sat数学考试试题.doc

sat数学考试试题.doc

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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

Question#1:

50%ofUScollegestudentsliveoncampus.Outofallstudentslivingoncampus,40%aregraduatestudents.WhatpercentageofUSstudentsaregraduatestudentslivingoncampus?

（A）90%（B）5%（C）40%（D）20%（E）25%

Question#2:

Inthefigurebelow,MNisparallelwithBCandAM/AB=2/3.WhatistheratiobetweentheareaoftriangleAMNandtheareaoftriangleABC?

（A）5/9（B）2/3（C）4/9（D）1/2（E）2/9

Question#3:

Ifa2+3isdivisibleby7,whichofthefollowingvaluescanbea?

（A）7（B）8（C）9（D）11（E）4

Question#4:

Whatisthevalueofb,ifx=2isasolutionofequationx2-b·x+1=0?

（A）1/2（B）-1/2（C）5/2（D）-5/2（E）2

Question#5:

Whichvalueofxsatisfiestheinequality|2x|

（A）-1/2（B）1/2（C）1（D）-1（E）2

Question#6:

Ifintegersm>2andn>2,howmany（m,n）pairssatisfytheinequalitymn<100?

（A）2（B）3（C）4（D）5（E）7

Question#7:

TheUSdeerpopulationincreaseis50%every20years.Howmaytimeslargerwillthedeerpopulationbein60years?

（A）2.275（B）3.250（C）2.250（D）3.375（E）2.500

Question#8:

Findthevalueofxifx+y=13andx-y=5.

（A）2（B）3（C）6（D）9（E）4

Question#9:

US

UK

Medals

3

2

gold

1

4

silver

4

1

bronze

Thenumberofmedalswonatatrackandfieldchampionshipisshowninthetableabove.WhatisthepercentageofbronzemedalswonbyUKoutofallmedalswonbythe2teams?

（A）20%（B）6.66%（C）26.6%（D）33.3%（E）10%

Question#10:

Theedgesofacubeareeach4incheslong.Whatisthesurfacearea,insquareinches,ofthiscube?

（A）66（B）60（C）76（D）96（E）65

Question#1:

Thesumofthetwosolutionsofthequadraticequationf（x）=0isequalto1andtheproductofthesolutionsisequalto-20.Whatarethesolutionsoftheequationf（x）=16-x?

（a）x1=3andx2=-3（b）x1=6andx2=-6

（c）x1=5andx2=-4（d）x1=-5andx2=4

（e）x1=6andx2=0

Question#2:

Inthe（x,y）coordinateplane,threelineshavetheequations:

l1:

y=ax+1

l2:

y=bx+2

l3:

y=cx+3

Whichofthefollowingmaybevaluesofa,bandc,iflinel3isperpendiculartobothlinesl1andl2?

（a）a=-2,b=-2,c=.5（b）a=-2,b=-2,c=2

（c）a=-2,b=-2,c=-2（d）a=-2,b=2,c=.5

（e）a=2,b=-2,c=2

Question#3:

Themanagementteamofacompanyhas250menand125women.If200ofthemanagershaveamasterdegree,and100ofthemanagerswiththemasterdegreearewomen,howmanyofthemanagersaremenwithoutamasterdegree?

（a）125（b）150（c）175（d）200（e）225

Question#4:

Inthefigurebelow,theareaofsquareABCDisequaltothesumoftheareasoftrianglesABEandDCE.IfAB=6,thenCE=

（a）5（b）6（c）2（d）3（e）4

Question#5:

Ifαandβaretheanglesoftherighttriangleshowninthefigureabove,thensin2α+sin2βisequalto:

（a）cos（β）（b）sin（β）（c）1（d）cos2（β）（e）-1

Question#6:

Theaverageofnumbers（a+9）and（a-1）isequaltob,whereaandbareintegers.Theproductofthesametwointegersisequalto（b-1）2.Whatisthevalueofa?

（a）a=9（b）a=1（c）a=0（d）a=5（e）a=11

Question#1:

Iff（x）=xandg（x）=√x,x≥0,whatarethesolutionsoff（x）=g（x）?

（A）x=1（B）x1=1,x2=-1

（C）x1=1,x2=0（D）x=0

（E）x=-1

Question#2:

WhatisthelengthofthearcABinthefigurebelow,ifOisthecenterofthecircleandtriangleOABisequilateral?

Theradiusofthecircleis9

（a）π（b）2·π（c）3·π（d）4·π（e）π/2

Question#3:

Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?

Eachdicehassidesnumberedfrom1to6.

（a）1/2（b）1/6（c）1/12（d）1/18（e）1/36

Question#4:

AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hourwhilehisreturnspeedis10miles/hour.Whatisthedistancebetweenthe2towns?

（a）11miles（b）18miles（c）15miles（d）12miles（e）10miles

Question#5:

Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2?

（a）2·a/π（b）a/π（c）a/（2·π）（d）a/π（e）a+π

Question#6:

Howmanyintegersxaretheresuchthat2x<100,andatthesametimethenumber2x+2isanintegerdivisiblebyboth3and2?

（a）1（b）2（c）3（d）4（e）5

Question#7:

sin（x）cos（x）（1+tan2（x））=

（a）tan（x）+1（b）cos（x）

（c）sin（x）（d）tan（x）

（e）sin（x）+cos（x）

Question#8:

If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:

（a）13（b）17（c）23（d）15（e）43

Question#9:

Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthesumx+y?

（a）11（b）17（c）13（d）15（e）9

Question#10:

Theinequality|2x-1|>5mustbetrueinwhichoneofthefollowingcases?

I.x<-5II.x>7III.x>0

1.Threeunitcirclesarearrangedsothateachtouchestheothertwo.Findtheradiiofthetwocircleswhichtouchallthree.

2.Findallrealnumbersxsuchthatx+1=|x+3|-|x-1|.

3.

（1）Givenx=（1+1/n）n,y=（1+1/n）n+1,showthatxy=yx.

（2）Showthat12-22+32-42+...+（-1）n+1n2=（-1）n+1（1+2+...+n）.

4.Allcoefficientsofthepolynomialp（x）arenon-negativeandnoneexceedp（0）.Ifp（x）hasdegreen,showthatthecoefficientofxn+1inp（x）2isatmostp

（1）2/2.

5.Whatisthemaximumpossiblevalueforthesumoftheabsolutevaluesofthedifferencesbetweeneachpairofnnon-negativerealnumberswhichdonotexceed1?

6.ABisadiameterofacircle.XisapointonthecircleotherthanthemidpointofthearcAB.BXmeetsthetangentatAatP,andAXmeetsthetangentatBatQ.ShowthatthelinePQ,thetangentatXandthelineABareconcurrent.

7.Fourpointsonacircledivideitintofourarcs.Thefourmidpointsformaquadrilateral.Showthatitsdiagonalsareperpendicular.

8.Findthesmallestpositiveintegerbforwhich7+7b+7b2isafourthpower.

9.Showthattherearenopositiveintegersm,nsuchthat4m（m+1）=n（n+1）.

10.ABCDisaconvexquadrilateralwitharea1.ThelinesAD,BCmeetatX.ThemidpointsofthediagonalsACandBDareYandZ.FindtheareaofthetriangleXYZ.

11.Asquarehastensdigit7.Whatistheunitsdigit?

12.Findallorderedtriples（x,y,z）ofrealnumberswhichsatisfythefollowingsystemofequations:

xy=z-x-y

xz=y-x-z

yz=x-y-z

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