SAT学真题精选.docx
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SAT学真题精选.docx
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SAT学真题精选
SAT数学真题精选
1.If2x+3=9,whatisthevalueof4x–3?
(A)5(B)9(C)15(D)18(E)21
2.If4(t+u)+3=19,thent+u=?
(A)3(B)4(C)5(D)6(E)7
3.Inthexy-coordinate(坐标)planeabove,thelinecontainsthepoints(0,0)and(1,2).IflineM(notshown)containsthepoint(0,0)andisperpendicular(垂直)toL,whatisanequationofM?
(A)y=-1/2x(B)y=-1/2x+1(C)y=-x(D)y=-x+2(E)y=-2x
4.IfKisdivisibleby2,3,and15,whichofthefollowingisalsodivisiblebythesenumbers?
(A)K+5(B)K+15(C)K+20(D)K+30(E)K+45
5.Thereare8sectionsofseatsinanauditorium.Eachsectioncontainsatleast150seatsbutnotmorethan200seats.Whichofthefollowingcouldbethenumberofseatsinthisauditorium?
(A)800(B)1,000(C)1,100(D)1,300(E)1,700
6.Ifrsuv=1andrsum=0,whichofthefollowingmustbetrue?
(A)r<1(B)s<1(C)u=2(D)r=0(E)m=0
7.Theleastintegerofasetofconsecutiveintegers(连续整数)is–126.ifthesumoftheseintegersis127,howmanyintegersareinthisset?
(A)126(B)127(C)252(D)253(E)254
8.Aspeciallotteryistobeheldtoselectthestudentwhowillliveintheonlydeluxeroominadormitory.Thereare200seniors,300juniors,and400sophomoreswhoapplied.Eachsenior’snameisplacedinthelottery3times;eachjunior’sname,2time;andeachsophomore’sname,1times.Ifastudent’snameischosenatrandomfromthenamesinthelottery,whatistheprobabilitythatasenior’snamewillbechosen?
(A)1/8(B)2/9(C)2/7(D)3/8(E)1/2
SAT考试数学练习题
(一)
1.Iff(x)=x²–3,wherexisaninteger,whichofthefollowingcouldbeavalueoff(x)?
I6
II0
III-6
A.Ionly
B.IandIIonly
C.IIandIIIonly
D.IandIIIonly
E.I,IIandIII
CorrectAnswer:
A
解析:
ChoiceIiscorrectbecausef(x)=6whenx=3.ChoiceIIisincorrectbecausetomakef(x)=0,x²wouldhavetobe3.But3isnotthesquareofaninteger.ChoiceIIIisincorrectbecausetomakef(x)=0,x²wouldhavetobe–3butsquarescannotbenegative.(Theminimumvalueforx2iszero;hence,theminimumvalueforf(x)=-3)
2.Forhowmanyintegervaluesofnwillthevalueoftheexpression4n+7beanintegergreaterthan1andlessthan200?
A.48
B.49
C.50
D.51
E.52
CorrectAnswer:
C
解析:
1<4n+7<200.ncanbe0,or-1.ncannotbe-2oranyothernegativeintegerortheexpression4n+7willbelessthan1.Thelargestvaluefornwillbeaninteger<(200-7)/4.193/4=48.25,hence48.Thenumberofintegersbetween-1and48inclusiveis50
3.Inthefollowingcorrectlyworkedadditionsum,A,B,CandDrepresentdifferentdigits,andallthedigitsinthesumaredifferent.WhatisthesumofA,B,CandD?
A.23
B.22
C.18
D.16
E.14
CorrectAnswer:
B
解析:
Firstyoumustrealizethatthesumoftwo2-digitnumberscannotbemorethat198(99+99).ThereforeinthegivenproblemDmustbe1.Nowusetrialanderrortosatisfythesum5A+BC=143.A+Cmustgive3intheunitsplace,butneithercanbe1sinceallthedigitshavetobedifferent.ThereforeA+C=13.Withonetocarryoverintothetenscolumn,1+5+B=14,andB=8.A+C+B+D=13+8+1=22
4.12litresofwaterapouredintoanaquariumofdimensions50cmlength,30cmbreadth,and40cmheight.Howhigh(incm)willthewaterrise?
