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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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Goodluck!

TheStaffofThePrincetonReview

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RegisterYourBookOnline!

GotoPrincetonReview.com/cracking

You’llseeawelcomepagewhereyoucanregisteryourbookusingthefollowingISBN:9780451487612

Afterplacingthisfreeorder,you’lleitherbeaskedtologinortoanswerafewsimplequestionsinordertosetupanewPrincetonReviewaccount.

Finally,clickonthe“StudentTools”tablocatedatthetopofthescreen.Itmaytakeanhourortwoforyourregistrationtogothrough,butafterthat,you’regoodtogo.

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Onceyou’veregistered,youcan…

• Accessandprintoutthreemorefull-lengthpracticetestsaswellasthecorrespondinganswersandexplanations

• Findanylate-breakinginformationreleasedabouttheSAT

• Readourspecial“SATInsider”andgetvaluableadviceaboutthecollegeapplicationprocess,includingtipsforwritingagreatessayandwheretoapplyforfinancialaid

• Sortcollegesbywhateveryou’relookingfor(suchasBestTheaterorDorm),learnmoreaboutyourtopchoices,andseehowtheyallrankaccordingtoTheBest381Colleges

• CheckoutbonusfeaturesinyourPremiumPortal,includingcomprehensivestudyguidesandshortvideostohelpenhanceyourtestprep

• Downloadprintableresourcessuchasscoreconversiontables,extrabubblesheets,andessayanswerformsforthepracticetests

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MoreGreatBooks

PartIOrientation1 TheSAT,ThePrincetonReview,andYou2 CrackingtheSAT:BasicPrinciples

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.

http://www.collegeboard.org



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.

PartIIHowtoCracktheReadingTest3 TheReadingTest:BasicApproach4 MoreQuestionTypes5 ReadingDrills

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.


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.


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.



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.


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.



3.ReadWhatYouNeed4.PredictYourAnswer

Asyoureadthewindow,lookforspecificlinesorphrasesthatanswerthequestion.Oftenwhatyou’relookingforwillbeinasentencebeforeorafterthelinereferenceorleadword,soit’scrucialthatyoureadthefullwindow.

Onceyou’vefoundtexttoanswerthequestion,underlineitifyoucan!Otherwise,jotdownapredictionfortheanswer,stickingasclosetothetextaspossible.

Let’stakealookatquestion12again,thistimewiththewindow.


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.



3.ReadWhatYouNeed4.PredictYourAnswer

5.UseProcessofElimination


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.

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.

Dual-PassageDrill

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.

ReadingDrill1

1. Basedonthepassage,theauthorwouldmostlikelyconsidertintobe

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.

ReadingDrill2


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



3.A) NOCHANGEB) AlthoughC) WhileD) Because



4.A) NOCHANGEB) wasnotablefortheir

C) werenotableforitsD) werenotablefortheir



5.A) NOCHANGEB) beautiful,asinsuperpretty.C) beautiful,likeeasyontheeyes.D) beautiful.



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.


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&LTest,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


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.


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.


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


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.


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,

don’tworry.Concentrateyoureffortsonprinciplesthatareeasiertounderstandbutthatyoustillneedtomaster.

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

solvequestionswithorwithoutyourcalculator.

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


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

correctdatainthegraphortodrawalineofbestfitifnecessary.

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

C) 18D) 40

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


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


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


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?


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)


Dependingonwhatyouseewhenyouapproachthisproblem,youmaychoosetosolvebydistributionor

factoring.Youmaynoticethatthereisanfineachtermoftheexpression.Inthiscase,youmaychooseto

factortheexpressionto ,butthatdoesn’tgiveyouapossibleanswer;however,youcaneliminate

(B),since isnotequivalent toyourexpression.Nowyouare leftwithanexpressionyoumay

findhardtomanipulate.Gobackandlookatthemathematicsbehindtheinitialfactorizationsothenext

stepintheprocesswillmakemoresense.

Whenyoufactoranfoutoftheexpression,whatyouarereallydoingisthis:

Multiplytheexpressionby1sothatyoudonotchangetheexpression.

Distributethe .

Cancelwherepossible.

Youcanfollowtheexactsamestepstofactoran likeyouseein(A).

