
0.4x+0.7y=48D) x+y=100
40x+70y=48
6. Whichofthefollowingequationsbestdescribesthefigureabove?A) y=–x4+6B) y=–(x2+6)C) y=–x2+6D) y=x4+6
7. Thepriceofanitemthatcost$43in2010alwaysincreasesby$3peryear.Thecurrent
priceindollars,P,oftheitemcanberepresentedbytheequationP=3t+10,wheretisthenumberofyearssincetheitemwasfirstmanufactured.Whichofthefollowingbestexplainsthemeaningofthenumber10intheequation?A) Itisthepriceoftheitemin1999.B) Itisthepriceoftheitemin2000.C) Itisthepriceoftheitemin2001.D) Itistheannualincreaseinthepriceoftheitem.
8.
InthecirclewithcenterOandradius10shownabove, AOB= .Whatisthelengthof
minorarcAB?A) πB) 2πC) 4πD) 20π
9. Clark’sRuleisaformulausedtodeterminethecorrectdosageofadultover-the-countermedicineachildcanreceive.Thechild’sweight,inpounds,isdividedby150,andtheresultismultipliedbytheadultdoseofthemedicine.Amotherneedstogiveherdaughteracetaminophen,whichhasanadultdoseof1,000milligrams.Shedoesnotknowherdaughter’sexactweight,butsheknowstheweightisbetween75and90pounds.Whichofthefollowinggivestherangeofcorrectdosage,d,inmilligramsofacetaminophenthedaughtercouldreceive?A) 50<d<60
B) 500<d<600C) 1,000<d<1,200D) 1,600<d<2,000
10. Ohm’sLaw,whichcanbewrittenasIR=V,relatesthecurrentIinamperesthatflows
throughaconductivematerialwithresistanceRohmstothevoltageVbetweenthetwo
ends.ThepowerPinwattscanberelatedtoIandRbytheequationI= .Whichofthe
followinggivesPintermsofVandR?
A) P=
B) P=
C) P=
D) P=V2R3
11.
Thefigureaboveshowsthegraphinthexy-planeofthefunctiong.Howmanydistinctrealrootsdoesghave?A) 1B) 2C) 3D) 4
12.
Note:Figurenotdrawntoscale.
Inthefigureabove, ABC CDE.Whichofthefollowingistrue?A) AB||CDB) BC||AEC) CD||AED) BC AE
13. Forwhichofthefollowingvaluesofwdoes ?
A) 2B) 3C) 4D) 6
14. Ifr=( a+b)2ands=–4ab+3b,whatisr–2s,intermsofaandb?
A) a2+b2–7ab–6b
B) a2+b2–7ab+6b
C) a2+b2+9ab–6b
D) a2+b2+9ab–6b
15. Whichofthefollowinglinescontainsallpointsequidistantfromthepoints(0,4)and(8,0)inthexy-plane?A) 2y=–x+8B) 2y=xC) y=2x–6D) y=–2x
DIRECTIONS
Forquestions16–20,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5. Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbe
interpretedas ,notas3 .)
6. DecimalAnswers:Ifyouobtainadecimalanswerwithmoredigitsthanthegridcanaccommodate,itmaybeeitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
16.
+ =1
p−3q=1
Basedonthesystemofequationsabove,whatisthevalueofp?
17.
y=x(y−2)2−4=−q
Thesystemofequationsaboveintersectsattwopoints.WhatisthesumofthecoordinatesofthepointofintersectioninQuadrantI?
18.
1<(c−1)2<36
Whatisthegreatestintegersolutiontotheinequalityabove?
19.
2y−x≤4−2y+y≥−4
Ifsisthesumofthex-andy-coordinatesofanypointinthesolutiontothesystemofinequalitiesaboveasgraphedinthexy-plane,whatisthegreatestpossiblevalueofs?
20.
Acubewithsidelength6isshowninthefigureabove.IfpointQliesonsquareABCDandisequidistantfrompointsA,B,C,andD,whatisthevolumeofpyramidEFGHQ?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
MathTest–Calculator55MINUTES,38QUESTIONS
TurntoSection4ofyouranswersheettoanswerthequestionsinthissection.
DIRECTIONS
Forquestions1–30,solveeachproblem,choosethebestanswerfromthechoicesprovided,andfillinthecorrespondingcircleonyouranswersheet.Forquestions31–38,solvetheproblemandenteryouranswerinthegridontheanswersheet.Pleaserefertothedirectionsbeforequestion31onhowtoenteryouranswersinthegrid.Youmayuseanyavailablespaceinyourtestbookletforscratchwork.
NOTES
1. Theuseofacalculatorispermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa
realnumber.
REFERENCE
Thenumberofdegreesofarcinacircleis360.
Thenumberofradiansofarcinacircleis2π.Thesumofthemeasuresindegreesoftheanglesofatriangleis180.
1. Anairpumpatagasstationdispenses90poundsofairfor$0.25.Whichofthefollowingexpressionsgivesthenumberofpoundsofairdispensed,P,forddollars?A) P=d+90B) P=d+360C) P=90dD) P=360d
2. Tayloris6feettall.If1footisequaltoapproximately0.3meters,thenwhichofthefollowingisclosesttoTaylor’sheightinmeters?A) 1.8B) 2C) 18D) 20
3. Adeveloperiscreatingaplanfora44-acreparkthatincludesa4-acrelakethatcannotbedeveloped.If8to10acres,inclusive,mustbereservedforsoccerfields,whichofthefollowinginequalitiesshowsallpossiblevaluesforp,theamountoflandthatwithintheparkthatisavailablefordevelopment?A) 26≤p≤40B) 30≤p≤32C) 34≤p≤36D) 36≤p≤40
4.
Thescatterplotaboveshowsthefuelefficiency,inmilespergallon,ofavarietyofvehiclesweighingbetween1.5and4tons.Basedonthelineofbestfittothedatarepresented,whichofthefollowingistheclosesttotheexpectedmilespergallonofavehiclethatweighs3tons?A) 20B) 24C) 27D) 28
5.
AspartofarecentwildlifeconservationeffortinGuatemala,parkrangersinTikalNationalParkhavetrackedthegrowingnumberofwhite-nosedcoatilivingwithinacertainprotectedregionovertheperiod1994-2004.
Accordingtothedataabove,ifthepopulationofcoatiintheprotectedregionofTikalNationalParkincreasedatthesameratefrom2004-2006asitdidfrom2000-2004,thenwhatwasthenumberofcoatiintheparkin2006?A) 180B) 190C) 200D) 210
6.
Iftheequationabovehasinfinitelymanysolutionsford,whatisthevalueofa?A) –10B) 10C) 15D) 20
7.
MaggieandGlennbothleavefromthesamehousetogoforajogalongatrail.Shortlyafterleaving,MaggierealizessheforgotheriPodandreturnshometofinditbeforeheadingbackoutontothesametrail.Thegraphaboveshowshowfareachofthemisfromhomeforthefirstfifteenminutesoftheirjogs.
WhatisGlenn’sapproximateaveragespeedinmeterspersecondfortheportionofhisjogshown?A) 3.3B) 15C) 200D) 12,000
8. EnvironmentalistshavebeenmonitoringtheareaofaglacierinCanada.Theglacierisslowlyshrinking.Theglacieroriginallyoccupied15,000squaremiles,butaftertwoyearsofmonitoringtheglacier,thescientistsdocumentthattheareaoftheglacierisnow14,910squaremiles.Ifyisthenumberofyearssincemonitoringbegan,whichequationbestdescribestheglacier’sarea,G(y),asafunctionoftime?
A) G(y)=15,000
B) G(y)=15,000(0.003)y
C) G(y)=15,000(0.997)y
D) G(y)=0.997y
9. Mikeconsumesanaverageof1,680caloriesperday.Eachdayhehasfinals,Mikeconsumes12%morecaloriesperdaythanheusuallydoes.Duringthelastdayoffinals,hecelebratesbyconsuminganadditional900calories.WhichofthefollowingrepresentsthetotalnumberofcaloriesMikeconsumesduringddaysoffinals?
A) 1.12(1,680d+900)B) 1.12(1,680d)+900C) 1.12(1,680+900)dD) (1,680+0.12d)+900
10. ThevarsityswimteamatNorthwestHighisplanningateamtripandneedstochoosebetweenAustin,TX,andPensacola,FL.Theteamtakesavoteandtheresultsofthevoteareshowninthetablebelow.
Giventheinformationshownabove,whichofthefollowingstatementsistrue?A) ThenumberofjuniorsthatpreferPensacola,FL,istwicethenumberofjuniorsthat
preferAustin,TX.B) TheseniorsaremorethanthreetimesaslikelytopreferPensacola,FL,thanarethe
juniors.C) ThenumberofseniorsthatpreferAustin,TX,is5%morethanthenumberofjuniors
thatpreferAustin.D) One-thirdofthejuniorspreferPensacola,FL.
11. The2013U.S.Censusrecordedthehighesteducationalattainmentofalladultsaged25yearsorolderincountyT,oneofthemosteducatedpartsofthecountry.Theresultsaregiveninthetwo-waytablebelow.
Accordingtothedatapresentedinthetableabove,ifyouweretochooseapersonatrandomoutoftheentirepopulationaged25yearsorolderincountyT,whatistheapproximateprobabilitythatthepersonyouchoseisamanwithadoctoraldegree(given
asapercent)?A) 2%B) 7%C) 28%D) 51%
12. Thecostindollars,C,ofproducingacustom-madeT-shirtwithateamlogoisgivenbytheformulaC=110+ ,wherexisthenumberofT-shirtsproduced.WheneveryT-shirt
producedissold,therevenuefromsellingthecustomizedT-shirtsisgivenbyR=15x−
.Whichoneofthefollowingwouldbetheformulafortheprofitfromproducingand
sellingxT-shirts?
(Profit=Revenue–Cost)
A) − − x+110
B) − − x+110
C) − + x−110
D) − + x−110
13. WhileonvacationinMorocco,Erikdecidedtosplurgeonafancyhotelthatcost2,000Moroccandirhamspernight.Ifhestayedinthatparticularhotelforthreenights,buthisbankonlyletshimwithdraw$200atatime,howmanyvisitstotheATMmustErikhavemadeinordertocoverthecostofhishotelstay?(Note:1Moroccandirham=$0.11)A) 1B) 2C) 3D) 4
14. Peter’sPetrolStationissellingregularunleadedgasfor$3.49agallonandpremiumgasfor$3.79agallon.Ifacarwashispurchased,thenadiscountof$0.10pergallonisapplied.Duringonemorning,atotalof850gallonsofgaswassold,and100gallonsweresoldatthediscountedrate.Thetotalcollectedinsaleswas$3,016.50.Solvingwhichofthefollowingsystemsofequationsyieldsthenumberofregularunleadedgallonsofgas,u,andthenumberofpremiumgallonsofgas,p,thatweresoldduringthatmorning?
A) u+p=8503.49u+3.79p=301.65
B) u+p=8503.49u+3.79p=3,016.50
C) u+p=8503.49u+3.79p=3,026.50
D) u+p=3,016.503.49u+3.79p=850
15. Ofthe784juniorsandseniorsatAbingdonHighSchool,319arecurrentlyenrolledinoneormoreAdvancedPlacement(AP)courses.OftheseAPstudents,75areenrolledinAPBiology,58areenrolledinAPU.S.History,and22areenrolledinbothAPBiologyandAPU.S.History.ApproximatelywhatpercentofthejuniorsandseniorsatAbingdonHighSchoolareenrolledinAPcoursesotherthanBiologyandU.S.History?A) 17%B) 27%C) 37%D) 47%
16. ToreceiveaBinhischemistryclass,Mateoneedstoearnanaveragescorefrom80to89,inclusive.Hisgradeisbasedonlyon3tests.Thehighestpossiblescoreoneachofthesetestsis100points.Hescored79onhisfirsttestand95onhissecondtest.Ifyrepresentshisscoreonthethirdtest,whichoftheinequalitiesbelowshowsallvaluesofythatwouldearnMateoaBinhischemistryclass?A) 66≤y≤93B) 66≤y≤100C) 80≤y≤89D) 80≤y≤93
17.
Agardenerpreparesamixtureoffertilizerwithconcentration,byvolume,equaltoY.ItispreparedbymixingavolumeoffertilizergivenbyAwithavolumeofwatergivenbyW.Theexpressionaboverepresentsthemixturedescribed.WhatphysicalquantitydoesthetermA+Wrepresentintheequationabove?A) Thevolumeofthemixture
B) ThemassoffertilizeraddedC) ThevolumeofthefertilizerinthemixtureD) Theconcentrationofthefertilizer
18. Twogroupsofsubjectsarecombinedinapsychologicalresearchexperiment.ThemodescoreforgroupAis7andthemodescoreforgroupBis6.Whichofthefollowingconclusionscanbemade?A) Themodeforthewholegroupis6.B) Themodeforthewholegroupisbetween6and7.C) Themodeforthewholegroupis7.D) Themodecannotbedeterminedfromthegiveninformation.
19. Themapbelowshowsthelayoutofstreetsinacityandthelocationofseveralplaces.Eachhorizontalorverticallinebetweentwoadjacentstreetsrepresentsacityblock,andeachcityblockrepresents0.6miles.
JoshneedstodrivefromKelly’sKitchentoGary’sGrocery.IfJoshdrivestheshortestdistancepossibleontheroadsshownaboveataconstantspeedof30milesperhour,howlongdoesittakehimtomakethetripfromKelly’sKitchentoGary’sGrocery?A) 6minutesB) 10minutesC) 12minutesD) 20minutes
20.
2s− t=10
5s=t+12−s
Whichofthefollowingisatruestatementaboutthesystemofequationsabove?A) Thereareinfinitelymanysolutionstothesystemofequations.B) Whenthesystemissolvedfors,theresultis5.