(1litre=1000cm³)
A.6
B.8
C.10
D.20
E.40
CorrectAnswer:
B
解析:
Totalvolumeofwater=12liters=12x1000cm3.Thebaseoftheaquariumis50x30=1500cm3.Baseoftankxheightofwater=volumeofwater.1500xheight=12000;height=12000/1500=8
5.SixyearsagoAnitawasPtimesasoldasBenwas.IfAnitaisnow17yearsold,howoldisBennowintermsofP?
A.11/P+6
B.P/11+6
C.17-P/6
D.17/P
E.11.5P
CorrectAnswer:
A
解析:
LetBen’sagenowbeB.Anita’sagenowisA.(A-6)=P(B-6)
ButAis17andtherefore11=P(B-6).11/P=B-6
(11/P)+6=B
SAT考试数学练习题
(二)
1.ThedistancefromtownAtotownBisfivemiles.CissixmilesfromB.WhichofthefollowingcouldbethedistancefromAtoC?
I11
II1
III7
A.Ionly
B.IIonly
C.IandIIonly
D.IIandIIIonly
E.I,II,orIII.
CorrectAnswer:
E
解析:
DonotassumethatABandCareonastraightline.MakeadiagramwithAandBmarked5milesapart.DrawacirclecenteredonB,withradius6.Ccouldbeanywhereonthiscircle.Theminimumdistancewillbe1,andmaximum11,butanywhereinbetweenispossible.
2.√5percentof5√5=
A.0.05
B.0.25
C.0.5
D.2.5
E.25
CorrectAnswer:
B
解析:
Wecanwritethestatementmathematically,usingxtomean‘of’and/100for‘percent’.So(√5/100)x5√5=5x5/100=0.25
3.Ifpqr=1,rst=0,andspr=0,whichofthefollowingmustbezero?
A.P
B.Q
C.R
D.S
E.T
CorrectAnswer:
D
解析:
Ifpqr=1,noneofthesevariablecanbezero.Sincespr=0,andsincepandrarenotzero,smustbezero.(Notethatalthoughrst=0,andsoeithersortmustbezero,thisisnotsufficienttostatewhichmustbezero)
4.
A.1/5
B.6/5
C.6³
D.64/5
E.64
CorrectAnswer:
E
解析:
65=64x6
(64x6)-64=64(6-1)=64x5Now,dividingby5willgiveus64
5.-20,-16,-12,-8....
Inthesequenceabove,eachtermafterthefirstis4greaterthantheprecedingterm.Whichofthefollowingcouldnotbeaterminthesequence?
A.0
B.200
C.440
D.668
E.762
CorrectAnswer:
E
解析:
Alltermsinthesequencewillbemultiplesof4.762isnotamultipleof4
SAT考试数学练习题㈢
1.Whichofthefollowingcouldbeavalueofx,inthediagramabove?
A.10
B.20
C.40
D.50
E.anyoftheabove
2.Helpersareneededtoprepareforthefete.Eachhelpercanmakeeither2largecakesor35smallcakesperhour.Thekitchenisavailablefor3hoursand20largecakesand700smallcakesareneeded.Howmanyhelpersarerequired?
A.10
B.15
C.20
D.25
E.30
3.Jo'scollectioncontainsUS,IndianandBritishstamps.IftheratioofUStoIndianstampsis5to2andtheratioofIndiantoBritishstampsis5to1,whatistheratioofUStoBritishstamps?
A.5:
1
B.10:
5
C.15:
2
D.20:
2
E.25:
2
4.A3by4rectangleisinscribedincircle.Whatisthecircumferenceofthecircle?