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


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


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).


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)


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.


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)


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.


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.


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


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


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, 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)


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


Lookupthenumbersyouneedonthechart,ignoringalltheextraneousinformation.Tofindouthowmany

5. Howmanymorecookiesweresoldbythe10thgradethanweresoldbythe12thgrade?

carsthe9thgraderswashed,taketheFundsRaisedanddividebythePriceperitemintherowforthe9th

graders. =51,whichis(B).

A) 60B) 90C) 120D) 150


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


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:

Probabilityofx=

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.


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


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)


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.


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)


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)


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:

Forf(x+c),thegraphwillshiftcunitstotheleft:

Forf(x−c),thegraphwillshifttotherightbycunits:

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

B) −1C) 0D) 1

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


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

andthey-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


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


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.


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


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.


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.

Inthefigureabove,x||y.Whatisthevalueofa?A) b+cB) 2b−cC) 180−b+cD) 180−b−c

28.

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


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.


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?

18. If =4,whatisthevalueofx?

19. If−1≤a≤2and−3≤b≤2,whatisthegreatestpossiblevalueof(a+b)(b−a)?

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?


Agarden,measuring10feetby12feet,containsindividualplotsthatmeasure1footby1foot.30%oftheplotscontainbellpeppers,30%containcherrytomatoes,25%containsquash,andtheremaining15%containeggplants.Eachbellpepperplotproduces2bellpeppersevery5days,atomatoplotproduces4cherrytomatoesevery6days,asquashplotproduces1squashevery15days,andaneggplantplotproduces3eggplantsevery10days.

37. Ina30-daymonth,howmanyvegetablesareproducedbythe10×12footgarden?

38. Anunusuallywarmandwetmonthcausesthemonthlyproductionofeggplantstodouble.Whatisthedailyaveragenumberofeggplantsproducedinthegardenduringa30-daymonthatthenewrate?


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.

PartVHowtoCracktheEssay18 ReadingandAnalyzingtheEssayPassage19 WritingtheEssay

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



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.)


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.


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.


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.


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.


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.


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!

PartVITakingtheSAT

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.


http://www.PrincetonReview.com/bookstore

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.

PartVIIPracticeTests

Chapter20PracticeTest1ClickheretodownloadthePDF.

http://rhlink.com/9780451487612a001

ReadingTest65MINUTES,52QUESTIONS

TurntoSection1ofyouranswersheettoanswerthequestionsinthissection.

DIRECTIONS



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.


Passage1isadaptedfromMartinLutherKing,Jr.,“BirthofaNewNation.”Originallydeliveredin1957.Passage2isadaptedfromFrantzFanon,“TheWretchedoftheEarth.”Originallypublishedin1961.

11. Asusedinline17,“break”mostnearlymeansA) separate.B) rupture.C) damage.

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.

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).

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


DIRECTIONS

Eachpassagebelowisaccompaniedbyanumberofquestions.Forsomequestions,youwillconsiderhowthepassagemightberevisedtoimprovetheexpressionofideas.Forotherquestions,youwillconsiderhowthepassagemightbeeditedtocorrecterrorsinsentencestructure,usage,orpunctuation.Apassageoraquestionmaybeaccompaniedbyoneormoregraphics(suchasatableorgraph)thatyouwillconsiderasyoumakerevisingandeditingdecisions.

Somequestionswilldirectyoutoanunderlinedportionofapassage.Otherquestionswilldirectyoutoalocationinapassageoraskyoutothinkaboutthepassageasawhole.

Afterreadingeachpassage,choosetheanswertoeachquestionthatmosteffectivelyimprovesthequalityofwritinginthepassageorthatmakesthepassageconformtotheconventionsofstandardwrittenEnglish.Manyquestionsincludea“NOCHANGE”option.Choosethatoptionifyouthinkthebestchoiceistoleavetherelevantportionofthepassageasitis.


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.


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


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.


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


Indeed,theUnitedStateshasaminimumwagetomedianincomeratiothatisoneofthetop10suchratiosworldwide.

Shouldthewritermakethisadditionhere?A) Yes,becauseitprovidesaconclusivebitofevidenceamidthevaguenessofthe

questionsaskedinthisparagraph.

