sat数学考试精彩试题Word文档下载推荐.docx
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sat数学考试精彩试题Word文档下载推荐.docx
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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<
(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|<
x+1?
(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
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
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
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
Themanagementteamofacompanyhas250menand125women.If200ofthemanagershaveamasterdegree,and100ofthemanagerswiththemasterdegreearewomen,howmanyofthemanagersaremenwithoutamasterdegree?
(a)125(b)150(c)175(d)200(e)225
Inthefigurebelow,theareaofsquareABCDisequaltothesumoftheareasoftrianglesABEandDCE.IfAB=6,thenCE=
(a)5(b)6(c)2(d)3(e)4
Ifαandβaretheanglesoftherighttriangleshowninthefigureabove,thensin2α+sin2βisequalto:
(a)cos(β)(b)sin(β)(c)1(d)cos2(β)(e)-1
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
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
WhatisthelengthofthearcABinthefigurebelow,ifOisthecenterofthecircleandtriangleOABisequilateral?
Theradiusofthecircleis9
(a)π(b)2·
π(c)3·
π(d)4·
π(e)π/2
Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6?
Eachdicehassidesnumberedfrom1to6.
(a)1/2(b)1/6(c)1/12(d)1/18(e)1/36
AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hourwhilehisreturnspeedis10miles/hour.Whatisthedistancebetweenthe2towns?
(a)11miles(b)18miles(c)15miles(d)12miles(e)10miles
Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2?
(a)2·
a/π(b)a/π(c)a/(2·
π)(d)a/π(e)a+π
Howmanyintegersxaretheresuchthat2x<
100,andatthesametimethenumber2x+2isanintegerdivisiblebyboth3and2?
(a)1(b)2(c)3(d)4(e)5
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)
If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:
(a)13(b)17(c)23(d)15(e)43
Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthesumx+y?
(a)11(b)17(c)13(d)15(e)9
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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