A.2.5π
B.3π
C.5π
D.4π
E.10π
5.Twosetsof4consecutivepositiveintegershaveexactlyoneintegerincommon.Thesumoftheintegersinthesetwithgreaternumbersishowmuchgreaterthanthesumoftheintegersintheotherset?
A.4
B.7
C.8
D.12
E.itcannotbedeterminedfromtheinformationgiven.
SAT考试数学练习题㈣
1.Iff(x)=(x+2)/(x-2)forallintegersexceptx=2,whichofthefollowinghasthegreatestvalue?
A.f(-1)
B.f(0)
C.f
(1)
D.f(3)
E.f(4)
2.ABCDisasquareofside3,andEandFarethemidpointsofsidesABandBCrespectively.WhatistheareaofthequadrilateralEBFD?
A.2.25
B.3
C.4
D.4.5
E.6
3.Ifn≠0,whichofthefollowingmustbegreaterthann?
I2n
IIn²
III2-n
A.Ionly
B.IIonly
C.IandIIonly
D.IIandIIIonly
E.None
4.Afterbeingdroppedacertainballalwaysbouncesbackto2/5oftheheightofitspreviousbounce.Afterthefirstbounceitreachesaheightof125inches.Howhigh(ininches)willitreachafteritsfourthbounce?
A.20
B.15
C.8
D.5
E.3.2
5.nandpareintegersgreaterthan1
5nisthesquareofanumber
75npisthecubeofanumber.
Thesmallestvalueforn+pis
A.14
B.18
C.20
D.30
E.50
SAT考试数学练习题㈤
1.Ifa²=12,thena4=
A.144
B.72
C.36
D.24
E.16
CorrectAnswer:
A
解析:
a4=a2xa2=12x12=144
2.Ifniseven,whichofthefollowingcannotbeodd?
In+3
II3n
IIIn²-1
A.Ionly
B.IIonly
C.IIIonly
D.IandIIonly
E.I,IIandIII
CorrectAnswer:
B
解析:
IncaseI,evenplusoddwillgiveodd.IncaseII,oddtimesevenwillgiveeven.IncaseIIIevensquarediseven,andevenminusoddisodd.(Youcancheckthisbyusinganeasyevennumberlike2inplaceofn).OnlycaseIIcannotbeodd.
3.Onesideofatrianglehaslength8andasecondsidehaslength5.Whichofthefollowingcouldbetheareaofthetriangle?
I24
II20
III5
A.Ionly
B.IIonly
C.IIIonly
D.IIandIIIonly
E.I,IIandIII
CorrectAnswer:
D
解析:
Themaximumareaofthetrianglewillcomewhenthegivensidesareplacedatrightangles.Ifwetake8asthebaseand5astheheightthearea=½x8x5=20.Wecanaltertheanglebetweenthesidestomakeitlessormorethan90,butthiswillonlyreducethearea.(Drawitoutforyourself).Hencetheareacanbeanythinglessthanorequalto20.
4.Acertainanimalinthezoohasconsumed39poundsoffoodinsixdays.Ifitcontinuestoeatatthesamerate,inhowmanymoredayswillitstotalconsumptionbe91pounds?
A.12
B.11
C.10
D.9
E.8
CorrectAnswer:
E
解析:
Foodconsumedperday=39/6.Intheremainingdaysitwillconsume91-39pounds=52pounds.Nowdividethefoodbythedailyconsumptiontofindthenumberofdays.52/(39/6)=52x(6/39)=8
5.Aperfectcubeisanintegerwhosecuberootisaninteger.Forexample,27,64and125areperfectcubes.Ifpandqareperfectcubes,whichofthefollowingwillnotnecessarilybeaperfectcube?
A.8p
B.pq
C.pq+27
D.-p
E.(p-q)6
CorrectAnswer:
C
解析:
Aperfectcu
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