C) Whenthesystemissolvedfort,theresultis6.D) Therearenosolutionstothesystemofequations.
21. ThestudentcouncilatShermerHighSchoolwantstousestudentopiniontodecideononeofthreepossiblehomecomingthemesfortheyear.PresidentPetersonthinksthatthebestwaytodeterminepopularopinionisforeachofthe10membersofthestudentcounciltopoll10oftheirfriendsandselectthethemethatreceivesthemostvotes.VicePresidentVaidyawantstogotothecafeteriaduringlunchandpoll100studentstodeterminethewinner.TreasurerThompsonsaysthebestmethodwouldbetoassignnumberstoeachofthe1,000studentsintheschool,randomlyselect100ofthemtopoll,andselectthewinnerbasedontheresults.SecretaryStephensarguesthattheymustpolleachofthe250membersoftheseniorclasstofindthemostpopulartheme.Whosemethodismostlikelytoaccuratelydetermineoverallstudentopinionregardingthemostpopularhomecomingtheme?A) PresidentPetersonB) SecretaryStephensC) TreasurerThompsonD) VicePresidentVaidya
22. Isthepoint(–2,–2)locatedinside,on,oroutsidethecirclewithequation(x+3)2+(y–1)2=9?A) InsidethecircleB) OnthecircleC) OutsidethecircleD) Itcannotbedeterminedfromthegiveninformation.
23. Iftheexpression ismostnearlyequalto –C,thenwhatisthevalueofC?
A) –3B) −
C) 2
D) 3
24. Asurveywasconductedamongarandomlychosensampleoffull-timesalariedworkersaboutsatisfactionintheircurrentjobs.Thetablebelowshowsasummaryofthesurveyresults.
Ofthepeoplewhosehighestlevelofeducationwasabachelor’sdegreewhoreportedjobsatisfaction,1,000peoplewererandomlyselectedtocompleteafollow-upsurveyinwhichtheywereaskedabouttheirsalarysatisfaction.Therewere658peopleinthisfollow-upsamplewhosaidthattheyweresatisfiedwiththeirsalaries,andtheother342peoplewerenotsatisfied.Usingthedatafromboththeinitialsurveyandthefollow-upsurvey,whichofthefollowingstatementsismostlikelytrue?A) Approximately16millionpeoplewithbachelor’sdegreesandwhoaresatisfied
withtheirjobswouldreportsalarysatisfaction.B) Approximately24millionpeoplewithbachelor’sdegreeswouldreportsalary
satisfaction.C) Approximately47millionpeoplewithbachelor’sdegreeswouldreportsalary
satisfaction.D) Approximately72millionpeoplewithbachelor’sdegreeswouldreportsalary
satisfaction.
25. Linedhasaslopeof andpassesthroughthepoint(1,1).Lineeisparalleltolinedand
hasay-intercept3timesthatoflined.Whichofthefollowingistheequationoflinee?
A) 5y–4x=3B) 5y–x=4C) 10y–8x=30D) 20y+25x=12
26.
Theequationabovecanbesolvedfortwosolutions,oneofwhichisextraneous.Whatis
thevalueoftheextraneoussolution?A) 5B) 6C) 8D) 9
27. Agamingcompanyconductedastudytofindoutwhatagegroupspreferredwhichtypesofgames.Thetablebelowoutlinesthesurveyresults.
Accordingtotheinformationprovidedinthetable,thegamingcompanyconcludesthatiftheycandoublethenumberof19-to22-yearoldsplayingsportsgames,andincreasethenumberofsportsgamersinthe9-to13-yearoldagegroup,theywillhaveequaltotalnumbersofplayersforeachgametypeiftheydoublethenumberofplayersofadventuregamesinwhichagegroup?A) 23-to60-yearoldsB) 19-to22-yearoldsC) 14-to18-yearoldsD) 9-to13-yearolds
28.V(t)=at+k
Atacertainmanufacturingplant,thetotalnumberofvacationdays,V(t),anemployeehasaccruedisgivenbythefunctionabove,wheretisthenumberofyearstheemployeehasworkedattheplant,andaandkareconstants.IfMartinhasaccrued9morevacationdaysthanEmiliohas,howmanymoreyearshasMartinworkedthanEmilio?
A)
B) 9–aC) 9+aD) 9a
29.
Inthefigureabove,sinx°= .Whatistheperimeterofthefigure?
A) 10+
B) 7+
C) 14+2
D) 39+2
30. AtSantaMonicaHighSchool,theratioofjuniorstoseniorsis4to3,theratioofseniorstosophomoresis5to4,andtheratiooffreshmentosophomoresis7to6.Whatistheratiooffreshmentoseniors?
A)
B)
C)
D)
DIRECTIONS
Forquestions31–38,solvetheproblemandenteryouranswerinthegrid,asdescribedbelow,ontheanswersheet.
1. Althoughnotrequired,itissuggestedthatyouwriteyouranswerintheboxesatthetopofthecolumnstohelpyoufillinthecirclesaccurately.Youwillreceivecreditonlyifthecirclesarefilledincorrectly.
2. Marknomorethanonecircleinanycolumn.3. Noquestionhasanegativeanswer.4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.
5. Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbe
interpretedas ,notas3 .)
6. DecimalAnswers:Ifyouobtainadecimalanswerwithmoredigitsthanthegridcanaccommodate,itmaybeeitherroundedortruncated,butitmustfilltheentiregrid.
Acceptablewaystogrid are:
Answer:201–eitherpositioniscorrect
NOTE:Youmaystartyouranswersinanycolumn,spacepermitting.Columnsyoudon’tneedtouseshouldbeleftblank.
31. Hayoungiscompetinginatriathloncomprisedofswimming,running,andbiking.Shestartsbyswimmingmmiles.Next,sheruns11timesthedistancethatsheswims.Finally,shebikes18timesthedistancethatsheswims.IfHayoungswims2.5miles,whatisthetotaldistance,inmiles,Hayoungtravelsasshecompetes?
32. Atthelocalmall,Casey’sCardCartsellscardsàlacarte.Casey’srevenueR,indollars,forxdaysisgivenbythefunctionR(x)=250x–20.IfCaseyearned$1,230,howmanydayshasshesoldcards?
33. Martyisplanningwhichcropstoplantonhisfarmfortheupcomingseason.Hehasenoughseedtoplant4acresofwheatand7acresofsoybeans,butthetotalareaoffarmlandheownsisonly9acres.Heearns$90peracreforeveryacreofwheatplantedand$120foreveryacreofsoybeansplanted,andhemustpaya10%taxonallmoneyheearnsfromsellinghiscrops.Whatisthemaximumprofit,indollars,thatMartycanearnfromplantingwheatandsoybeansthisseason?
34.
Whatistheareaoftheshadedregionofthecircle,boundbythex-axisandtheliney=–x,
roundedtothenearestwholenumber?
35.
Inthefigure,ACisbisectedbyBD.IfBCis7,thenwhatisthelengthofBD?
36. Thedailyrecommendedservingofproteinis50grams.Anutritionalbarcontains32%ofthedailyrecommendedservingofproteinand10%ofthedailyrecommendedservingoffat.Ifthenutritionalbarcontains700%moregramsofproteinthangramsoffat,whatisthedailyrecommendedservingoffat,ingrams?(Disregardunitswhengriddingyouranswer.)
Questions37and38refertothefollowinginformation.
SetRconsistsofalltheone-digitprimenumbers.SetScontainsalloftheelementsofSetR,aswellasanadditionalpositiveinteger,x.
37. IfthesumofalloftheelementsofSetSis30,whatisthevalueofx2–11x–25?
38. MichaelwantstochangethevalueofxsothatthemeanofSetSisequaltothemedianofSetSandforSetStohavenomode.Whatvalueofxwouldaccomplishhisgoal?
STOPIfyoufinishbeforetimeiscalled,youmaycheckyourworkonthissectiononly.
Donotturntoanyothersectioninthetest.
SATEssay
ESSAYBOOK
DIRECTIONS
Theessaygivesyouanopportunitytoshowhoweffectivelyyoucanreadandcomprehendapassageandwriteanessayanalyzingthepassage.Inyouressayyoushoulddemonstratethatyouhavereadthepassagecarefully,presentaclearandlogicalanalysis,anduselanguageprecisely.
Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteinprintsothatwhatyouarewritingislegibletothosereaders.
Youhave50minutestoreadthepassageandwriteanessayinresponsetothepromptprovidedinsidethisbooklet.
REMINDER
— Donotwriteyouressayinthisbooklet.Onlywhatyouwriteonthelinedpagesofyouranswerbookletwillbeevaluated.
— Anoff-topicessaywillnotbeevaluated.
Asyoureadthepassagebelow,considerhowRobertSterlingYarduses
• evidence,suchasfactsorexamples,tosupportclaims.• reasoningtodevelopideasandtoconnectclaimsandevidence.• stylisticorpersuasiveelements,suchaswordchoiceorappealstoemotion,to
addpowertotheideasexpressed.
HelenKeller’sAddressbeforetheNewYorkAssociationfortheBlind,January15,1907
1 ItisagreatpleasuretometospeakinNewYorkabouttheblind.ForNewYorkisgreatbecauseoftheopenhandwithwhichitrespondstotheneedsoftheweakandthepoor.ThemenandwomenforwhomIspeakarepoorandweakinthattheylackoneofthechiefweaponswithwhichthehumanbeingfightshisbattle.Buttheymustnotonthataccountbesenttotherear.Muchlessmusttheybepensionedlikedisabledsoldiers.Theymustbekeptinthefightfortheirownsake,andforthesakeofthestrong.Itisablessingtothestrongtogivehelptotheweak.Otherwisetherewouldbenoexcuseforhavingthepooralwayswithus…
2 Foritisthecommunitywheretheblindmanlivesthatultimatelydetermineshissuccessorhisfailure.TheStatecanteachhimtowork,supplyhimwithrawmaterialsandcapitaltostarthisbusiness.Buthisfellow-citizensmustfurnishthemarketforhisproductsandgivehimtheencouragementwithoutwhichnoblindmancanmakeheadway…
3 Itisnothelpful,inthelongrunitisharmful,tobuyworthlessarticlesoftheblind.Formanyyearskind-heartedpeoplehaveboughtfutileandchildishthingsbecausetheblindmadethem.Quantitiesofbeadworkthatcanappealtonoeye,savetheeyeofpity,havepassedasspecimensoftheworkoftheblind.Ifbeadworkhadbeenstudiedintheschoolsfortheblindandsupervisedbycompetentseeingpersons,itcouldhavebeenmadeaprofitableindustryforthesightless.Ihaveexaminedbeautifulbeadworkintheshops,purses,bags,belts,lamp-shadesanddress-trimmings,someofitveryexpensive,importedfromFranceandGermany.Underpropersupervisionthisbeadworkcouldbemadebytheblind…
4 InBoston,inafashionableshoppingdistrict,theMassachusettscommissionhasopenedasalesroomwherethebesthandicraftofallthesightlessintheStatemaybeexhibitedandsold.Therearehand-wovencurtains,table-covers,bed-spreads,sofa-pillows,linensuits,rugs;andthearticlesareofgooddesignandworkmanship.Peoplebuythemnotoutofpityforthemaker,butoutofadmirationforthething.OrdershavealreadycomefromMinnesota,fromEngland,fromEgypt.SotheblindoftheNewWorldhavesentlightintoEgyptiandarkness!
5 …Nay,Icantellyouofblindmenwhooftheirownaccordenterthesharpcompetitionofbusinessandputtheirhandszealouslytothetoolsoftrade.Itisourparttotraintheminbusiness,toteachthemtousetheirtoolsskillfully.Beforethisassociationwasthoughtof,blindmenhadgivenexamplesofenergyandindustry,andwithsuchexamplesshininginthedarkotherblindmenwillnotbecontenttobenumberedamongthosewhowillnot,orcannot,carryburdenonshoulderortoolinhand—thosewhoknownotthehonourofhard-wonindependence.
6 Thenewmovementfortheblindrestsonafoundationofcommonsense.Itisnotthebaselessfabricofasentimentalist’sdream.Wedonotbelievethattheblindshouldbesegregatedfromtheseeing,gatheredtogetherinasortofZionCity,ashasbeendoneinRoumaniaandattemptedinIowa.Wehavenoqueentopresideoversuchacity.Americaisademocracy,amulti-monarchy,andthecityoftheblindiseverywhere.Eachcommunityshouldtakecareofitsownblind,provideemploymentforthem,andenablethemtoworksidebysidewiththeseeing.Wedonotexpecttofindamongtheblindadisproportionatenumberofgeniuses.Educationdoesnotdevelopinthemremarkabletalent.Liketheseeingman,theblindmanmaybeaphilosopher,amathematician,alinguist,aseer,apoet,aprophet.
7 Butbelieveme,ifthelightofgeniusburnswithinhim,itwillburndespitehisinfirmity,andnotbecauseofit…
8 Iappealtoyou,givetheblindmantheassistancethatshallsecureforhimcompleteorpartialindependence.Heisblindandfalters.Thereforegoalittlemorethanhalfwaytomeethim.Remember,howeverbraveandself-reliantheis,hewillalwaysneedaguidinghandinhis.
Writeanessay inwhichyouexplainhowHelenKellerdevelopsherargumentabout thenecessityof industries for theblind.Inyouressay,analyzehowKellerusesoneormoreofthefeatureslistedabove(orfeaturesofyourownchoice)tostrengthen the logic and persuasiveness of her argument. Be sure that your analysis focuses on the most relevantaspectsofthepassage.
Your essay should not explain whether you agree with Keller’s claims, but rather explain how the author builds anargumenttopersuadeheraudience.
ENDOFTEST
DONOTRETURNTOAPREVIOUSSECTION.