B) Yes,becauseitprovidessupportfortheargumentsmadebythesmallandlargebusinessesmentionedinthisessay.

C) No,becauseitrepeatsinformationthatisgivenelsewhereinthisparagraph.D) No,becauseitdoesnotaccuratelyreflectdatafromthegraphgiveninthepassage.

33.A) NOCHANGEB) blazesatrail,C) rageson,D) burnsitdown,


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


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?

A)

B)

C)

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=


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


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?



MathTest–Calculator55MINUTES,38QUESTIONS


DIRECTIONS


NOTES

1. Theuseofacalculatorispermitted.2. Allvariablesandexpressionsusedrepresentrealnumbersunlessotherwiseindicated.3. Figuresprovidedinthistestaredrawntoscaleunlessotherwiseindicated.4. Allfigureslieinaplaneunlessotherwiseindicated.5. Unlessotherwiseindicated,thedomainofagivenfunctionfisthesetofallrealnumbersxforwhichf(x)isa

realnumber.

REFERENCE




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)

C)

D)

16.

Whichofthefollowingequationsrelatesytoxforthevaluesinthetableabove?

A)

B)

C)

D)

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

D) |x+5|=2

DIRECTIONS





,notas3 .)





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?



SATEssay

ESSAYBOOK

DIRECTIONS

Theessaygivesyouanopportunitytoshowhoweffectivelyyoucanreadandcomprehendapassageandwriteanessayanalyzingthepassage.Inyouressayyoushoulddemonstratethatyouhavereadthepassagecarefully,presentaclearandlogicalanalysis,anduselanguageprecisely.

Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteorprintsothatwhatyouarewritingislegibletothosereaders.

Youhave50minutestoreadthepassageandwriteanessayinresponsetothepromptprovidedinsidethisbooklet.

REMINDER

— Donotwriteyouressayinthisbooklet.Onlywhatyouwriteonthelinedpagesofyouranswerbookletwillbeevaluated.

— Anoff-topicessaywillnotbeevaluated.

Asyoureadthepassagebelow,considerhowRobertSterlingYarduses



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

DONOTRETURNTOAPREVIOUSSECTION.

Chapter21PracticeTest1:AnswersandExplanations

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).


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).


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).


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).


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.



DIRECTIONS



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.

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.


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.


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.


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.





DIRECTIONS





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,



11. Supposethewriter’sgoalhadbeentowriteanessaythatcriticizestheAmericanjusticesystem.Wouldthisessayfulfillthatgoal?A) Yes,becauseitreferstomuchofwhatAmandalearnsas“conundrums.”B) Yes,becauseitshowsthattheU.S.justicesystemhassomeproblems.C) No,becauseittellsthestoryofonepersonbecominginterestedinthejusticesystem.D) No,becauseitsuggeststhatworkinginthejusticesysteminspiredoneperson’s

entirecareer.


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


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


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.





DIRECTIONS


NOTES


realnumber.

REFERENCE




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)

D)

13.

Whichofthefollowinggraphsshowsthesolutiontothesystemofinequalitiesabove?A)

B)

C)

D)

14.

IfrectangleABCDhasanareaof48andthetangentof BCA(notshown)is ,then

whichofthefollowingisthelengthofBD(notshown)?A) 5B) 10

C) 13D) Itcannotbedeterminedfromthegiveninformation.


A)

B)

C)

D) m–6

DIRECTIONS





,notas3 .)





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?





DIRECTIONS


NOTES


realnumber.

REFERENCE




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)


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.




,notas3 .)





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.)


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?



SATEssay

ESSAYBOOK

DIRECTIONS


Youressaymustbewrittenonthelinesprovidedinyouranswersheetbooklet;exceptfortheplanningpageoftheanswerbooklet,youwillreceivenootherpaperonwhichtowrite.Youwillhaveenoughspaceifyouwriteoneveryline,avoidwidemargins,andkeepyourhandwritingtoareasonablesize.Rememberthatpeoplewhoarenotfamiliarwithyourhandwritingwillreadwhatyouwrite.Trytowriteinprintsothatwhatyouarewritingislegibletothosereaders.


REMINDER






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.


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


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


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


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


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.


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.



