PAT考试数学部分例题Word格式文档下载.docx
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PAT考试数学部分例题Word格式文档下载.docx
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7.Aperfectcubeisanintegerwhosecuberootisaninteger.Forexample,27,64and125areperfectcubes.Ifpandqareperfectcubes,whichofthefollowingwillnotnecessarilybeaperfectcube?
A.8pB.pqC.pq+27D.-pE.(p-q)6
8.Whatisthelengthofthelinesegmentinthex-yplanewithendpointsat(-2,-2)and(2,3)?
A.3B.√31C.√41D.7E.9
9.nisanintegerchosenatrandomfromtheset{5,7,9,11}pischosenatrandomfromtheset{2,6,10,14,18}Whatistheprobabilitythatn+p=23?
A.0.1B.0.2C.0.25D.0.3E.0.4
10.Adressonsaleinashopismarkedat$D.Duringthediscountsaleitspriceisreducedby15%.Staffareallowedafurther10%reductiononthediscountedprice.IfastaffmemberbuysthedresswhatwillshehavetopayintermsofD?
A.0.75DB.0.76DC.0.765DD.0.775DE.0.805D
11.Sheilaworks8hoursperdayonMonday,WednesdayandFriday,and6hoursperdayonTuesdayandThursday.ShedoesnotworkonSaturdayandSunday.Sheearns$324perweek.Howmuchdoessheearnindollarsperhour?
A.11B.10C.9D.8E.7
12.ABCDisaparallelogram.BD=2.TheanglesoftriangleBCDareallequal.Whatistheperimeteroftheparallelogram?
A.12B.9√3C.9D.8E.3√3
13.Iftheproductof6integersisnegative,atmosthowmanyoftheintegerscanbenegative?
A.2B.3C.4D.5E.6
14.Ifapositiveintegern,dividedby5hasaremainder2,whichofthefollowingmustbetrue?
(I)nisodd(II)n+1cannotbeaprimenumber(III)(n+2)dividedby7hasremainder2
A.noneB.IonlyC.IandIIonlyD.IIandIIIonlyE.I,IIandIII
15.Asolidcubeofside6isfirstpaintedpinkandthencutintosmallercubesofside2.Howmanyofthesmallercubeshavepaintonexactly2sides?
A.30B.24C.12D.8E.6
16.Linelcontainsthepoints(3,1)and(4,4).Iflinemisadifferentline,paralleltolinelinthesamecoordinateplane,whichofthefollowingcouldbetheequationoflinem?
A.y=3x-8B.y=1/3x-3C.y=-3x-8D.y=3x+1E.y=-8x+3
17.Inthefigureabovethesquarehastwosideswhicharetangenttothecircle.Iftheareaofthecircleis4a²
π,whatistheareaofthesquare?
A.2a²
B.4aC.4a²
D.16a²
E.64a²
18.Atrianglehasaperimeter13.Thetwoshortersideshaveintegerlengthsequaltoxandx+1.Whichofthefollowingcouldbethelengthoftheotherside?
A.2B.4C.6D.8E.10
19.Amachineputsccapsonbottlesinmminutes.Howmanyhourswillittaketoputcapsonbbottles?
A.60bm/cB.bm/60cC.bc/60mD.60b/cmE.b/60cm
20.Paintneedstobethinnedtoaratioof2partspaintto1.5partswater.Thepainterhasbymistakeaddedwatersothathehas6litresofpaintwhichishalfwaterandhalfpaint.Whatmustheaddtomaketheproportionsofthemixturecorrect?
A.1litrepaintB.1litrewaterC.½
litrewaterandonelitrepaintD.½
litrepaintandonelitrewater
E.½
litrepaint
21.Whichofthefollowingcanbeusedtoillustratethatnotallprimenumbersareodd?
A.1B.2C.3D.4E.5
22.Whatisthegreatestof3consecutiveintegerswhosesumis24?
A.6B.7C.8D.9E.10
23.Consideringthepositionsonthenumberlineabove,whichofthefollowingcouldbeavalueforx?
A.5/3B.3/5C.-2/5D.-5/2E.none
24.Apieceofribbon4yardslongisusedtomakebowsrequiring15inchesofribbonforeach.Whatisthemaximumnumberofbowsthatcanbemade?
A.8B.9C.10D.11E.12
25.Howmanynumbersbetween200and400beginorendwith3?
A.20B.60C.100D.110E.120
26.Iff(3)=15andf(5)=45,whichofthefollowingcouldbef(x)?
A.4x+3B.2x²
–2xC.2x²
-xD.2x²
-5E.5x²
27.PQRSisaparallelogramandST=TR.WhatistheratiooftheareaoftriangleQSTtotheareaoftheparallelogram?
A.1:
2B.1:
3C.1:
4D.1:
5E.itcannotbedetermined
28.Apictureiscopiedontoasheetofpaper8.5inchesby10inches.A1.5inchmarginisleftallaround.Whatareainsquareinchesdoesthepicturecover?
A.76B.65C.59.5D.49E.38.5
29.Thetableshowstheresultsofapollwhichaskeddrivershowmanyaccidentstheyhadhadovertheprevious5years.Whatisthemediannumberofaccidentsperdriver?
A.0.5B.1C.1.5D.2E.4
30.IfV=12R/(r+R),thenR=
A.Vr/(12-V)B.Vr+V/12C.Vr-12D.V/r-12E.V(r+1)/12
31.Thenumber0.127ishowmuchgreaterthan1/8?