PRACTICETEST4ANSWERKEY
Section1:Reading
1. A2. D3. D4. D5. C6. C7. D8. B9. A10. A11. D12. B13. B14. C15. B16. A17. A18. C19. C20. D21. A22. C23. B24. D25. C26. B27. B28. A29. C30. C31. D32. D33. C
34. B35. A36. B37. C38. C39. A40. D41. A42. C43. B44. B45. B46. D47. B48. C49. D50. C51. C52. B
Section2:Writing&Language
1. B2. C3. B4. D5. D6. C7. A8. A9. C10. B11. D12. C13. B14. D15. D16. A17. B
18. D19. A20. C21. C22. B23. B24. D25. D26. A27. C28. D29. C30. C31. A32. B33. A34. C35. B36. A37. D38. A39. C40. B41. B42. D43. D44. A
Section3:Math(NoCalculator)
1. B2. C3. C4. D5. A6. B7. A8. C9. B
10. C11. D12. A13. B14. C15. C
16. or2.33
17. 618. 619. 820. 72
Section4:Math(Calculator)
1. D2. A3. B4. B5. C6. B7. A8. C9. B10. D11. B12. C13. D14. C15. B16. A17. A18. D19. C20. D21. C22. C23. D24. A
PRACTICETEST4EXPLANATIONS
Section1:Reading1. A ThemainideaofthepassageisthattheScarletPimpernelrescuesFrenchnoblesbecauseit
isfun.Choice(A)iscorrectbecausethatisthereasonbehindthePimpernel’sactions.ThecharactersneverdiscussthecauseoftheFrenchRevolution,so(B)cannotbetheanswer.Because the youngman is amember of the Scarlet Pimpernel’s team, and both are self-confident, (C) is incorrect. Both characters presumably disagree with the Frenchgovernment, andneither ever questions that thegovernment is ruthless.Therefore, (D) isincorrect.
2. D Because there isno indication that thecart ismovingquickly, (A) is incorrect.Since theComtesse isherself escapingarrest, (B) is incorrect; themobwouldnotbepunished forcatchinga fugitive.Choice (C) iswrong,asyoudonotknowthat thewomandriving thecart is violent, only frightening. In the sixteenth paragraph, the driver causes themob toretreatbymentioningtheplague.Therefore,(D)iscorrect.
3. D TheanswertothepreviousquestionisthatthecrowddidnotapproachtheComtesse’scartbecausetheywereafraidofcontractingadisease.Choice(D)iscorrectbecauseit is theonlyanswerchoicethatmentionsdiseaseorplague.
4. D In this sentence, the flower isdrawn in red.Therefore,designatedmustmean somethinglike“drawn.”Onlyillustratedhasthismeaning.Therefore,(D)iscorrect.
5. C In thepassage,LordAntonyexplains that theScarletPimpernelandhiscompanionssaveFrencharistocratsbecauseitisexciting,likepullingtheharefrombetweentheteethofthehound.Choice (A) is too literal, andLordAntonyspeaksmetaphorically. In thepassage,there is no mention of dead Englishmen, so eliminate (B). Choice (C) is an accuratecharacterizationofLordAntony’suseofthephraseinquestion:InLordAntony’smetaphor,the French aristocracy is the hare, and the harm is the teeth of the hound. Because thepassageconcernsthecrueltyofFrenchrevolutionariestowardnobles,(D)contradictsthepassageandisincorrect.
6. C The answer to the previous question is that LordAntony uses the phrase in question todescribethesensationofdeliveringFrenchnoblesfromharm.Choice(A)doesnotmentioneither thearistocratsor thedanger theyare in, so it is incorrect.Choice (B) is incorrectbecauseitdescribesthedangertothePimpernelandhiscompanions,nottheFrenchnobles.Choice(D)describesonlythedangerthattheComtessehasfoundherselfin,so(D)canbeeliminated. Choice (C) is correct because it describes the Pimpernel’s men deliveringFrenchnoblesfromharm.
7. D Inthesentenceinquestion,theComtesseisdescribedasincredulous,whichmeansthatshehas troublebelieving the reasongiven toexplainwhy thePimpernel andhis companions
havegone toFrance to rescuearistocrats.She isnotcritical; therefore, (A) is incorrect.Sheisnotanxious,soeliminate(B).WhiletheComtessemayberelievedthatshehasbeenrescued,thesentenceinquestiondescribesherasincredulous.Therefore,(C)isincorrect.Perplexedmeans“puzzled”;becausetheComtessefindsthegivenexplanationinadequatetoexplainthebehavior,sheispuzzled.Choice(D)iscorrect.
8. B Bearded describes thePimpernel’smen,whocanbe consideredcourageous for rescuingtheComtesse.Therefore,beardedmustmeansomethinglike“facedwithcourage.”Ofthefouranswerchoices,only(B)capturestheircourageandiscorrect.
9. A ThetwosentencesinquestiondrawacontrastbetweenthepeaceofEnglandandthechaosof France. Tranquility means “peace” and turmoil means “chaos.” Therefore, (A) iscorrect. Choice (B) is also incorrect: Although the inn is old-fashioned, there is noindicationthatFranceshouldbethoughtofasmodern.WhiletheComtesseisfree,thatfactis not mentioned in the description of the inn or England, nor does she actually everdescribe themobas ignorant. (Infact, fleeing theplagueseemsavery intelligent thing todo.)Therefore, (C) is incorrect.Becauseausteritymeans“extremesimplicity,” (D)doesnotaccuratelydescribethecontrastbetweenEnglandandFrance.
10. A Intheparagraphinquestion,theComtessecomparesherperceptionofSirAntony’smotiveswith those of Sir Andrew. Therefore, (A) is a good description of the distinctionemphasized by the italics. There is never any indication that Sir Antony’smethods aredifferent from Sir Andrew’s, so (B) is incorrect. While the Comtesse feels there is adistinction between SirAndrew’smotivations and those of SirAntony, (C) is incorrect:Antonyismotivatedbyexcitement,notmoney.AndwhiletheComtesseseesadistinctionbetweenAntony’smotivations(aloveofadventure)andSirAndrew’smotive(onethatishigherandnobler),(D)isincorrectbecausethereisnoindicationthatAndrewisseekingadmirationandpraise(whichseemsunlikelytobethehighermotivesheimplies).
11. D ThepassageisprimarilyconcernedwithdescriptionsofRomanbaths,howtheycameintobeing,andtheirsignificance.Choice(A)isincorrectbecauseverylittleisdiscussedinthepassage regarding sanitation. Choice (B) is too limited in scope, and (C) is incorrectbecausereligionisneverdiscussedinthepassage.Choice(D)bestexpressestheoverallideaofthepassageandisthecorrectanswer.
12. B ThefirstsentencedrawsacontrastbetweenGreekandRomanarchitecture,sousePOEtofindananswerchoicethatreflectsthis.Eliminate(A)becausethepassagedoesn’tsuggestthatRomanarchitectureimproveduponGreekarchitecture.Choice(B)worksbecausenewtrendsshowshowRomanarchitecturedifferedfromGreekarchitecture;keepit.Choice(C)istooextremebecausenothingisproven,soeliminateit.Choice(D)isincorrectbecausereligionisnotdiscussedmuchinthepassage,soeliminate(D).Choice(B)iscorrect.
13. B Crossoutomnipresentanduse thecontext to findanacceptable replacement.Thecurvesare also described as dominating, and later in the paragraph the world the architectscreatedisdescribedasonethatwastransformedintoanewcurvesomeness.Thissuggeststhat the curves are a characterizing feature, so find the choice that matches these
descriptions.Choice(B) isamatch,sincepervasivemeans“everywhere.”Choice(A) istoo limited, and (C) is a trap because the ceilings, not the curves, reached up to theheavens. Choice (D) is incorrect because imposing means “impressive in appearance.”Choice(B)iscorrect.
14. C Thesecondparagraphstates that thisgrandRoman innovation inarchitecturewouldbeaccomplished in two centuries as the essential ingredient, concrete, was perfectedgradually by trial and error. Choice (C) matches this information. The other answerchoicespertaintothepassage,butsincethequestionisaskingforthecriticalcomponent,(C)isthecorrectanswer.
15. B Lines15–18identifyconcreteastheessentialingredientinRomaninnovationandstatethatitwasperfectedgraduallybytrialanderror.Choice(B)iscorrect.
16. A The third paragraph states that the new architectural creations arose from the needs oftheseRomancities,sothecorrectanswerwillreflectthisidea.Choice(A)isagoodmatchbecause the needs of the new Roman cities are what prompted the differences betweenGreekandRomanarchitecturediscussed in the firstparagraph.Choice (B)doesn’tworkbecause thepassagedoesnotreinforce thiscontrast,but ratherexplains it.Choice(C) isalludedtoattheendoftheparagraph,butitishardlytheprimarypurpose.Theauthordoesnotdismissanything,so(D)isincorrectaswell.Choice(A)isthecorrectanswer.
17. A The first sentenceof thisparagraphdescribes thegrandStabianbaths andhowsomeoftheir featureswould show up in thePantheon three centuries later. Therefore, replaceanticipated with something that means “indicated” or “suggested.” Choice (A) is theclosesttothismeaningandthecorrectanswer.
18. C Use POE to find an answer choice consistent with what is in the last paragraph. Theparagraphdetailsthevariouslyheatedandcooledspaceswithinthebaths,whichsupports(C), as the baths were a critical part of Roman life and offered the opportunity toexperience different temperatures. Eliminate (A) because there is no comparison withmodernbaths,andeliminate(B)becausegymsarenotmentioned.Choice(D)isincorrectbecauseunparalleledinhistorygoestoofar.Choice(C)iscorrect.
19. C Thesecond-to-lastsentence in the lastparagraphstates thatThebathsat theirbestwerepublicartmuseumsandmuseumsofcontemporaryart.Choice(C)reflectsthisideaandisthecorrectanswer.Theotheranswerchoiceshavesomerelevancetothepassage,butthephrase“mostexemplary”inthequestionmakes(C)correct.
20. D ThepreviousanswerisbestsupportedbythesentenceThebathsattheirbestwerepublicartmuseumsandmuseumsofcontemporaryart.Therefore,(D)iscorrect.
21. A Thepassagestatesthatmostpublicbathshadanunheatedfrigidariumpartlyopentothesky.Thegraphicalsoincludesafrigidariuminthecenterofthestructure.Therefore,(A)issupportedbyboththepassageandthediagram.Choice(B)issupportedbythegraphic,butthere is no mention of palestrae in the passage. Therefore, (B) is incorrect. While the
passagementions that commercial contractorsbuiltpublicbathsand thegraphic showsarectangularstructure,thereisnoevidencethatcontractorsalwaysbuiltbathsinthisshape;(C)isincorrect.Andthepassagenevermentionsnatatio,sothereisnoevidencethatthisiswherehoop-rollingandwrestlingoccurred,so(D)isincorrect.Theansweris(A).
22. C Palmaarguesthatwomenshouldbeallowedtovote,soheisnotdiscussingbothsidesoftheissue;heisfocusingspecificallyonthearguments insupportofonesideof theissue.Thus,(A)isincorrect.Palmaisarguinginfavorofareform—therightforwomentovote—notcautioningagainst reform, so (B) is incorrect.Givingwomen the right tovote is asocialchange.Palmaarguesforthischange,so(C)accuratelydescribesPalma’srolewhengivingthespeech.Palmaisapolitician,buthisfocusisonrousingsupportforabillthatwill give women the right to vote, not gaining support for his party. Therefore, (D) isincorrect.Choice(C)istheanswer.
23. B ThepassagedoesnotprovideanyinformationaboutthosewhosupportedPalma,so(A)isincorrect.Inthefirstparagraph,Palmastatesthatheisadvocatingacausethatcannotberepresented or defended in this chamber—that is, in the chamber of the legislature—bythose directly and particularly affected by it. Thosedirectly and particularly affectedwould bewomen. Palma is saying that women could not defend their own cause in thelegislature, which supports the idea that women were not allowed to speak before theFilipinolegislatureatthattime;thus,(B)iscorrect.PalmadoesnotdiscusswhetherotherFilipino leaders of his time supported female suffrage, so (C) is incorrect. The passagedoesnotdiscusshowmembersofthelegislatureviewedwomen,so(D)isalsoincorrect.
24. D Inthesentenceinquestion,Palmasaysthatwecannotdetainthecelestialbodiesintheircourse;neithercanwecheckanyofthosemoralmovements.Agoodreplacementwordforcheck is something like “detain,” so go to the answer choices to find one that has ameaninglike“detain.”Certify,inspect,andadviseallhavemeaningsthataredifferentfromthemeaningoftheworddetain,whilestophasasimilarmeaning,sothecorrectansweris(D).
25. C Palma states thatwe cannot detain the celestial bodies in their course. However, rightbeforethathestatesthatfemalesuffrageisareformdemandedbythesocialconditionsofourtimes.Immediatelyafterhediscussesthemovementsofcelestialbodies,healsosaysneithercanwecheckanyofthosemoralmovementsthatgravitatewithirresistibleforcetowardtheircenterofattraction:Justice.Thus,hediscusses thedifficultyofhaltingthestars,orcelestialbodies,inordertoshowthatfemalesuffrageisinevitable.Thisdoesnotrelatetotheclaimsofthosewhoopposefemalesuffrage,soeliminate(A).Palmadoesnotsay that thosewhooppose thebill areprejudiced against the causesofmodernmen andwomeningeneral,onlythattheyareprejudicedagainstthecauseoffemalesuffrage.Thus,(B)isincorrect.Inlines46–51,Palmastatesthattheeternalcalamityhowlersandfalseprophets of evil raise their voices on this present occasion, in protest against femalesuffrage, invoking the sanctity of the home and the necessity of perpetuating customsthathavebeenobservedformanyyears.Inotherwords,manywhoopposethebilldosobecause they claim that givingwomen the right to votemay threaten the sanctity of thehome and disrupt customs that have been observed for many years. Therefore, (C) is
supportedbythepassageandisthecorrectanswer.Choice(D)focusesoncivicratherthansocial institutions and is too extreme, stating that giving women the right to vote willpermanentlyparalyzethecountry.Thosewhooppose thebilldonotmakesuchextremeclaims,so(D)isincorrect.
