美国高中数学试题范文word版 11页Word格式.docx
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美国高中数学试题范文word版 11页Word格式.docx
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y>
0,Xiaoliroundedxupbyasmallamount,roundedydownbythesameamount,andthensubtractedherroundedvalues.Whichofthefollowingstatementsis
necessarilycorrect?
A)Herestimateislargerthanx-yB)Herestimateissmallerthanx-yC)Herestimateequalsx-yD)Herestimateequalsy-xE)Herestimateis0
Problem7
Forascienceproject,Sammyobservedachipmunkandasquirrelstashingacornsinholes.Thechipmunkhid3acornsineachoftheholesitdug.Thesquirrelhid4acornsineachoftheholesitdug.Theyeachhidthesamenumberofacorns,althoughthesquirrelneeded4fewerholes.Howmanyacornsdidthechipmunkhide?
Problem8
Whatisthesumofallintegersolutionsto
Solution?
Problem9
Twointegershaveasumof26.Whentwomoreintegersareaddedtothefirsttwointegersthesumis41.Finallywhentwomoreintegersareaddedtothesumofthepreviousfourintegersthesumis57.Whatistheminimumnumberofevenintegersamongthe6integers?
Problem10
Howmanyorderedpairsofpositiveintegers(M,N)satisfytheequation
=
Problem11
AdessertchefpreparesthedessertforeverydayofaweekstartingwithSunday.Thedesserteachdayiseithercake,pie,icecream,orpudding.Thesamedessertmaynotbeservedtwodaysinarow.TheremustbecakeonFridaybecauseofabirthday.Howmanydifferentdessertmenusfortheweekarepossible?
Problem12
PointBisdueeastofpointA.PointCisduenorthofpointB.ThedistancebetweenpointsAandCis,and=45degrees.PointDis20metersdueNorthofpointC.ThedistanceADisbetweenwhichtwointegers?
Problem13
IttakesClea60secondstowalkdownanescalatorwhenitisnotoperating,andonly24secondstowalkdowntheescalatorwhenitisoperating.HowmanysecondsdoesittakeCleatoridedowntheoperatingescalatorwhenshejuststandsonit?
Problem14
Twoequilateraltrianglesarecontainedinsquarewhosesidelengthis
arhombus.Whatistheareaoftherhombus?
.Thebasesofthesetrianglesaretheoppositesideofthesquare,andtheirintersectionis
Problem15
Inaround-robintournamentwith6teams,eachteamplaysonegameagainsteachotherteam,andeachgameresultsinoneteamwinningandoneteamlosing.Attheendofthetournament,theteamsarerankedbythenumberofgameswon.Whatisthemaximumnumberofteamsthatcouldbetiedforthemostwinsattheendonthetournament?
Problem16
Threecircleswithradius2aremutuallytangent.Whatisthetotalareaofthecirclesandtheregionboundedbythem,asshowninthefigure?
Problem17
Jessecutsacircularpaperdiskofradius12alongtworadiitoformtwosectors,thesmallerhavingacentralangleof120degrees.Hemakestwocircularcones,usingeachsectortoformthelateralsurfaceofacone.Whatistheratioofthevolumeofthesmallerconetothatofthelarger?
Problem18
Supposethatoneofevery500peopleinacertainpopulationhasaparticular
disease,whichdisplaysnosymptoms.Abloodtestisavailableforscreeningforthisdisease.Forapersonwhohasthisdisease,thetestalwaysturnsoutpositive.Forapersonwhodoesnothavethedisease,however,thereisa
otherwords,forsuchpeople,falsepositiverate--inofthetimethetestwillturnoutnegative,but
ofthetimethetestwillturnoutpositiveandwillincorrectlyindicatethatthepersonhasthedisease.Letbetheprobabilitythatapersonwhoischosenatrandomfromthispopulationandgetsapositivetestresultactuallyhasthedisease.Whichofthefollowingisclosestto?
Problem19
Inrectangle,,
topoint
?
andisthemidpointof.Segmentandisextended2unitsbeyond.Whatistheareaof,andistheintersectionof
篇二:
201X年美国高中数学竞赛(AMC12)A卷试题
201X年美国高中数学竞赛(AMC12)A卷试题
篇三:
美国高中学生数学竞赛题
1.(1995年文理)设(3x-1)6=a6x6+a5x5+a4x4+a3x3+a2x2+a1x+a0,求a6+a5+a4+a3+a2+a1+a0的值。
答案:
64。
2.(1989年文)如果(1-2x)7=a0+a1x+a2x2+…+a7x7,那么a1+a2+…+a7的值等于()
A.-2B.-1C.0D.2
答案:
(A)
3.(1989年理)已知(1-2x)7=a0+a1x+a2x2+…+a7x7,那么a1+a2+…+a7=____。
-2。
题源:
(美28届10题)若(3x-1)7=a7x7+a6x6+…+a0,那么a7+a6+…+a0等于()
A.0B.1C.64D.-64E.128
(E)
改编点评:
1题将指数7改为6,改为简答题;
2题将底数(3x-1)改为(1-2x),展开式改为x的升幂排列,所求结论中去掉了常数项a0,3题改编方法同2题,改为填空题。
4.(1990年文)已知f(x)=x5+ax3+bx-8,且f(-2)=10,那么f
(2)等于()
A.-26B.-18C.-10D.10
(美33届12题)设f(x)=ax7+bx3+cx-5,其中a.b和c是常数,如图f(-7)=7,那么f(7)等于()
A.-17B.-7C.14D.21E.不能唯一确定
降低了次数,减少了一个字母系数,降低了难度。
5.(1990年文理)如果实数x、y满足等式(x-2)2+y2=3,那么的最大值是()
A.B.C.D.