A.½
B.2/10C.1/50D.1/500E.2/500
32.Whichofthefollowingcouldnotbethelengthsofthesidesofarightangledtriangle?
A.3,4,5B.5,12,13C.8,15,17D.12,15,18E.9,12,15
33.Twoequalcirclesarecutoutofarectangleofcardofdimensions16by8.Thecircleshavethemaximumdiameterpossible.Whatistheapproximateareaofthepaperremainingafterthecircleshavebeencutout?
A.104B.78C.54D.27E.13
34.(a2-b2)/(a+b)=
A.a²
+b²
+1B.a+bC.a-bD.abE.itcannotbesimplifiedfurther
35.x=y-(50/y),wherexandyareboth>
0
Ifthevalueofyisdoubledintheequationabove,thevalueofxwill
A.decreaseB.staythesameC.increasefourfoldD.doubleE.increasetomorethandouble
36.Whichofthefollowingcouldbeasolutionoftheequation│x│=│4x-3│
A.-1B.-0.6C.0D.0.6E.1.5
37.Thenumberofdegreesthatthehourhandofaclockmovesthroughbetweennoonand2.30intheafternoonofthesamedayis
A.720B.180C.75D.65E.60
38.8.Jefftakes20minutestojogaroundtheracecourseonetime,and25minutestojogaroundasecondtime.Whatishisaveragespeedinmilesperhourforthewholejogifthecourseis3mileslong?
A.6B.8C.10D.12E.14
39.AandBareequidistantfromthelinel.HowmanycirclescanbedrawnwiththeircentersonlinelandthatpassthroughbothAandB?
A.1B.2C.3D.4E.>
10
40.Awheelhasadiameterofxinchesandasecondwheelhasadiameterofyinches.Thefirstwheelcoversadistanceofdfeetin100revolutions.Howmanyrevolutionsdoesthesecondwheelmakeincoveringdfeet?
A.100xyB.100y-xC.100x-yD.100y/xE.100x/y
41.3x+y=19,andx+3y=1.Findthevalueof2x+2y
A.20B.18C.11D.10E.5
42.Thepriceofacycleisreducedby25percent.Thenewpriceisreducedbyafurther20percent.Thetworeductionstogetherareequaltoasinglereductionof
A.45%B.40%C.35%D.32.5%E.30%
43.xandyareintegers;
x+y<
11,andx>
6;
Whatisthesmallestpossiblevalueofx-y?
A.1B.2C.4D.-2E.-4
44.Ifx5y4z2<
0,whichofthefollowingmustbetrue?
Ixy<
0IIyz<
0IIIxz<
0
A.IB.IIC.IIID.IandIIE.None
45.BCDisalinesegmentandAngleBAC=¼
AngleACB;
AngleACD=?
A.140B.100C.120D.60E.itcannotbedeterminedfromtheinformationgiven
46.Whichofthefollowingintegersisinthesolutionsetof│1–3x│<
5?
(I)-1(II)1(III)2
47.Inacertainvillage,mlitresofwaterarerequiredperhouseholdpermonth.Atthisrate,iftherearenhouseholdsinthevillage,howlong(inmonths)willplitresofwaterlast?
A.p/mnB.mn/pC.mp/nD.np/mE.npm
48.Inthefigurebelow,whatistheslopeoflinel?
A.-3B.-1/3C.0D.1/3E.3
49.RadiusofcirclecenterOis3timestheradiusofcirclecenterC.
AngleACB=AnglePOQ
IftheshadedareaofcircleCis2thenwhatistheareaoftheshadedpartofcircleO?
A.6B.12C.18D.36E.3/2
50.(3x104)+(2x10²
)+(4x10)=
A.302400B.32400C.30240D.3240E.324
51.Andysolvesproblems74to125inclusiveinaMathexercise.Howmanyproblemsdoeshesolve?
A.53B.52C.51D.50E.49
52.Ifxandyareintegers,and3x+2y=13,whichofthefollowingcouldbethevalueofy?
A.0B.1C.2D.3E.4
53.IntriangleABC,AD=DB,DEisparalleltoBC,andtheareaoftriangleABCis40.WhatistheareaoftriangleADE?
A.10B.15C.20D.30E.itcannotbedeterminedfromtheinformationgiven
54.Ifn>
0,whichofthefollowingmustbetrue?
In²
>
1IIn-n²
<
0III2n-1>
A.IonlyB.IIonlyC.IIIonlyD.IandIIonlyE.none
55.Iftheslopeofalineis½
andthey-interceptis3,whatisthex-interceptofthesameline?
A.6B.3/2C.0D.-2/3E.-6
56.6peoplemeetforabusinesslunch.Eachpersonshakeshandsoncewitheachotherpersonpresent.Howmanyhandshakestakeplace?
A.30B.21C.18D.15E.10
57.Ifx²
-y²
=55,andx-y=11,theny=
A.8B.5C.3D.-8E.-3
58.9.Inasportsclubwith30members,17playbadmintonand19playtennisand2donotplayeither.Howmanymembersplaybothbadmintonandtennis?
A.7B.8C.9D.10E.11
59.RectangleABCDhasaperimeterof26.ThehalfcirclewithdiameterADhasanareaof8π.Whatistheperimeterofthepartofthefigurethatisnotshaded?
A.26+4πB.18+8πC.18+4πD.14+4πE.14+2π
60.Courierchargesforpackagestoacertaindestinationare65cen
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