26. B As determined in the previous question, the opponents claim thatwomen’s suffragewilldamage home life and perhaps disrupt long-established customs. Choice (A) mentionsfemale suffrage, but only as something the times demand and without listing negativeconsequences.Choice(C)doesmentionthatthingstheretoforelookeduponasimmovablehave given way, but this sentence describes only what the country experienced duringprevious revolutions, not what is forecast. Choice (D)mentions a few reactionists andultra-conservativesbutdoesnotdetailtheirobjections;(D)isincorrect.Choice(B)fullysupports the answer for question 25 by naming the objections of those who opposewoman’ssuffrage.
27. B Palma says that sudden changes have been carried on most successfully, withoutparalyzation,retrogression,disorganization,ordestruction.Therefore,heisnotshowinghowthesethingscandamageasociety,so(A)isincorrect.However,heusesthislist toshowhow social changes canoccurwithout paralyzing a nationor causing it to regress,becomedisorganized,orbedestroyed.Therefore,(B) is thecorrectanswer.SincePalmasaysthat thePhilippinesexperiencedchangewithoutanyof thenegativeconsequenceshelists, (C) does not agreewith the information in the passage, and is therefore incorrect.Palmadoesnotsuggestthatthenationshouldbeparalyzed,regress,becomedisorganized,orbedestroyed,soyoucaneliminate(D).
28. A Inthesentenceinquestion,Palmaindicatesthatthegreatsocialupheavalshavecausedoldinstitutions to crumble to pieces. However, later in that same sentence, he states thatdespiteallthoseupheavals…ourpeoplehasbecomeapeoplewithmodernthoughtsandideals…robust and strong. In the next paragraph, he goes on to say that in view of thefruitful results which those institutions of liberty and democracy have brought to ourcountry…I do not and cannot, understand how there still are serious people whoseriously object to the granting of female suffrage. These quotes indicate that heintroduces thesocialupheavalsof thepast inorder toshowthat thecountrywillsurviveanyupheavalscausedbygivingwomentherighttovote.Thus,heusesananalogytoshowthatallowingwomentovotewouldnotpermanentlyweakenthenation,making(A) thecorrectanswer.Choice(B)istheoppositeofwhatPalmaisattemptingprove—hedoesnotbelieve that giving women more rights would cause the nation to crumble—so (B) isincorrect.Palmadoesmentiontheories,beliefs,andcodesofethics,butwhilehesaysthattheywerelookeduponasimmovable,hegoesontosaythathehasseenthemgivewaytodifferent principles andmethods based upon democracy and liberty. Thus, while theyappearedunchangeable,theydidinfactchange,so(C)isincorrect.BecausePalmastatesthat theold institutionsgaveway toprinciplesandmethodsbasedupondemocracyandliberty,thenew,nottheold,institutionsaretheonesthatupholdliberaldemocracy.Thus,(D)isincorrect.
29. C Palma discusses the country’s previous social upheavals in lines 61–62 in order to
demonstrate (in the lines that follow) that the countrywill be able to survive any socialupheavalbroughtaboutbyfemalesuffrage,justasitsurvivedturmoilinthepast.Choices(A),(B),and(D)donotdirectlyaddresstheideathatthecountryhasfacedandsurvivedupheavalbefore,sotheydonotsufficientlysupporttheanswertoquestion28.Choice(C)clearlysupportsPalma’spointbynotingthatDespiteallthoseupheavalsandchanges,thecountry has emerged with a robust and strong constitution and a people with modernthoughtsandmodernideals.
30. C Inthefinalparagraphofthepassage,Palmadiscussesthe fruitfulresultsof thecountry’snewinstitutions,anddiscussesthemarkedprogress that theseinstitutionshavebrought toalltheordersofnationallife.Therefore,agoodwordtodescribethatprogressmightbe“serious”or“noticeable.”Of theanswerchoices,onlysignificant isclose inmeaning to“serious” or “noticeable,” so (C) is the correct answer. There is no evidence that thecountry’sprogressisfixedorguaranteedtocontinue,so(A)and(B)areincorrect.Choice(D),underlined,relatestotheliteralmeaningofmarked,butdoesnotmatchthemeaningintendedbythecontextofthepassage.
31. D Although the passage suggests that Palma is perplexed by those who oppose femalesuffrage, it does not indicate that his attitude toward them ismournful, so (A) incorrect.Palmasupportsthecauseoffemalesuffragethroughouthisspeech,soheisnotunbiasedorviewing thematter academically; (B) is incorrect. He is not deferential, or submissive,towardthosewhoopposefemalesuffrage,so(C)isincorrect.Inlines85–87,Palmasays,Idonotandcannot,understandhowtherestillareseriouspeoplewhoseriouslyobjecttothe granting of female suffrage. These lines suggest that his attitude is one ofbewildermentanddissent.Therefore,(D)isthecorrectanswer.
32. D The thirdparagraphstates that thesizeofelkpopulationsandwolfpopulationscouldberelated,so(A) is incorrect.Thefirstsentenceof thesecondparagraphstates thatWolvesare part of a naturally functioning ecosystem, so (B) is incorrect. The first paragraphmentionsthatpredatorcontroleffortseradicatedthegraywolffromYellowstone,so(C)isincorrect. In the first paragraph, the passage mentions that wolves were regarded asdangerousandweredeliberatelyexterminated.However,therestofthepassagefocusesonhowwolveshavebeenrestoredtotheirnaturalhabitat.Therefore,(D)iscorrect.
33. C Thepassageusesthewordnativetodescribespeciesthathadexistedinparticularplacesuntil human interference affected their populations; therefore, the word is being used todescribeanimalsthatoriginatedinorhadlonginhabitedanarea.Although(A)mightsoundlike it could have such ameaning, inborn actually describes factors or traits present atbirth,so(A)isincorrect.Choice(B),constitutional,isusedtorefertosomeone’sphysicalormentalconditionandisalso incorrect.Choice(C), indigenous,meansoriginating inaspecific area,making it the correct answer.Choice (D), canine, can be used to refer toanimalsof thedogfamily,which includeswolves;however,canine isnota synonymfornative,so(D)isincorrect.
34. B Thepassagementions that thewolfhuntsharvested thewolves.Thewordhunt suggeststhatthewolvesweretrappedorkilled.Thenextsentencereinforcesthisideabynotingthat
thenumberofwolvesintheinteriordeclinedless,andtheparagraphasawholediscussesthedecliningwolfpopulation.Therefore,theonlyanswerchoicethatmakessenseis(B),killed.
35. A Theauthor’sargumentinlines30–32isthatthewolvesinYellowstonehaveamorestablepopulationbecausetheyeatbisoninadditiontoelk.Choice(A)proposesthattheDeltaandBechlerpacks survivedwithouteatingmuchbison,whichundermines theauthor’s theorythat eating bison is what prevented thewolf populations from declining as dramaticallywithin the park as without. Therefore, (A) is correct. Choice (B) indicates that wolvesentering theparkhavemorestablepopulations,whichagreeswith theauthor’spoint thatwolves in theparkhaveamorestablepopulation.Choice(C)says that thepopulationofwolves in Yellowstone has declined, but the author acknowledges that the populationdeclined; his point is that the population has declined less in the park than elsewhere.Therefore,(C)isincorrect.Because(D)doesnotmentionwolves,itcannotbecorrect.
36. B Theparagraph explains howdata onwolf-prey relationshipswas gathered butmakes noclaimsregardingwhatpatternsthatdatarevealed,so(A)isnotsupportedbytheparagraphand is incorrect. Because the paragraphmentions a wolf pack for which predation datacouldnotbegathered,(B)isstronglysupportedbythecontentofthefifthparagraph.Theparagraphnotes that someof the packsweremonitored by radio-tracking, ground teams,andaircraft,whileothersweremonitoredbyonlyaircraftornotmonitoredatall,sothereis no indication that most of the packs were monitored by ground teams, and (C) isincorrect. Because it is noted that researchers also documented things like percentconsumptionbyscavengers,(D)isincorrect.Choice(B)isthecorrectanswer.
37. C Theanswertothepreviousquestionisthatthepredationdataisincomplete.Choices(A)and(B)describethemethodofgatheringdatabutdonotmentiongapsinthedatacollected.Therefore,bothareincorrect.Choice(C)mentionstwopacksthatwerenotmonitoredfully,which supports the idea that the predation data is incomplete. Therefore, (C) is correct.Choice (D)describessomeof thedatagatheredwithoutalluding toanygaps in thedata.Therefore,(D)isincorrect.
38. C Choice(A)isextreme;whilethesizeofwolfpacksisalimitingfactor,thereisnoevidencein the passage to suggest that it is the major limiting factor. And though the passagediscusseshowwolvesandother factorsaffect theelkpopulation, itdoesnotmention thesuperiorhuntingtacticsofwolves,so(B)isincorrect.Becausethepassagediscussestheeffectofwolfpopulationsandelkpopulationsononeanother,(C)accuratelydescribestherelationshipbetweenelkandwolfpopulations.Choice(D)isalsoextreme;whilethesizeof elk packs affects wolf populations, there is no evidence to suggest it is the majorlimitingfactor.Therefore,thecorrectansweris(C).
39. A Theanswertothepreviousquestionisthatthesizesofwolfandelkpopulationsaffectoneanother. Choice (A) notes that wolf population numbers in YNP have declinedmostlybecauseofasmallerelkpopulation.BecausewolvesprimarilypreyonelkinYNP,theirpopulationmust affect the elk population; the explicit statement here that the smaller elkpopulation affected the number ofwolves shows that the elk population also affects the
wolfpopulation.Choice(B)discussesbison,soitisnotrelevantasevidenceabouttheelkandwolfpopulations.Choice(C)notesthatwolf-preyrelationshipswerestudieddoesnotgiveanyspecific informationabout thoserelationships.Choice(D)offerssupport for theclaimthat thewolfpopulationaffects theelkpopulationbut lackssupportfor thereverserelationship.Thus,(B),(C),and(D)areincorrect,and(A)isthecorrectanswer.
40. D Thesentencestatesthatweatheraffectstheabilityofelktoforage.ThishasnothingtodowithtrackingwolvesinYellowstone.Therefore,(A)isincorrect.Thereisnoevidencethatthe quality of the food has improved, so (B) is incorrect. Choice (C) is also incorrect;while the paragraph mentions predation studies, it does not argue for them. Becauseweather patterns influence forage quality and availability and forage quality andavailability in turn affect the elk population, the reference to the weather does provideadditionalinformationaboutacauseofthedeclineofelkinYellowstone.Therefore,(D)iscorrect.
41. A The graph shows that the wolf population in 2010–2011 was about 40, while the elkpopulationwasabout4,500.Thewolfpopulationhasneverreachedasmanyas120duringthe time reflected in the graph,while the elk population had not dipped below themid-4,000s in 2011; therefore, the graph supports the claim that elk populations currentlyoutnumber wolf populations in YNP, and (A) is supported by the graph. Because elkpopulations increased from 1998 to 2000 and in other years, (B) is incorrect. Elkpopulationswereattheirlowestin2010–2011,butwolfpopulationswereattheirhighestin 2003–2004, so (C) is incorrect.Because there are about 40wolves and 4,500 elk inYellowstoneasof2011,(D)isincorrect.Ifyouanswered(D)oreliminated(A),youlikelydidnotnoticethatthewolfpopulationisontheleftaxisofthegraphandtheelkpopulationisontheright.
42. C ThequestionaskswhattheauthorsuggestsaboutmammalsinthefirstparagraphofPassage1.Choice(A)isincorrectbecausetheparagraphstatesthatmorethanhalfofallspecieswere wiped out in the KT extinction, so species other than mammals must also havesurvived. Choice (B) sounds good, since mammals were not dominant, but the authordoesn’tsaythat theywereveryrare;eliminate(B).Whilemanyspecieswerewipedout,manymammalssurvived,so(D)istooextreme.ThepassagestatesthatmammalsbecamedominantaftertheKTextinction,so(C)isthecorrectanswer.
43. B Asdeterminedinthepreviousquestion,mammalswerenotdominantonEarthuntilaftertheasteroid hit. Since question 42 asks specifically about the first paragraph, the firstparagraph is probably thebest place to find support for a claimmade in that paragraph.Choice(A)isfromthefirstparagraphbutsimplystatesthatexpertsreviewedtheresearch.Choice(B)isalsofromthefirstparagraphandexplicitlystatesthatTheextinctionwipedoutmore thanhalfofall specieson theplanet, thusclearing theway formammals tobecome the dominant species onEarth, so (B) is the correct answer.While (C) comesimmediatelyafter thefirstparagraphandcouldcommentuponit, thelinesdonotaddressmammals or their dominance.Choice (D) is from the sixth paragraph, andwhile it doessupporttheideathathumanswerenotdominantuntilaftertheKTextinction,thefactthathumans were not dominant does not in and of itself indicate that no mammals were
dominant.Choice(D)isnotbetterthan(B).
44. B The word spewed is used in the passage to describe the process of volcanic eruptionsreleasing vast amounts of lava that spread across the land. Thus, spewed must meanssomethinglike“toreleaseorexpelsubstancesout.”Choice(B)iscorrect,asitmeans“toejectsomething.”Choice(A)means“tosetfire,”andalthoughlavaishotandburnswhatittouches, the correct answer needs to address the issue of releasing the lava.Choice (C)means “to dig out of the earth,” and (D)means “to draw off or convey liquid.”Neitherreflectsthesensethatthelavaisbeingpushedoutofthevolcano,andsoneitherchoiceisbetterthan(B).
