psat sample test math only

7/27/2019 PSAT Sample Test Math Only

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Directions: For thiri soction, olveeachproblemanddecidewhich is the bestofthe choicesgiven, ril1 n the corresponding val on the answersheet.You mayuse rnvavailable pace or scratchwork.

1. Calculatoluse s pelmitted.2. A11numbers sedale teal numtlers.3. Figuresareprovideclor someprobierrs.Al l figules aredrawnto scaleand ie in a planeUNLIISS otherwiseindicated.4. Unlessotherwise pecifiecl,he dornainof any urLction/is assumedo be theset of'all real numbers forwhich/(.r) is a real number.

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The sum of themeasuresn degleesof the anglesof a tliangle sThe nurnbelof degleesof'arc n a cilcle is i]60.A straightanglehas a degreemeasure f 180.

V ,= ftr2lt

Al1 of the followinS;are equal o 9xz or all x EXCEPT(A) x2 t- Bx2(B) 4"r+ 5x(C) (e.rX.r)(D) (3x)(3"r)(E) (-3xX-3x)

1 , ,2

bc 2 - 0 2 + b 2 SpecialRight 1'riangles

I Wirat s thehundredthsigit n thenumber123,4!i631\9(A) 1(B ) 4(c)s(D) 8/ t r \ Q

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2/12

E 1 llf 1Qx) = ;( I 0), what s the valueof x ?(A)3+

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(B) s(c)s+--)(D) 6(E ) 10

p A rectangles cut n half, resultingn squares hicheachhavean area f 25,What s theperimeter f theoriginalectangle?(A) 10(B) 20(c) 30(D) 40(E) s0

Drivingat anaverageateof 48 milesperhour, ohnreached isdestinationn exactly hours nd 5minutes. odrive hesameoute n exactly hours,Johnwouldhave o driveat whataveraseate(A) 50 milesperhour(B) 54 milesperhour(C) 55 milesperhour(D) 60 milesperhour(E) 64 milesperhour@ fne circlegraphabove epresentsouseholdxpenses1in dollars. f 33; percentof expenses o toward rent,Jwhich egion n hegraph est epresentsollars penton rent?

(A) A(B ) B(C) C(D) D(E) E


3/12

l l tt xz=7,whatis hevalue f (x + 1Xr -1)?(A) 6(B ) 8(c ) 48(D)s0(E) It cannot be determinedrom the nfomation given.

p A numberhat s divisibleby4,5, and10mustbedivisibleby all of the ollowing EXCEPT(A) 8(B ) 12(c) 1s(D) 20(E) 30

t l l 1 i 1I t t h c c i l m - + - l - - +Z 4 8 *+ -i. e isexprerssedin simplesterms,what s thenumeratorf thesum?(A) 1(B ) 3(c) 6(D) 12(E) 63

tt x is 66lpercentof ), theny s whatpercent f ;r?(A) zzlv,

J(B) l5VoG) n3+Eo(D ) 1507o@)166+Eo

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4/12

@ Letr; y bedefined sx2+ { for all x andy.2If 3 i 4 = 5 Ln,what s thevalueof n ?(A) -28(B) -7

1'.)rc) f(D) 6(E) 60

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In the figureabove, he shaded egion s a square farea3, andAABC s equilateral.What is theperimeterol AABC ?(A)3v5(B)e\6(c) 2+t / i(D)3 + 6\6(E)6+3t/ i

Vq l+ f n+ f 4=(A) \/63@) 7./1G) zofa(D)3 + aVls@) 30+V5

If theaveragearithmeticmean)of threedistinctpositive ntegers s 4, what s thegreatest ossible aluefor one of those ntegers?(A) s(B ) 6(c) e(D) 11(E) 12

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5/12

E If the ength f one eg of a right riangies r +- , andthe ength f thehypotenuses r + :],where ), -2,what s the engthof theother eg rr termsof .r ?(A) x(B ) .r-r I(c ) .r-rV5(D) 4+s(E) \/2x 11

l! Wnen hepositiventeger is divided y 9, theremainders 7. What s the ernainderhen5n sdivided y 9 ?(A) 4(B)s(c) 6(D) 7(E) 8

p nox d contains blackmarbles nd1 whitemarble.Box B contains4 blackmarblesand 3 white rnarbles.What is the minimum number of marbles hat must bemoved rom Box A to Box B so that heratio of blackmarbles o whitemar:bless the same n the two bcrxes?(A) 1(B) 2(c) 3(D) 4(E) The atioof blackmarblesowhitemarbles 'illnever e hesamen the woboxes.