DIRECTIONS



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.


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.


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”)


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.

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.





DIRECTIONS





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


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


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


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.



44. Supposetheauthor’sgoalhadbeentopresentanargumentthatsuggestsBlackFridayshoppingisananimalisticbehavior.Wouldtheinformationinthisessaysupportthatargument?A) Yes,thisessayestablishesaparallelbetweenhumansandchimpanzeesandexplores

itindetail.B) Yes,thisessaysuggeststhatchimpshaveadaptedBlackFridaybehavioreasily.C) No,thisessaysuggeststhatchimpanzeesaremoreadvancedthanmostBlackFriday

shoppers.D) No,thisessayismoreconcernedwithdescribingabehaviorofchimpanzeesthanin

passingjudgmentonhumans.





DIRECTIONS


NOTES


realnumber.

REFERENCE




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



2. Marknomorethanonecircleinanycolumn.

3. Noquestionhasanegativeanswer.

4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.

5.Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbeinterpreted

as ,notas3 .)





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?





DIRECTIONS


NOTES


realnumber.

REFERENCE




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)

B)

C)

D)

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



2. Marknomorethanonecircleinanycolumn.

3. Noquestionhasanegativeanswer.

4. Someproblemsmayhavemorethanonecorrectanswer.Insuchcases,gridonlyoneanswer.


,notas3 .)





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?


Thechartbelowshowsthepopulationdistributionforthe2,400occupantsofthecityofCentreHill.

37. Ifthereareanequalnumberofadultsandchildren,andadultfemalesoutnumberadultmalesby200,whatisthesumofthewomenlivinguptownandthechildrenlivinginthesuburbsofCentreHill?

38. CentreHillplanstoannextheareaaroundanearbylake.ThisnewpartofCentreHillwillbecalled,appropriately,TheAnnex.TheAnnexwilladdtothecurrentpopulationofCentreHill.ThepercentofadultmaleslivinginUptownwilldecreaseto6%afterincorporatingTheAnnexintoCentreHill.IftheinformationfromPart1holdstruefortheoriginalfourdistrictsofthecityofCentreHill,thenhowmanyadultmalesliveinTheAnnex?



SATEssay

ESSAYBOOK

DIRECTIONS




REMINDER






“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.


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


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


1. C2. C3. D4. A5. A6. D7. D8. D9. C

10. C11. A12. D13. B14. A15. C16. 2817. 018. 9419. 7

20.


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

25. D26. A27. B28. A29. D30. B31. 3032. 433. 13.5

34. 2or

35. 536. 5,40637. 86038. 250


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.


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.



DIRECTIONS



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.

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.


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.


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.


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.





DIRECTIONS





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.


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.


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,


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.





DIRECTIONS


NOTES


realnumber.

REFERENCE


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.


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




5. Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbe

interpretedas ,notas3 .)

6. DecimalAnswers:Ifyouobtainadecimalanswerwithmoredigitsthanthegridcanaccommodate,itmaybeeitherroundedortruncated,butitmustfilltheentiregrid.




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?





DIRECTIONS


NOTES


realnumber.

REFERENCE


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




5. Mixednumberssuchas3 mustbegriddedas3.5or7/2.(If isenteredintothegrid,itwillbe

interpretedas ,notas3 .)

6. DecimalAnswers:Ifyouobtainadecimalanswerwithmoredigitsthanthegridcanaccommodate,itmaybeeitherroundedortruncated,butitmustfilltheentiregrid.




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.)


SetRconsistsofalltheone-digitprimenumbers.SetScontainsalloftheelementsofSetR,aswellasanadditionalpositiveinteger,x.

37. IfthesumofalloftheelementsofSetSis30,whatisthevalueofx2–11x–25?

38. MichaelwantstochangethevalueofxsothatthemeanofSetSisequaltothemedianofSetSandforSetStohavenomode.Whatvalueofxwouldaccomplishhisgoal?



SATEssay

ESSAYBOOK

DIRECTIONS




REMINDER



Asyoureadthepassagebelow,considerhowRobertSterlingYarduses



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.


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


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


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


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

25. A26. B27. D28. A29. C30. D31. 7532. 533. 91834. 1935. 636. 2037. 138. 8


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.


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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