45. B Passage1statesthattheasteroidcausedfires,earthquakes,andtsunamis,butitisn’tclearthatthosearewhatkilledmostofthedinosaurs.Infact,thepassagearguesthatitwasthedustcloudthatshieldedthesunthatdealtthefinalblow.So,(A)isincorrect.Choice(C)makesacausallinkbetweentheasteroidandthevolcanoes,butthisrelationshipisneverput forward in the passage, so (C) is incorrect. The passage states that scientists havepreviouslyarguedaboutthecauseoftheextinction,butthisdoesnotmeantheyarestillincompletedisagreement,particularlygiventheagreementsurroundingthenewstudy;(D)isincorrect.Thecorrectansweris(B).
46. D Bothpassagesusethesayingnailinthecoffintostatethatsomethingcametoaclearend.Choice (D) is the correct answer because the saying refers to an event that causedsomethingtoend,thatis,aterminatingevent.Choice(A)isincorrect,asthesayingisnotadeduction. Choice (B) is tempting because the nail in that coffin in Passage 1 is theasteroidthatendedthereignofthedinosaurs,butinPassage2,thenailinthecoffinistheendofthebeliefthatthedinosaurscouldhavediedbeforetheasteroid’simpact.Choice(C)looksgoodbecause thesayingisametaphor,but thequestionaskswhat thepassagesareusingthemetaphortoreferto,notwhattypeofliterarydeviceisbeingused.
47. B Thereasontheauthormentionsthehigh-precisionradiometricdatingtechniquesistojustifythestudy’sclaimsthatthetimespanbetweentheasteroidhittingearthandtheextinctionofthedinosaurswasshorterthanhadbeenpreviouslythought.Thus,(B)iscorrect.Thedata,notthetechniques,wasusedtoproposeanewtheory.Similarly,theauthordoesn’tmentionthetechniquesinordertoprovetheconclusioncorrect.Theauthorwantstomakesurethatpeople understand that the data was better than before, so (A) and (C) are not correct.Choice(D)canbemistakenformeaningthatthenewdatacounterstheoldassumption,butthepurposeofmentioningthedeviceistolendauthoritytotheclaim.
48. C Thewordprecludeisusedtodescribewhatwouldhappentoacausalrelationshipbetweentheasteroidandthedinosaurextinctionifthepreviousdatawascorrect.Thescientistwhousesthewordexplainsthatthepreviousdatashowedtheextinctiontohaveoccurredbeforethe asteroid hit, and that would completely undermine any claims that the asteroid hadcaused the extinction. Therefore, preclude must means something like “prevent fromhappening.”Choice(B)isclosetothismeaning,but(C)isthecorrectanswerbecausetobarmeanstostopsomethingcompletely,ratherthanjustlimitit.Choice(A)doesnotmakesense; no matter what the older data showed, the data could not cause a relationship
betweentheasteroidandtheextinction;itcouldonlyconfirmordisprovehypothesesabouttherelationship.Choice(D)means“tostrikewithlightblows”anddoesnotmakesenseinthecontextofthesentence.
49. D TheauthorofPassage2mentionstektitesbecausetheyrepresentresiduefromtheasteroid,whilevolcanicashprovidesinformationaboutthetimingofthelarge-scalevolcanoesthaterupted.Theagingof thesesamplesaffectedthetheories thatweresetforth.Thus,(D)iscorrect.Thetektitesdon’tsuggestanothercause,(A);theydefinitelydon’tdiminishtheroleof the asteroid in the demise of the dinosaurs, (B); and they don’t substantiate that thevolcanoes caused the most damage, (C), since that’s too vague and unsupported by thepassage.
50. C Thinkabout theevidencefromthepassage thathelpedyouanswer thepreviousquestion:Tektiteswerementionedbecausetheyhelpedprovethattherewasnotacausalrelationshipbetweentheimpactandtheextinction.Only(C)works,andit’sthecorrectanswer.
51. C Thecorrectansweris(C),asPassage1mentionsmammalsandtheirrisetodominanceandPassage2doesnot.Bothpassagesdescribedthesizeof theasteroid,so(A)is incorrect.Bothpassagessaythattheprimarycauseoftheextinctionwasanasteroidthathitbeforetheextinction took place, so (B) is incorrect. Both passages indicate that previous theorieshave been reconsidered and adjusted in light of an evaluation of evidence, so (D) isincorrect.
52. B Themain difference between the passages is that Passage 2 puts forth the idea that theecosystemswerealreadyindeclinewhentheasteroidhit,whilePassage1doesn’tmentionthat possibility when it discusses the volcanoes. Otherwise, both passages ultimatelyascribe the KT extinction to the asteroid. Thus, (B) is correct. Choice (A) is incorrectbecause theasteroiddidn’tcause thevolcaniceruptions.Choice(C) is incorrectbecausePassage2clarifiesthetimingoftheimpactandstatesthatpastestimateswereinaccurate.Passage2doesn’tdiscussmammalsatall,so(D)isincorrect.
Section2:WritingandLanguage
SLP,OMG!1. B Noticethequestion!Itasksforachoicethatwouldbest introducethemainsubject.The
restoftheparagraphisaboutthespokenword,so(B)iscorrect.Theotheranswerchoicesdonotintroducethisparagraph’sdiscussionofthespokenword.
2. C Keep theverb tense in thissentenceconsistent.Theotherverbsare isandwrite. Choice(C)istheonlychoicethatusesthepresenttense(speak)andmatchestheparallelstructuresetupbythecomparison:mostyoungerpeoplewrite…morethantheyspeak….Therefore,(C)isthecorrectanswer.
3. B Checktheanswerchoicesagainstthegraphs.Choice(A)canbeeliminatedbecauseSLPsdonotoverwhelminglywork inhospitals; thepercentagesfornon-residentialhealth-care
facilitiesandschoolsarebothhigherthanforhospitals.Choice(B)iscorrectbecause53%isabouthalf.Choice(C)canalsobeeliminatedbecausethenumberofSLPsworkinginschoolscannotbedeterminedfromthegraphprovided.53%ofSLPsworkinschools,butyou don’t know the total that 53% is out of. Choice (D) can be eliminated because thepercentagesprovideddon’trepresentbudgetamounts.
4. D Understatementisthemoreappropriatechoicebecausetherestofthepassagedetailsthewide range of duties that a speech-language pathologist could undertake; therefore, thesentenceshouldbekeptasisforthereasonstatedin(D).
5. D Noticethequestion!Choices(A)and(C)donotcombinethesentencestogether.Also,(C)hasaperiodseparatingacompleteideaandanincompleteidea,whichisincorrect.Choice(B)flowsessentiallythesamewayas(A)byinsertingasemicoloninplaceoftheperiod,so you can eliminate (B). Choice (D) incorporates the two ideas together in one fluidsentence,connectingtheincompleteidea(particularlythecomponents…) tothephraseitdescribes (attentionandmemory).Therefore, (D)offers thebest combination and is thecorrectanswer.
6. C Possessivepronounsdonotuseapostrophes,whilecontractionsdo.Choices(B)and(D),therefore, are both contractions for one is and it is, respectively. Since a possessivepronounisneededinthissentence,eliminate(B)and(D).Therespiratoryaspectsbelongtospeech,whichissingular.Thus,(C)iscorrectbecauseitsisthesingularpossessiveform.
7. A ThecorrectphraseshouldconveythattheSLPandmedicaldoctorworkingtogethercouldrestoreaninfant’sesophagealfunctiontoproperworkingorder.Choices(C)and(D)donotconveythisidea.Choice(B)isanidiomthatcouldexpressthisideabutcouldalsosimplymeanthatsomethingisneatandtidy,whichwouldn’texpresstheintendedmeaning.Choice(A)clearlyconveystherightmeaning,sothesentenceiscorrectaswritten.
8. A Noticethequestion!Itasksforachoicethatwouldbestmaintainthissentence’sfocusonthe actions an SLP might take to address a swallowing disorder. Only (A) details aspecificactionanSLPmighttake,whiletheothersareeitherofftopicordonotmentionanactionthatanSLPmighttaketoaddressaswallowingdisorder.
9. C Ifyoucannotciteareasontouseacomma,don’tuseone!Commasarenotneededforanyreasoninthissentence,sothecorrectansweris(C).
10. B Notice what changes in the answer choices: punctuation! Choice (A) creates a commasplice,and(D)createsarun-onsentence,sobothchoicescanbeeliminated.Choices(B)and (C) both use correct STOPpunctuation; the only difference is the use ofbut, whichcreatesacontrast.Thereisacontrast inthesentence;however, it isalreadysetupinthefirsthalfofthesentencebythephraseafterallnotmerely.Thus,but isnotneededinthesecondhalf,andyoucaneliminate(C)andchoose(B).
11. D Notice thatpronounuse ischanging in theanswerchoices.UsePOE.Choice (A)canbeeliminated because the machine (what itself would refer back to) is not being fixed or
replaced. Choices (B) and (C) can also be eliminated because it could suggest that thepronoun refers back tomachine, the rise, or the digital age, whereas them could referbacktobasicsorfacets. Ineithercase, thepronounisnotprecise.Choice(D) iscorrectbecausethepronounneededshouldreferbacktopeopleingeneral(noticeourlivesandususedin thesentence).Thesentencemeans that therearesomebasics thatnomachinecanreplaceorfixforuseventhoughthedigitalagehaschangedmanyfacetsofourlives.
TheOtherSteelCity12. C Notice the question! It asks for a choice thatbest introduces the historical tone of this
essay. Only (C) contains a historical reference. The other answer choices mentioninformation related to its locationorpopulation,and informationabout those topicsdoesnotfulfillthestatedpurposeofthequestion.
13. B Noticethequestion!Thequestionaskswhichistheleastacceptable.Theoriginalsentenceuses diversity to convey the vast range of indigenous people who once inhabitedBethlehem.Only(B)changesthemeaning(thesentenceisn’tdiscussinghowtheinhabitantswereorderedorgrouped)andisthereforetheleastacceptable.
14. D Choice(D)providesthemostclaritybyindicatingwhospecificallytradedwiththesettlers.You may have been tempted to choose (A), but it is incorrect because it includes thepotentiallyambiguousthey.
15. D Allfourchoicesmeanessentiallythesamething,sochoosetheonethatismostconciseandmakessenseincontext.Inthiscase,thatis(D),continued.
16. A Thephraseatthebeginningofthesentenceisanintroductoryidea(EvenaftertheinitialEuropean settlement on Christmas Eve in 1741) and should have a comma following1741,soeliminate(B)and(C).Thephrase in1741 isnecessaryinorder toknowwhichChristmasEve isbeingdiscussed, so (D)canbeeliminatedbecausecommasbeforeandafterthephrasewouldindicatethatthephraseisunnecessary.Thus,thesentenceiscorrectaswritten,making(A)theanswer.
17. B Notice thequestion!Itasksforachoice thathelps tomaintain the focuson theway theMoraviansettlershavebeencharacterizedthroughouttheessay.UsePOE.Choices(C)and (D) do not maintain the focus on the Moravian settlers, as both choices are aboutEuropeaninfluence.Choice(A)doesnotpresentinformationthatisconsistentwithhowtheMoraviansettlershavebeencharacterizedthroughouttheessay;theremainderofthethirdparagraph presents the Moravian influence in a positive light, which leaves (B) as thecorrectanswer.
18. D Choices (A), (B), and (C) all say essentially the same thing. Unlike the other choices,however, (D)contains thatof.Theas in theoriginal sentence indicates a comparison isbeing made, which, in this sentence, is its (the Moravian) religious influence to othergroups. However, the comparison should be consistent in structure, so (D) is correctbecausethepronoun that (referringto thereligiousinfluence) isusedtomakethesecond
partofthecomparisonconsistentwiththefirstpartsothatthecomparisonisinfluencetoinfluenceratherthaninfluencetogroups.
19. A Remember that possessive pronouns do not use apostrophes, while contractions do useapostrophes.Choice(C)isthecontractionfortheyare,and(D)isthecontractionforitis.Neither iscorrect in thiscasebecauseapossessivepronounisneededto indicatewhosefactorywasprovidingarmorandsteel.ThefactorybelongstoBethlehem,whichissingular.Eliminate(B)becausetheirisplural.Therefore,thesentenceiscorrectaswritten,so(A)istheanswer.
20. C Noticethattheanswerchoicesallcontainverbs(somepluralandsomesingular)andcheckforsubject/verbconsistency.Thesubjectforthesecondclauseisfurnaces,whichisplural.Eliminate (A) and (B) because both are singular. Next, check the verb tense. Since thefurnaces presently stand and will continue to stand (their presence appears to bepermanent),thesimplepresenttense(remain) isneeded,so(C) iscorrect.Choice(D) isnot correct because it uses the wrong verb tense and would change the meaning of thesentence.
21. C Noticethequestion!Itasksforachoicethatwouldbestconcludetheessaybypreservingitsstyleandtone.Thestyleandtoneofthisessayisinformativeandformal,so(C)ismostappropriate. The rest of the choices are all too conversational in tone, which is notconsistentwiththeessayasawhole.
22. B UsePOE.ThesentenceshouldbeaddedtotheparagraphthattalksabouttheMoravians,soeliminate (A) and (D). The proposed insertion does not contain information that shouldconcludeparagraph3.Thefinalsentenceofthethirdparagraphisprimarilytalkingaboutamusicfestival,sotodoublebackandmakeabroadpointaboutintellectuallifeaftersuchanarrowexamplewouldbeawkward.Eliminate(C).Also,thesentencebefore(B)usesthephrasesetupmissionstoconverttheLenapeandnon-English-speakingChristianstothetenetsofMoravianism,whichisconsistentwiththenewsentence’suseofAfteryearsofteaching….Thus,(B)isthebestplacementforthesentenceandthecorrectanswer.