In the equatio V= [nrt,if the value of r isthen he value of V is multiolied bv

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6/12

E fn the igure above, heareaof the circle with centerOis 36n and he ength t arcABC s 4zr.What s thelength f chord C?(A) 3(B) e(c) 12(D)3v3(E)6v5

@ fne population f DistrictA is 3 times he averagepopulationof the other 9 districtsin the city. Whatpercentof thecity's population ives n DistrictA ?(A) l07oB\ r2!vo2(c) 20ok(D) 257o

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7/12

Time-25 Minutes18QuestionsDirections: This sectioncontains wo typesof questions. ou have25 minutes o completebothtypes.For questions1-8, solveeachquestionand determinewhich of thechoicesgivenis best,Fili in the con'esponding val on the answelsheet.You may useany available pacefor scratchwork,

1. Calculatoruse s permitted.2. Al1 numbelsusedare eal numbet's.3. Figuresareplovided or someproblems.Al l figuresaredrawn to scaleand ie in a planeUNLESS otherwiseindicated.4. Unlessotherwise pecified, hedornainof any unction/is assumedo be thesetof all r'ealnumbers r folwhich/(x) is a real nutnber.

c2= ctz b2 SpecialRight Triangles C = 2rT.r"

LV = lwltb,q= an2

The sum of the measuresn degrees f the anglesof a triangle s 180.The numbel of degrees f arc n a circle s 360.A straightanglehas a degreemeasure f 180,

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x # O , t h e nA =\2- )(A)x1(B) ,(c)

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A I f . r = - s1 , l - q - z l x7 , h e n x =(A) -',74(B) -4e(c ) 32(D) 4e(E) 74


8/12

Ql lt +n- 15= 17 ,hen n+ 9=0815

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(A)(B)(c)(D)(E)(c) 12( D ) 12

a The atioof 2l tonumber?(A) I(B ) 3(c) s(D ) 10(E ) 12

p Wtratnumber ecreasedy4 equals times heoriginalnumber?r /A\ - ,

(B ) -1

(E) 1

15 s equal o theratioof 9 to what p Set./ is the set of all negativeodd ntegers, nd setK isthe setof all negative ven ntegers.Which of thefollowing representshe union of these ets?(A) All integers(B) All negative ntegers(C) All negativeodd ntegers(D) All negativeeven ntegers(E) None of the above

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9/12

If n't. 8, what is the value of(A) - 64

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(B ) 1o416i81

64

(c)(D )(E )

. lExactly; lard of rope s neededo tie up a certalnLbag.Which of t he following lengthsof rope couldbeused o tie up the bag with the leastamount of roperemaining?

1(A) ;- yardo '4(B) - vard 5 ')(C) ^ yaLd. t '1(D) - vat'df(E) | yardo

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10/12

Directions: For Student-Producedesponse uestions -18, use hegridsat the bottom ofthe answersheet ageon whichyouhaveanswered uestions-8.Eachof theremaining 10questionsequires ou to solve heproblemand enteryour answerby marking he ovals n the specialgrid, as shown n the examples elow.You mayuse any availablespaceor scratchwork.

Answer :.25or] o rs t+Write answer +in boxes.

the ovals correctly.. Grid onlyoneanswer o aquestion, ven hough omeproblems avemore hanonecorrect nswer.. Darkenno more hanoneoval n a column,. No answers re negative.. Mixed numbers cannotbegridded.For example: heInumber ; mustbe gridded s1.25or 5/4.+

FractionIine+Decimal

pointYou may startyour answersn any column,space ermitting.Columns ot neededshould e ef tblank.

Eitherposition s correct.. It is recommended,hough ot required,hatyou write . DecimalAccuracy:Decimalanswersmustbe enteredyouranswern theboxes t he opof the columns. asaccurately spossible. or example,f youobtainanHowever, ou will receive redit only for darken ing answer uchas0.1666. .,yottshould ecord he esultaE.166 r .167.Lessaccurate alues uchas 16or,17 are notacceptable.

Acceptable ays ogrio ] = .1666. .o

(If ffi isgridded,t willbe nterpreted, +,not f.)

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11/12

E Halfthe productof 8 and 9 isnumber? the square oot of whal: A At-BA1 B8

@ tia andB representistinctdigits n thecorectlyworked additionproblemabove,what s the value of A ?

What s theaveragearithmetic ean) f J4^td lt

E tn the igureabove,B ir p"rpendicularo,4E. f themeasuref 1-BADs 53 degrees,nd hemeasurefZCAE s 73 degrees,hat s thedegreemeasurefICAD?

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12/12

E In the figure above,X andY are he centersof the twocircles. If eachcircle hascircumference r, what s theperimeterof therectangle?

Nualabaked64 cookies or a party. After eachpartyguestaten cookies,9 cookieswere eft uneaten.ftherewere more han 9 guests t theparty,and f n is anintegergreater han 1, what s thevalue of n ?

Boxes of candy were sold for a school fund-raiser.Small boxescost$2 eachand argeboxescost$5 each.If 150of these oxesweresold or a total of $444,howmany largeboxes were sold?

@ Wtrat s the maximumpossibleareaof a rectanglewitha perimeterof 14 ?

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psat sample test math only

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