SAT考试数学练习题.docx
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SAT考试数学练习题.docx
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SAT考试数学练习题
SAT考试数学练习题2
来源:
91SAT考试网 时间:
2009年08月20日
1.Iff(x)=│(x²–50)│,whatisthevalueoff(-5)?
A.75
B.25
C.0
D.-25
E.-75
2.(√2-√3)²=
A.5-2√6
B.5-√6
C.1-2√6
D.1-√2
E.1
3.230+230+230+230=
A.8120
B.830
C.232
D.230
E.226
4.AmyhastovisittownsBandCinanyorder.Theroadsconnectingthesetownswithherhomeareshownonthediagram.HowmanydifferentroutescanshetakestartingfromAandreturningtoA,goingthroughbothBandC(butnotmorethanoncethrougheach)andnottravellinganyroadtwiceonthesametrip?
A.10
B.8
C.6
D.4
E.2
5.InthefigureaboveAD=4,AB=3andCD=9.WhatistheareaoftriangleAEC?
A.18
B.13.5
C.9
D.4.5
E.3
答案:
1.CorrectAnswer:
B
Explanation:
Ifx=-5,then(x²–50)=25–50=-25
Butthesign│x│meanstheabsolutevalueofx(thedistancebetweenthenumberandzeroonthenumberline).Absolutevaluesarealwayspositive.
│-25│=25
2.CorrectAnswer:
A
Explanation:
Expandasfor(a+b)2.
(√2-√3)(√2-√3)=2-2(√2+√3)+3=5-2√6
3.CorrectAnswer:
C
Explanation:
Allfourtermsareidenticalthereforewehave4(230).
But4=22,andsowecanwrite22.230
Whichisequivalentto232
4.CorrectAnswer:
B
Explanation:
Amycantravelclockwiseoranticlockwiseonthediagram.
Clockwise,shehasnochoiceofroutefromAtoB,achoiceofoneoutoftworoutesfromBtoC,andachoiceofoneoutoftworoutesfromCbacktoA.Thisgivesfourpossibleroutes.
Similarly,anticlockwiseshehasfourdifferentroutes.
Totalroutes=8
5.CorrectAnswer:
D
Explanation:
IfwetakeAEasthebaseoftriangleAEC,thentheheightisCD.
Theheightofthetriangleistherefore,9(given).
TofindthebaseweneedtoseethattrianglesAEBandCDEaresimilar.TheratioAB:
CD,isthereforeequaltotheratioAE:
ED.Thegiveninformationshowsthattheratiois3:
9,or1:
3.NowdividingAD(4)inthisratiogivesusAEas1.
TheareaofAEC=½basexheight
=1/2x9=4.5
SAT考试数学练习题3
来源:
91SAT考试网 时间:
2009年08月20日
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.
答案:
1.CorrectAnswer:
B
Explanation:
Themarkedangle,ABCmustbemorethan90degreesbecauseitistheexternalangleoftriangleBDC,andmustbeequaltothesumofanglesBDC(90)andDCB.AlsoABCisnotastraightlineandmustbelessthan180.Therefore90<5x<180Theonlyvalueofxwhichsatisfiesthisrelationis20.
2.CorrectAnswer:
A
Explanation:
20largecakeswillrequiretheequivalentof10helpersworkingforonehour.700smallcakeswillrequiretheequivalentof20helpersworkingforonehour.Thismeansifonlyonehourwereavailablewewouldneed30helpers.Butsincethreehoursareavailablewecanuse10helpers.
3.CorrectAnswer:
E
Explanation:
Indianstampsarecommontobothratios.MultiplybothratiosbyfactorssuchthattheIndianstampsarerepresentedbythesamenumber.US:
Indian=5:
2,andIndian:
British=5:
1.Multiplythefirstby5,andthesecondby2.
NowUS:
Indian=25:
10,andIndian:
British=10:
2HencethetworatioscanbecombinedandUS:
British=25:
2
4.CorrectAnswer:
C
Explanation:
Drawthediagram.Thediagonaloftherectangleisthediameterofthecircle.Thediagonalisthehypotenuseofa3,4,5triangle,andistherefore,5.Circumference=π.diameter=5π
5.CorrectAnswer:
D
Explanation:
Iftwosetsoffourconsecutiveintegershaveoneintegerincommon,thetotalinthecombinedsetis7.,andwecanwritethesetsasn+(n+1)+(n+2)+(n+3)and(n+3)+(n+4)+(n+5)+(n+6)Notethateachterminthesecondsetis3morethantheequivalentterminthefirstset.Sincetherearefourtermsthetotalofthedifferenceswillbe4x3=12
SAT考试数学练习题4
来源:
91SAT考试网 时间:
2009年08月20日
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
答案:
1.CorrectAnswer:
D
Explanation:
Youcansolvethisbybacksolving–substitutetheanswerchoicesintheexpressionandseewhichgivesthegreatestvalue.sat
A(-1+2)/(-1-2)=-2/2=-1;
B(0+2)/(0-2)=2/-2=-1;
C(1+2)/(1-2)=3/-1=-3;
D(3+2)/(3-2)=5/1=5;
E(4+2)/(4-2)=6/2=3
Ifyouhadjustchosenthelargestvalueforxyouwouldhavebeenwrong.Soalthoughitlooksalongmethod,itisactuallyquickandaccuratesincethenumbersarereallysimpleandyoucandothemathinyourhead.
2.CorrectAnswer:
D
Explanation:
(Totalareaofsquare-sumoftheareasoftrianglesADEandDCF)willgivetheareaofthequadrilateral9-(2x½x3x1.5)=4.5
3.CorrectAnswer:
E
Explanation:
Rememberthatncouldbepositivenegativeorafraction.Tryoutafewcases:
IncaseI,ifnis-1,then2nislessthann.IncaseII,ifnisafractionsuchas½thenn2willbelessthann.IncaseIII,ifnis2,then2-n=0,whichislessthann.Therefore,noneofthechoicesmustbegreaterthann
4.CorrectAnswer:
C
Explanation:
Ifaftereachbounceitreaches2/5ofthepreviousheight,thenafterthesecondbounceitwillreach2/5x125.Afterthethirditwillreach2/5x2/5x125.Afterthefourthitwillreach2/5x2/5x2/5x125.Thiscancelsdownto2x2x2=8
5.CorrectAnswer:
A
Explanation:
Thesmallestvaluefornsuchthat5nisasquareis5.75npcannowbewrittenas75x5xp.Thisgivesprimefactors....3x5x5x5xpTomaketheexpressionaperfectcube,pwillhavetohavefactors3x3,andhencep=9n+p=5+9=14
SAT考试数学练习题5
来源:
太傻网考试频道整理 时间:
2009年08月27日
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’sagenowis
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