LookItUp!23. B Withoutthephrasewhatifyoudon’t?,thenextsentence(Well,UrbanDictionarycansave
theday.)doesnotmakesense.Therefore,thephraseshouldbekept,andeliminate(C)and(D). Because the sentence following the phrase answers the question being asked, thecorrectansweris(B).
24. D Thecorrectidiomaticexpressiontousewhenlookingfor(ortryingtodiscover)someoneor something is turnup.All the other choices could follow turn in other circumstances(turndownthevolume,turninyourhomework,turnbackbeforeit’stoolate).However,inthissentence,thereaderisinstructedtolookforsomethinginaGooglesearch.Whatthereaderfindswouldbewhatthereaderturnsup,making(D)thecorrectanswer.
25. D Thecorrectchoicewillfeaturewordsthatareaspreciseaspossible.Wheresentence2is
currentlyplaced,itisunclearwhattheyisreferringbackto,soeliminate(A).Therewouldbe nothing for they to refer back to if sentence 2 were placed at the beginning of theparagraph, so eliminate (B). In placing sentence 2 after sentence 5, they seems to bereferring back to Urban Dictionary, which is singular. They is plural and, therefore,inconsistent, so (C) is also incorrect. Choice (D) is correct because the construction isconsistentwithsentences8and9,andtheyisappropriatelyplacedsothattheyrefersbacktothepluralnoundictionaries.
26. A Theverb in theunderlinedportion shouldbeconsistentwith the restof theverbphrase:werenot,didnot,anddidnothave can’t comebeforeexisted, so (B), (C), and (D) areincorrect.Theverbphrasehavenot…existedisthereforecorrectaswritten.Choice(A)iscorrect.
27. C Thewordpronunciationmaybemorecommon,butthatdoesnotmakeitmorerelevantinthe circumstances, so (A) is incorrect.Diction does have a precisemeaning (that is, thechoiceanduseofwordsorphrasesinspeechandwriting),so(B)isincorrect.Choice(D)is incorrect because the twowords donot have radically different definitions.Since thebeginningofthesentencementionsthetermdictionaryandwhenthiswordwascoined,thephraseshouldbekeptforthereasonstatedin(C).
28. D Thesentencealreadycontainsfurthermore,whichisnotunderlined,sousingindeedwouldbe redundant. Eliminate (B). Both (A) and (C) mean the same thing, but (A) is moreconcise;eliminate(C).However,youcanhaveacommabetweentwocompleteideasonlywhen it accompanies a FANBOYS; therefore, eliminate (A) as well. The first idea(Furthermore…Modern period) needs to be incomplete because the idea following thecomma is complete. By adding while before numerous dictionaries, the first idea isincomplete,making(D)thecorrectanswer.
29. C There should be a comma after every item in a list—in this case, consistent spellings,variantdefinitions,textualusages,andalphabeticalarrangements.Thiseliminates(D).Choice(B)isincorrectbecauseacommaisnotneededafterand.Thephrasealphabeticalarrangementsneeds tobe together,so thereshouldnotbeacommaseparating those twowords,whichmeans(A)isincorrectand(C)istheanswer.
30. C IfthephraseAnAmericanDictionaryoftheEnglishLanguagewereremoved,themeaningandcompletenessofthesentencewouldnotchange.Eventhoughitisthetitleofthebook,the rest of the sentence indicates thisworkwasWebster’s best-known andwhen itwaspublished,sothisphraseisnotessentialtothemeaningofthesentence.Commasshouldgobeforeandafterunnecessaryinformationsuchasthis,as(C)indicates.
31. A Noticethequestion!ItasksforachoicethatwouldbestemphasizetheuniqueachievementofWebster’sdictionary.Only(A)noteswhathedidthatwasunique.TheotherchoicesfailtoindicatehowWebster’sdictionarywasdifferentfrompreviouslypublisheddictionaries.
32. B ThesentencesetsupacontrastbetweenthewayAmericanswritetwospecificwordsandthewayEnglishwritethem.Only(B)completesthatcontrast,givingtheclearestsenseof
howtheEnglishspellthosewords,andisthecorrectanswer.
33. A The entire underlined phrase is serving as the subject of this sentence and cannot be acomplete idea, so eliminate (D). Choice (C) leaves out the phrasewhat is interesting,whichiswhatthesecondhalfofthesentenceexplains.Choice(B)createsapluralsubjectwiththephrasebothwhatisinterestingaboutthesetwodictionariesand…dictionariesingeneral,which isnotconsistentwith thenon-underlined, singularverb is.Therefore, thesentenceiscorrectaswritten,so(A)istheanswer.
Goodnight,sleeptight…34. C UsePOE,testingtheunderlinedportionineachplacesuggestedbytheanswerchoices.The
bestplacementfortheunderlinedportionisafterthewordform,(C),becausetheaftermathofabedbugbitetakestheformofanitchywelt.Placementoftheunderlinedportioninanyotherplacewouldnotconveythisintendedmeaning.
35. B Thesentencebeginswithacomparison(Likethemostannoyingvampire…),sothewordafterthecommashouldcompletethecomparison.Sincetheauthoriscomparingvampirestobedbugs,(B)istheonlyoption.Thetwopartsofthecomparisonshouldmatch,whichiswhytheremaininganswersareincorrect.Choices(A)and(D)arecomparingvampires tohumanblood,and(C)iscomparingvampirestoatypicalmeal.
36. A Theprevious sentence states Interest in bed bugs seems to be nearly as old aswrittenhistory itself, so the correct answerwill provide support for this statement (that is, bedbugshavebeenaroundforalongtime).UsePOE.Choices(C)and(D)canbeeliminatedbecause they do not mention the presence of bed bugs throughout history. While (B)containsareferencetohistory,itdoesnotsupporttheprevioussentence(again,nomentionthat bed bugs have been around for a really long time).Choice (A) contains the neededsupportandisthecorrectanswer.
37. D Since(D)providestheoptiontodelete,looktoseeifthevariationoftheunderlinedphraseisevenneeded,especiallysincetheotherthreechoicesallsayessentiallythesamething.Thephraseisn’tneededbecauseearlierinthesecondclausethebedbugsarementionedashelpingtoextractthetoxins,whichmakestheoptionsin(A),(B),and(C)redundantandunnecessarytothesentence.Choice(D)iscorrect.
38. A Choice (B) canbe eliminatedbecause the singular pronoun itwould be referring tobedbugswhich is plural.Choice (C) changes themeaning of the sentence by indicating thatsomebedbugsareanuisance,whereastheoriginalsentenceissuggestingthatbedbugsasa whole are a nuisance. Choices (A) and (D) are similar in meaning; however, (D) iswordy,while(A)maintainsthesimplepresenttense,whichisneeded,sonochangeshouldbemadetothesentence.
39. C Noticewhatischanginginthechoices.Whendealingwithpronouns,possessivesuseNOapostrophes, but contractions do use apostrophes. So, they’re is the contraction for theyare.Theirshowspluralpossession.There isused to refer to location.Eliminate (A)and
(B)becausethesentenceneedsapossessivepronoun:Itisthebedbugs’prevalencethatisbeing discussed. Choice (D) is incorrect because the use of the would provide noownershipofprevalenceandwouldnotbeprecise.Thus,(C)iscorrect.
40. B Notice thequestion! It askswhetherornot theauthorhasachieved thegoalofprovidingcontinuity between the two paragraphs. The third paragraph describes the significantproblembedbugswereduringthetwentiethcenturybecauseoftheirprevalenceandlistsevents in1933andduringWorldWarII for support.The fourthparagraphcontinues thistimeline of events by mentioning the efforts of the United States in the 1940s and thereappearanceofbedbugs in the1980s.Thus, thegoal for continuitybetweenparagraphshasbeenachievedforthereasonstatedin(B).
41. B The author is explaining that the resurgence of bed bugs is due to two causes:pesticide_____andinternationaltravel.Thepartofspeechneededisanountobeconsistentwiththeothernounused(international travel), soeliminate (A), (C), and (D).Choice (B) iscorrect,asitusesthecorrectnountoconveytheintendedmeaning.
42. D Noticewhatischangingintheanswerchoices:punctuation!Periodsandsemicolonscanbeusedonlytoseparatecomplete ideas.Inthissentencethereisacompleteideabeforethepunctuationandanincompleteideaafterthepunctuation,soneither(A)nor(B)iscorrect.Choice(C)isincorrectbecauseanddoesnotreflectthecontrastbetweentwoideasinthesentence.Choice (D) is correctbecause it ties the two ideas togetherwitha commaandthough,whichaccuratelyreflectsthewaythesecondstatementqualifiesthefirst.
43. D Noticethequestion!Itasksforachoicethatwouldbestmaintainthefocusofthissentenceandparagraph.Thefocusofthisparagraphisontheunexpecteddiscoverythatbedbugscan transmitdisease.Theonlyoption thatdoes this is (D),as theparagraphreferencesanewreasonandworry.Choices(A),(B),and(C)bringupirrelevantpointsaboutmiceorratsinthecontextofthisparagraphandarenotconsistentwiththefocusofthesentenceorparagraph.
44. A Usethefirstphraseinthesixthparagraph(Ifthesefindingsaretrue)tohelp.Thephrasethese findings is referring back to the study that was discussed at the end of the fifthparagraph.Therefore,theonlylogicalplaceforthesixthparagraphiswhereitiscurrently,which is (A). Otherwise, the flow of the passage would be disrupted and inconsistentbecausethesefindingswouldnotbereferringbacktothestudy.
Section3:Math(NoCalculator)1. B BecauseMarcoalreadyhas75poundsofsalt,heneeds200−75=125additionalpounds.
Estimatethenumberofbagsheneeds.125iscloseto120,and120÷30=4,sohemustneedmore than4bags (because125 ismore than120).Thismeans thatMarconeeds atleast5morebags.Therefore,thecorrectansweris(B).
2. C Whenevertherearevariablesinthequestionandintheanswers,thinkPluggingIn.Letd=2.Thenumberofsubscribersthewebsitehassignedupsofarcanbecalculatedas500(2)
= 1,000. Therefore, the website needs to sign up 100,000 − 1,000 = 99,000 additionalsubscribers.Plug2inforwintheanswerstoseewhichanswerequalsthetargetnumberof99,000.Choice(A)becomesW=500(2)=1,000.Thisdoesn’tmatchthetargetnumber,soeliminate(A).Choice(B)becomesW=99,500(2)=199,000.Eliminate(B).Choice(C)becomesW=100,000−500(2)=100,000−1,000=99,000.Keep(C),butcheck(D)justincase italsoworks.Choice (D)becomesW=100,000+500(2)=100,000+1,000=101,000.Eliminate(D).Thecorrectansweris(C).
3. C Sincethequestionstatesf(4)=5,thenwhenx=4,theresultshouldbe5.Pluginx=4intoeachanswerchoicetoseewhichequationdoesNOTequal5.Choice(A)becomesf(4)=4+1=5.Thisworks,soeliminate(A).Choice(B)becomes f(4)=2(4)−3=8−3=5.Eliminate(B).Choice(C)becomesf(4)=3(4)−2=12−2=10.Thecorrectansweris(C).
4. D Factortheexpressiontoget .Reducethefractiontoget ,or .Anotherwayof
writing isx−1.Therefore,thecorrectansweris(D).
5. A StartwiththeeasierequationfirstanduseProcessofElimination.Theeasierequationhastodowiththetotalnumberofsolutions.Accordingtothequestion,Réginemeasuresatotalof100solutions.Thisinformationcanbeexpressedasx+y=100.Eliminate(B)and(C)becauseneitherof these includes thisequation.Remember thatpercentagemeansdividedby 100. Therefore, 40% = 0.4 and 70% = 0.7. Given this information, x should beassociatedwith0.4andyshouldbeassociatedwith0.7.Onthisbasis,eliminate(D).Thecorrectansweris(A).
6. B Thegraphshownisaregularparabolathathasbeenturnedupsidedownandmoveddown6.Theequationofaregularparabolathatpointsupwardisy=x2.Therefore,thegraphofaparabolathatpointsdownwardsisy=−x2.Eliminate(D)becausethatanswerismissingthe negative sign. To move a parabola down 6 units, a 6 must be subtracted from theequationof theparabola.Eliminate(A)and(C),whichadd6instead.Choice(B)canberewrittenasy=−x2−6.Thecorrectansweris(B).
7. A Startbylabelingtheequationwiththeinformationinthequestion.ThequestionsaysthatPisthepriceoftheitemandtisthetimeinyears,solabelthese.Thequestionalsostatesthatthepriceincreasesby$3peryear,sothe3intheequationisthepriceincrease.Nowlookattheanswerchoices,whichareaboutthenumber10intheequation,andseewhatcanbeeliminated.Choice(D)referstothepriceincrease,whichis3,soeliminate(D).Theotheranswerchoicesrefertotheyear.Pluginthepricegiveninthequestion,$43,tosolvefort.Theequationbecomes43=3t+10,so3t=33,andt=11.Thatrepresentsthenumberofyearsfromwhentheitemwasmanufactureduntiltheyear2010,theyearofthegivenprice.Subtract11yearsfrom2010toget1999,whichis(A).
8. C Usetheformulaarc=rθ,whereristheradiusandθisthemeasureofthecentralanglein
radians.Becausetheangleisalreadyinradians,youjustneedtoplugin10fortheradius
andtheangle intotheformula.Youthengets=(10) or4π,whichis(C).
9. B Start by calculating the least amountof acetaminophen the childneeds. If the child is 75
pounds,thentheamountofacetaminophenneededcanbecalculatedas ×1,000= ×
1,000=500.Sinceonly(B)gives500asthelow-endvalue,thecorrectansweris(B).
10. C Whenevertherearevariablesinthequestionandintheanswerchoices,thinkPluggingIn,
pickingnumbersthatensurethatIisaninteger.IfP=18andR=2,thenI=
=3.BecauseV=IR,V=3×2=6.PlugP=18,R=2,andV=6intotheanswerstosee
whichanswerworks.Choice(A)becomes18= .Solvetherightsideoftheequationto
get18= .Thisstatementisnottrue,soeliminate(A).Choice(B)becomes18= .This
statementisnottrue,soeliminate(B).Choice(C)becomes18= .Solvetheleftsideof
theequation toget18= .This statement is true, sokeep (C),but check the remaining
answerjustincase.Choice(D)becomes18=(62)(23)or18=36×8.Thisstatementisnot
true,soeliminate(D).Thecorrectansweris(C).
11. D Arootoftheequationisthesameasanx-intercept.Inthegraph,thefunctioncrossesthex-axisat4points.Therefore,thecorrectansweris(D).
12. A Labelthecongruentangles, ABCand CDE,assuch.Inordertofindthemeasureofthoseangles,usetheformula180(n−2),wherenisthenumberofsides,todeterminethesumofthe interior anglesof the figure.Because the figurehas five sides, plug5 in forn to get180(5−2),or180(3),whichequals540.Subtract120toget420.Subtract100toget320.Subtract40toget280.Sincethetworemaininganglesarecongruent,divideby2tofindthat the two unlabeled angles are both equal to 140.Because ABC and BCD have acombinedmeasureof180,ABandCDareparallel.Therefore,(A)accuratelydescribestherelationshipsinthefigure.
13. B Takingthe4throotofanumberisthesameastakingthenumbertothe power.Therefore,
the equation can be rewritten as . Divide both sides by 2 to get
.Therefore,intheequation, and ,sow=3.The
correctansweris(B).
14. C Whenevertherearevariablesinthequestionandintheanswers,thinkPluggingIn.Ifa=2
andb=3,r=[ (2)+3]2=(1+3)2=16,ands=−4(2)(3)+3(3)=−24+9=−15.The
expressionr−2sbecomes16−2(−15)=16+30=46.Plug2inforaand3inforb in
each of the answers to see which answer equals the target number of 46. Choice (A)
becomes (22)+32−7(2)(3)−6(3)=1+9−42−18=−50.Thisdoesnotmatch the
targetnumber,soeliminate(A).Choice(B)becomes (22)+32−7(2)(3)+6(3)=1+9−
42+18=−14.Eliminate(B).Choice(C)becomes (22)+32+9(2)(3)−6(3)=1+9+54
−18=46.Keep(C),butcheck(D)justincaseitalsoworks.Choice(D)isthesameas(C)
except for thecoefficienton thea2 term,so itcan’tequal46.Eliminate (D).Thecorrect
answeris(C).
15. C First,startwithasketchofthetwopointstoseewhatthelineinquestionmightlooklike.
Thepointdirectlybetweenthetwopointswilldefinitelybeontheline,sofindthemidpoint
of thetwopoints.Midpoint= =(4,2).Check thispoint in
theanswerchoicesandeliminateanythatdonotcontainit.Choice(A)becomes2(2)=−4
+8or4=4,whichistrue.Choice(B)becomes2(2)=4,and(C)becomes2=2(4)−6or
2=8−6.Thesearealsotrue,but(D)becomes2=−2(4),whichisfalse.Eliminate(D).To
sketchtheremainingequations,rewritetheminslope-interceptformoftheequationy=mx
+b,wherem istheslopeandb isthey-intercept.Choice(A)becomesy=− x+4, (B)
becomesy= x, and (C) is already in the right form.Now sketch the graphs of eachof
theseonthexy-plane.
The line in (A) contains both the given points, but all the points to the left of (0, 4) arecloser to that point and all those to the right of (8, 0) are closer to it. So eliminate (A).Manypointsonline(B)arealsoclearlyclosertooneortheotherofthegivenpoints,soeliminate (B).Line (C) appears to be perpendicular to the line formedby the twogivenpoints,andthisisinfactwhatwillmakeall thepointsonalineequidistantfrom2givenpoints.Therefore,thecorrectansweris(C).
16. or2.33
Getridofthefractionsinthefirstequationbymultiplyingtheentireequationby6,toget2p
+ 3q = 6.Whenever there are two equations with the same two variables, they can be
solved simultaneously by adding or subtracting them. The key is to get one variable to
disappear.Stacktheequationsandaddthem.
Therefore,p= .
17. 6 Substitutexforyinthesecondequationtoget(x−2)2−4=−x.Expandtheleftsideofthe
equationtoget(x−2)(x−2)−4=−xorx2−4x+4−4=−x.Simplifytheequationtoget
x2−4x=−x.Settheequationto0togetx2−3x=0.Factoranxoutoftheequationtoget
x(x−3)=0.Therefore,eitherx=0orx−3=0,andx=3.Accordingtothequestion,the
point of intersection is in Quadrant I, where the x- and y-values are both positive.
Therefore,x=3andy=3.Thesumof3+3=6.Thecorrectansweris6.
18. 6 Trypluggingindifferentvaluesofctoseewhichoneswork.Makeatabletokeeptrackof
allthenumbers.
c= (c−1)2=
1 (1−1)2=0
2 (2−1)2=1
3 (3−1)2=4
4 (4−1)2=9
5 (5−1)2=16
6 (6−1)2=25
7 (7−1)2=36
Thelargestvalueofcthatworkswithouthittingtheboundariesoftheinequalityis6,sothecorrectansweris6.
19. 8 Whennopictureisprovided,ithelpstodrawone.First,rewriteeachequationsothatitis
intheslope-interceptformofaline,whichisy=mx+b,wheremistheslopeandbisthe
y-interceptoftheline.Thefirstequationbecomes2y≤x+4,ory≤ x+2.Thesecond
equationbecomesy≥2x−4.Theresultinggraphlooksasfollows:
Asthegraphshows,thegreatestx+yisthepointatwhichthetwolinesintersect.Setthe
equationsofthetwolines,y= x+2andy=2x−4,equaltoeachotherandsolveforx.
Theresultingequationis x+2=2x−4.Solveforxtoget− x+2=−4or− x=−6,so
x=4.Next,plug4intooneofthetwoequationstosolvefory.Therefore,y=2(4)−4=4
andx+y=4+4=8.Thecorrectansweris8.
20. 72 Theformulaforthevolumeofapyramid,givenatthestartofeachmathsection,isV=
lwh,wherelisthelengthofthebase,wisthewidthofthebase,andhistheheight.Since
thecubehasside6,thelengthandwidthofthebaseareboth6.Theheightofthepyramidis
alsotheheightofthecube,whichisalso6.PlugtheseintotheformulatogetV= (6)(6)(6)
=72.
Section4:Math(Calculator)1. D Whenevertherearevariablesinthequestionandintheanswers,thinkPluggingIn.Letd=
2.For$1theairpumpdispenses90×4=360poundsofair.Therefore,for$2theairpumpwilldispense360×2=720poundsofair.Plug in2 ford in theanswerchoices to seewhichanswerequals720.Choice(A)becomesP=2+90=92.Eliminate(A).Choice(B)becomes P = 2 + 360 = 362. Eliminate (B). Choice (C) becomes P = 90(2) = 180.Eliminate (C).Choice (D) becomesP = 360(2) = 720.Therefore, the correct answer is(D).
2. A Setupaproportion: .Cross-multiplytogetx=6×0.30=1.8meters.
Therefore,thecorrectansweris(A).
3. B Inordertofindtheundevelopedarea,taketheentireareaoftheparkandsubtracttheareaofthedevelopedportions.Subtractthe4acrelaketoget44−4=40undevelopedacres.Next,subtractthelargestandsmallestpossiblesoccerfieldarea:40−10=30,and40−8=32.Therefore,thecorrectansweris(B).
4. B Weight is shown on the horizontal axis of the graph, given in tons. Look for the markindicating3onthisaxis;thendrawaverticallinefromthatmarktothelineofbestfit.Onceyouhitit,drawahorizontallineovertotheverticalaxis.Itshouldhitbetween20and25miles per gallon, slightly closer to themark for 25. Thismakes (B) the correct answer.Drawyourlinescarefully,usingyouranswersheetasastraightedgeifnecessary,toavoidtrapanswersliketheclose-but-not-quite(C).
5. C Youcanseefromthegraphthatfrom2000to2002,thenumberofcoatiincreasedfrom140to160.From2002to2004,thenumberincreasedfrom160to180.Therefore,thenumberofcoatiisincreasingatarateof20every2years.In2006,iftherateofincreaseremainsthesame,thenumberofcoatishouldbe180+20=200,whichis(C).
6. B Thequestionstatesthatthereareinfinitelymanysolutionstotheequation.Thatmeansany
realnumbershouldworkford.Pluginaneasynumberlike0foreverydintheequationto
get .Simplifytheequationto = ,soa=10,whichis(B).
7. A First, convert the minutes shown in the graph to seconds. Multiply 15 minutes by 60secondstoget900seconds.Then,sincespeedisdistancedividedbytime,simplydivide3,000metersby900seconds.Theansweris3.3m/s,whichis(A).
8. C Plug2inforyintheanswerstoseewhichfunctionmostcloselyequalstheareaof14,910.
Choice (A) becomes 15,000 = 7,500. This does not match the target number, so
eliminate (A). Choice (B) becomes 15,000(0.003)2 = 0.135. Eliminate (B). Choice (C)
becomes15,000(0.997)2≈14,910.Thecorrectansweris(C).
9. B First, calculatewhatMike’s daily calorie consumption is during finals. 12%of 1,680 is0.12×1,680=201.6.DuringfinalsMikeconsumes1,680+201.6=1,881.6caloriesperday. Whenever the question includes variables, Plug In. Let d = 2. Over 2 days Mikeconsumes2×1,881.6=3,763.2calories.Healsoadds900caloriesat theendoffinals.Histotalconsumptionovertheentirefinalsperiodis3,763.2+900=4,663.2calories,so4,663.2 is the target number. Plug in 2 for d in each of the answer choices. In (A),1.12[1,680(2) + 900] = 4,771.2, which is not the target number. Eliminate (A). In (B),1.12[1,680(2)]+900=4,663.2,whichisthetarget.Leave(B),butchecktheotheranswerchoicesjustincase.In(C),1.12(1,680+900)(2)=5,779.2,andin(D),[1,680+(0.12)(2)]+900=2,580.24.Eliminateboth(C)and(D).Thecorrectansweris(B).
10. D UseProcessofEliminationon thisquestion.Choice (A)cannotbecorrectbecausemorejuniorspreferAustintoPensacola.Choice(B)soundsappealing,but“morethanthreetimesaslikely”meanstheseniorsasawholeneedtopreferPensacolamorethanthreetimesasmuchasthejuniorsdoasawhole.SeniorspreferPensacola23outof42,or55%.Juniorspreferit7outof21,or33%.So,seniorsdonotpreferPensacolamorethanthreetimesasmuchasjuniorsdo.Youcanalsoeliminate(C)becausemorethanhalfofalljuniorspreferAustin,while less than half of all seniors preferAustin. The statement in (D) is correctbecause7isone-thirdofthetotalof21juniors.
11. B Youarelookingfortheprobabilitythatarandomlyselectedpersonisamanwithadoctoral
degree. There are 16,232men with doctoral degrees, and 220,532 total adults aged 25
yearsorolder.Sotheprobabilitythatarandomlyselectedpersonfitsthecategoryyouare
lookingforis =0.07=7%,whichis(B).
12. C Whenevertherearevariablesinthequestionandintheanswers, thinkPluggingIn.Ifx=
10,thenC=110+ =100+5=115andR=15(10)− =150− =150−10=
140. Therefore, the profit can be calculated as 140 − 115 = 25. Plug 10 in for x in the
answerstoseewhichanswerequalsthetargetnumberof25.Choice(A)becomes− −
(10)+110=− −31(5)+110=−10−155+110=−55.Thisdoesn’tmatchthetarget
number,soeliminate(A).Choice(B)becomes− − (10)+110=− −29(5)+110
=−10−145+110=−45.Eliminate(B).Choice(C)becomes− + (10)−110=−
+29(5)−110=−10+145−110=25.Keep(C),butcheck(D)justincaseitalsoworks.
Choice(D)becomes− + (10)−110= +31(5)−110=−10+155−110=35.
Eliminate(D)andchoose(C).
13. D Tostayathisfancyhotelforthreenightsat2,000Moroccandirhamspernight,Erikwillneed 6,000 dirhams. Using the currency conversion rate of 1 dirham = $0.11, you canmultiply 6,000× 0.11 to determine thatErik’s hotel staywill cost $660. Since his bankallowshimtowithdrawonly$200atatime,ErikmustgototheATMfourtimes:(D).
14. C Start with the easier equation first and use Process of Elimination. The easier equationinvolves the totalamountofgassold.According to thequestion,850gallonsofgasolineweresold,whichcanbeexpressedasu+p=850.Eliminate(D)sinceitdoesnotincludethisequation.Theotherequationintheanswersisrelatedtotheamountofmoneycollected.Accordingtothequestion,$3,016.50wascollected;however,thissumincludedadiscountof $0.10 per gallon for 100 of the gallons that were purchased or $0.10 × 100 = $10.Withoutthediscountunleadedgascosts$3.49andpremiumgascosts$3.79agallon,andtheamountofmoneycollectedwouldhavebeen$3,016.50+$10=$3,026.50.Only (C)providesthecorrecttotal.Therefore,thecorrectansweris(C).
15. B First,figureouthowmanystudentsareenrolledinAPcoursesotherthanBiologyandU.S.
History.Thereare319studentsareenrolledinatleastoneAPcourse,andofthose,75+58
=133areenrolledinBiologyandU.S.History.However,since22studentsareenrolledin
both of those courses, you need to subtract 22 from 133 (so as not to double-count the
studentstakingbothcourses).Thatleaves133−22=111totalstudentswhoaretakingAP
BiologyandAPU.S.History.Ofthe319studentstakingAPcourses,thatmeansthereare
319−111=208studentstakingAPcoursesotherthanBiologyandU.S.History.Thereare
784 juniors and seniors total, so = 0.265, or approximately 27% of all juniors and
seniors,whichis(B).
16. A Totalscore=averagescore× thenumberof tests. Inorder forMateo to receiveaB,heneedshistotalscoreoverthe3teststobebetween3×80=240pointsand3×89=267points. On his first and second tests, Mateo scored a total of 79 + 95 = 174 points.Therefore,onhisthirdtestMateomustscorebetween240−174=66and267−174=93pointsinordertoreceiveaB.Thecorrectansweris(A).
17. A Use Process of Elimination to solve this question. Choice (A) is possible so leave it.Choice (B) discusses themass of the fertilizer, but no reference tomass ismade in thequestion. Eliminate (B). According to the question, the quantity described in (C) isrepresentedbyA,soeliminate(C).Accordingtothequestion,thequantitydescribedin(D)
isrepresentedbyY,soeliminate(D).Thecorrectansweris(A).
18. D The mode of the combined groups cannot be determined without knowing exactly whatscoreseachgroupreceived.Toillustratethis,PlugIn!SaythatthescoresofGroupAwere{1,1,7,7,7},andthescoresforGroupBwere{1,1,6,6,6}.Thescoresofthewholegroup would, therefore, be {1, 1, 1, 1, 6, 6, 6, 7, 7, 7}. This set has a mode of 1, soeliminate(A),(B),and(C)andchoose(D).
19. C First,countthenumberofblocksthatJoshneedstodrive.Heneedstodrive4blocksnorth
and6blockseastforatotalof10blocks.Youneedtoconvertthisintomiles,whichcanbe
donewith the following proportion: . The drive is a total of 6miles.
Since Josh drives at 30 miles per hour, you can set up a second proportion:
.Cross-multiplyandsolvetogetthatx= or ofanhour.Thisequals
12minutes,asin(C).
20. D Thefirststepistorewritethebottomequationsothatit isinthesameformatasthefirstequation.Moveallofthevariablesinthebottomequationtotheleftsideoftheequationtoget6s−t=12.Iftheansweris(A)andthereareinfinitelymanysolutionstothesystemofequations,thenthetwoequationsmustbethesameequation.Todeterminewhetherthisisthecase,multiplythetopequationthroughby3toget6s−t=30.Since itcannotbe thecasethattheequation6s−tequalsboth12and30,thecorrectansweris(D).Therearenosolutionstothesystemofequations.
21. C Twofactorsareimportantindetermininghowtopollagroup:thesizeofthesampleandhow that sample is selected. Secretary Stephens’s plan has the largest samplewith 250students,butall thosestudentsbelongto theseniorclass.Perhaps theseniorclasswouldprefer a theme that the other three classes would not. The sample is skewed and notnecessarilyrepresentativeoftheentirestudentbody,soeliminate(B).Theotherthreeplansall poll 100 students, so themanner inwhich those students are selected becomesmoreimportant.PresidentPeterson’s plan is also skewed specifically to friendsof the studentcouncil members, whose opinionsmight not reflect themajority, so eliminate (A). VicePresidentVaiyda’splanhasmorepotentialforavariedsample,butitisstillnotasgoodasTreasurerThompson’splan,whichguaranteesthatarandomassortmentofpeoplewillbechosenforthepoll.Eliminate(D)andchoose(C).
22. C Sincexandy arepointson thecircle,plug in thepoint (−2,−2) into the left sideof theequation.Thisgivesyou(−2+3)2+(−2−1)2,whichequals12+(−3)2.Simplifying,youget 10.Because 10 is greater than r2 (which is 9), the pointmust be outside the circle,whichis(C).
23. D Whenever the question includes variables, think Plugging In.According to the question,
= −C.Plugin12forxtoget = −C,or = −C.Solvefor
Ctoget0= −C,then0=3 =C,andfinally3 =C.Thecorrectansweris(D).
24. A Alloftheanswerchoicesrefertothenumberofsalary-satisfiedbachelor’s-degree-holders,soyoumustusethefollow-upsurveyresultstocalculatethatnumber.First,findthepercentof bachelor’s-degree-holders who reported also being salary-satisfied in the follow-upsurvey.This numberwas 658 out of the 1,000 people, so divide 658 by 1,000 and thenmultiplyby100togetthepercent.Theresultis65.8%salary-satisfiedbachelor’s-degree-holders for the follow-up survey. Since the people in the follow-up were randomlyselected, you can assume that they aregenerally representativeof thebachelor’s-degree-holdingpopulationatlarge.Therefore,the65.8%ofsalary-satisfiedindividualsshouldbetrueofall24,236,000job-satisfiedbachelor’s-degree-holders.Watchtheunitsoncharts—thisone is in the thousands, so thereare24,236,000not24,236 job-satisfiedbachelor’s-degree-holders.Multiply65.8%,or .658,by the totalnumberof job-satisfiedbachelor’s-degree-holders,24,236,000, to find that thereshouldbe15,947,288salary-satisfied, job-satisfied bachelor’s-degree-holders. Choice (A) is the closest to this and is the correctanswer.
25. A Theequationofalineexpressedinslope-interceptformisy=mx+b,wheremistheslope
andbisthey-intercept.Onewaytofindthey-interceptoflinedistoplugintheslopeand
givenpointandsolveforb.Theequationy=mx+bbecomes1= (1)+b.Subtract from
bothsidestogetb= .They-interceptoflineeis3times ,sothey-interceptoflineeis
.Additionally,parallel lineshaveslopes thatareequal toeachother.Therefore, linee
willalsohaveaslopeequalto .Therefore,theequationoflineeisy= x+ .Rewrite
thisinaformthatlooksmoreliketheanswerchoicesbymultiplyingeverythingby5toget
5y=4x+3.Subtract4xfrombothsidestoget5y−4x=3.Therefore,thecorrectansweris
(A).
26. B Anextraneous solution isananswer thatwhenpluggedback into theequationcauses the
equation to be false.Begin by factoring and reducing the fraction on the left side of the
equationtoget = orq−7= .Squarebothsidesoftheequationto
getq2 − 14q + 49 = q − 5. Set the equation to 0 to getq2 − 15q + 54 = 0. Factor the
quadratic to get (q − 9)(q − 6) = 0. Therefore,q = 9 orq = 6. Eliminate (A) and (C)
becauseneitheroftheseanswersisapossiblesolutionforq.Plug6inforqintheequation
to see if this value ofqworks. The equation becomes = . Solve both
sidesof theequation toget =1.Since this statement isnot true,6 is theextraneous
solution.Thecorrectansweris(B).
27. D First,determine the totalnumberofgamers ineachgame typebyaddingup thecolumns.There are 110,000,000 gamers preferring first person shooters, 52,000,000 preferringsportsgames,and85,000,000preferringadventuregames.Youdon’tknowbyhowmuchthe 9- to 13-year old groupwill increase in sport game preference, but presumably theincreasewillbemadetomatchthecurrentlylargestgroup,firstpersonshooters.Therefore,in order to raise adventure games to the level of first person shooters, you need to add110,000,000−85,000,000=25,000,000gamerstotheadventuregamesgroup.Ifyouaregoingtodosobydoublingoneoftheagegroups,then25,000,000isequaltothesizeofthecurrentgroup.9-to13-yearoldscurrentlyhave25,000,000preferringadventuregames,so(D)istheanswer.
28. A Whenevertherearevariablesinthequestionandintheanswers,thinkPluggingIn.Saythat
forEmilioa=2,t=4,andk=10.ThenEmilio’saccruedvacationdayscanbecalculated
asV(t)=2(4)+10=18.ThismeansthatMartinhasaccrued18+9=27vacationdays.
Becauseaandkareconstants,theirvaluesdonotchange.ThenumberofyearsthatMartin
hasworkedatthemanufacturingplantcanthereforebecalculatedas27=2t+10.Solvefor
ttoget17=2tort= =8.5.Therefore,Martinhasworked8.5−4=4.5moreyearsthan
Emilio.Plug2inforaintheanswerstoseewhichanswerequals4.5.Choice(A)becomes
=4.5.Keep(A),butchecktheremaininganswersjustincase.Choice(B)becomes9−2
=7,(C)becomes9+2=11,and(D)becomes9(2)=19.Eliminate(B),(C),and(D).The
correctansweris(A).
29. C SOHCAHTOA tells you that sine is , so if the side opposite the angle with
measurex° isOand thehypotenuse isH, then .SolveforO, andyougetO=
.Now,youcanuse thePythagoreanTheoremwith thegivensideandsubstituting
forO inorder tosolveforH: .Solve theexponents,and then
reducethefraction:100+ =H2;100+ =H2.Subtract frombothsides:100
= .Dividebothsidesby ,so116=H2.Squarerootbothsides,andyoufindthatH
=2 .Using fromabove,youcansolveforO:O= =4.Addthe
sidesandyouget14+2 ,whichis(C).
30. D AgoodapproachtothisquestionwouldbetoPlugIn.Startwiththenumberofjuniorsand
pluginanumberthatiseasytodealwith,suchas200.Thenyoucansetupaproportion
usingtheratiogiveninthequestionstem: = = .Cross-multiplyandsolveforx
todeterminethatthenumberofseniorswouldbe150.Next,usetherelationship
= .Using150forseniors,youget = = .Cross-multiplyandsolveforxto
determine that the number of sophomores would be 120. Next, use the relationship
= .Using120forsophomores,youget = = .Cross-multiply
and solve for x to determine that the number of freshmen would be 140. The ratio of
freshmentoseniors,therefore,wouldbe = = ,whichis(D).
31. 75 Hayoungswims2.5miles.She runs11×2.5=27.5miles, andshebikes18×2.5=45miles.Hertotaltriathlonmileage=2.5+27.5+45=75miles.Thecorrectansweris75.
32. 5 Plug1,230inforthevalueofthefunctiontoget1,230=250x−20.Solveforxtoget1,250=250xandx=5.Thecorrectansweris5.
33. 918 Inordertofindthegreatestprofit,maximizethenumberofacresofsoybeansMartyplants,sincesoybeansbringinmoremoneyperacrethandoeswheat.Atmost,Martycanplant7acresofsoybeans.Therefore,themostmoneyhecanmakeonsoybeansis7×120=840.Hethenhas9−7=2acres leftonwhichtoplantwheat.Themoneyhemakesfromthiswheatis2×90=180.ThetotalamountMartymakesbeforetaxesistherefore840+180=1,020.Thetaxonthismoneyequals1,020×0.10=102.SubtracttheamountMartypaysintaxestoget1,020−102=918profit.Thecorrectansweris918.
34. 19 TheformulafortheareaofacircleisA=πr2.Ifafullcirclewereshown,itsradiuswould
be4,sotheareaofthefullcirclewouldbeA=π42=16π.Theinteriorangleofthefraction
of the circle shown can be calculated as 90 + 45 = 135 degrees. Therefore, the figure
shownis of theareaofa fullcircle.Theareaof thefigurecanbecalculatedas
(16π)=0.375(16π)=6π≈18.8≈19.Thecorrectansweris19.
35. 6 The two triangles share three angles; thus theyare similar.AC is twice the lengthofBCbecause it is bisected by BD. This relationship is constant between the two similartriangles.Therefore,BDishalfofAE:12÷2=6.
36. 20 First, determine the grams of protein in the bar. If the bar contains 32% of the daily
recommended serving of protein, and the daily recommended serving of protein is 50
grams,thenthebarcontains0.32×50=16gramsofprotein.Next,determinethegramsof
fatinthebarbyusingthepercentchangeequation:percentchange= ×100.The
percentchangeis700,andtheoriginalisthegramsoffat(becausepercentmoremeansthe
original is the smaller number),whichmeans 700= × 100.Divide both sides by
100:7= .Multiplybothsidesbyxtoget7x=16−x.Addxtobothsidestoget8x=
16.Dividebothsidesby8andyoufindx=2.Thatisthenumberofgramsoffatinthebar.
To find thedaily recommended servingof fat, translateEnglish tomath.2 is10%of the
dailyrecommendedserving,so if thedailyrecommendedserving isy,2=0.10y.Divide
bothsidesby0.10,andyoufindthatthedailyrecommendedservingoffatis20.
37. 1 First,youneedtodeterminethecontentofSetR.IfSetRconsistsofalltheone-digitprimenumbers,thenR={2,3,5,7}.ThesumoftheelementsofSetSwouldthereforebe2+3+5+7+x=30.Combineliketerms:17+x=30.Subtract17frombothsides,andyoufindx=13.Plugx=13intotheequationandsolve:(13)2−11(13)−25=1.
38. 8 Theadditionalpositive integerx cannot equal 2, 3, 5, or 7 (otherwise therewouldbe a
mode).Next,determinewhatthemediancouldbeforvariousrangesofx.Ifxislessthan2,
thenthesetwouldbe,inconsecutiveorder,{x,2,3,5,7},makingthemedian3.Trythis
set.Ifthemedianequalsthemean,thenthesumoftheelementsdividedby5(thenumberof
elements)mustequal3: =3.Multiplybothsidesby5andcombine like
terms:x+17=15.Subtract17frombothsides,andyoufindx=−2.However,xmustbea
positiveinteger,sothisdoesn’twork.Tryanewmedian.Ifx=4,thenthesetis{2,3,4(x),
5, 7), with amedian of 4. However, themean is = 5.25, not 4, so this
doesn’twork.Ifxis6orgreater,thesetwouldeitherbe{2,3,5,6(x),7}or{2,3,5,7,
x}. In either case, the median is 5. Set up the average equal to the median of 5:
= 5. Multiply both sides by 5 and combine like terms: 17 + x = 25.
Subtract17frombothsides,andyoufindthatx=8.
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