(D)
(美35届29题)在满足方程(x-3)2+(y-3)2=6的实数对(x,y)中,的最大值是()
A.3+2B.2+C.3D.6E.6+2
圆方程中的圆心坐标、半径作了改变,题设的叙述方式也作了变化。
6.(1990年文理)函数y=+++的值域是()
A.{-2,4}B.{-2,0,4}
C.{-2,0,2,4}D.{-4,-2,0,4}
(B)
(美28届8题)非零实数的每一个三重组(a,b,c)构成一个数。
如此构成的所有数的集是()
A.{0}B.{-4,0,4}
C.{-4,-2,0,2,4}D.{-4,-2,2,4}
E.这些都不对
将a、b、c改为三角函数,考查的知识面更广。
7.(1992年文理)长方体的全面积为11,十二条棱长度之和为24,则这个长方体的一条对角线长为()
A.2B.C.5D.6
(C)
(美35届25题)一个长方体的表面积为22cm2,并且它的所有棱的总长度为24cm,那么它的对角线的长度(按cm计)是()
A.B.C.D.E.不能被唯一确定
作了两个方面的变化:
将全面积22cm2改为11,去掉单位。
8.(1992年文理)如果函数f(x)=x2+bx+c对任意实数t都有f(2+t)=f(2-t),那么()
A.f
(2)<f
(1)<f(4)B.f
(1)<f
(2)<f(4)
C.f
(2)<f(4)<f
(1)D.f(4)<f
(2)<f
(1)
(美35届16题)函数f(x)对于一切实数x都满足f(2+x)=f(2-x),如果方程f(x)=0恰好有四个不同的实根,那么这些根的和是()
A.0B.2C.4D.6E.8
题源是一个抽象函数问题,有一些难度,作为高考题是不合适的,8题主要采用题源中对称轴的表达方式,通过设计一个二次函数,结合对称性考查函数的单调性。
9.(1994年文理)已知sinθ+cosθ=,θ∈(0,π),则ctgθ的值是____。
-。
(美29届15题)若sinx+cosx=,且0≤x≤π,那么tgx是()
A.-B.-C.D.
x改为θ,将求正切值改为求余切值,改成填空题。
10.(1995年文理)等差数列{an},{bn}的前n项和分别为Sn和Tn,若=,则等于()
A.1B.C.D.
(美20届32题)设Sn和Tn分别为两个等差数列的前n项和,如果对所有的n,有=,则第一个数列与第二个数列的第十一项的比是()
A.B.C.D.E.不能确定
改变的比值,设问方式作了较大变化,将求某一项的比值改为求比值的极限。
11.(201X年文理)不等式(1+x)(1-|x|)>0的解集是()
A.{x|0≤x<1}B.{x|x<0且x≠-1}
C.{x|-1<n<1}D.{x|x<1且x≠-1}
(美27届7题)若x是实数,那么(1-|x|)(1+x)是正数的充分必要条件是()
A.|x|<1B.x<1C.|x|>1D.x<-1E.x<-1或-1<x<1答案:
改变了设问方式,将求充要条件改为求不等式解集。
篇四:
美国高中优秀学生的数学测试题
Test
1.Howmanytermsarethereinthearithmeticsequence13,16,19,,70,73?
A.20B.21C.24D.60E.61
2.TwoyearsagoPeterwasthreetimesasoldashiscousinClaire.Twoyearsbeforethat,PeterwasfourtimesasoldasClaire.Inhowmanyyearswilltheratiooftheiragesbe2:
1?
A.2B.4C.5D.6E.8
3.Theratioofthelengthtothewidthofarectangleis4:
3.Iftherectanglehasdiagonaloflengthd,thentheareamaybeexpressedankd2forsomeconstantk.Whatisk?
2312163A.B.C.D.E.7725254
4.Pointsa)
andb)aredistinctpointsonthegraphof
y2?
x4?
2x2y?
1.Whatisa?
b?
A.1B.?
C.2
E.12
5.Ify?
4?
(x?
2)2,x?
(y?
2)2,andx?
y,whatisthevalueofx2?
A.10B.15C.20D.25E.30
6.TheisoscelesrighttriangleABChasrightangleatCa
ndarea12.5.Theraystrisecting?
ACBintersectABatDandE.Whatistheareaof?
CDE?
25575150?
3
B.
C.
D.E.A.64382
7.TetrahedronABCDhasAB?
5,AC?
3,BC?
4,BD?
4,AD?
3and
.Whatisthevolumeofthetetrahedron?
24A
B.C.
D.
E5
8.Thezerosofthefunctionf(x)?
x2?
ax?
2aareintegers.Whatisthesumofthepossiblevaluesofa?
A.7B.8C.16D.17E.18CD?
9.Forsomepositiveintegersp,quadrilateralABCDwithpositiveintegersidelengthshasperimeterp,rightanglesatBandC,AB?
2,andCD?
AD.Howmanydifferentvaluesofp?
201Xarepossible?
A.30B.31C.61D.62E.63
10.LetSbeasquareofsidelength1.TwopointsarechosenindependentlyatrandomonthesidesofS.Theprobabilitythatthestraight-linedistancebetweenthe1a?
pointsisatleastis,wherea,b,carepositiveintegersandgcd(a,b,c)2c
c?
A.59B.60C.61D.62E.63
11.Positivenumbersx,y,zsatisfyxyz?
1081and
log10xlog10yz?
log10ylog10z?
468.
Find.
12.Findtheremainderwhen9?
99?
999?
13.Supposethaty?
asarationalnumber3xandxy?
yx.Thequantityx?
ycanbeexpressed4?
999isdividedby1000.9999'
sr,whererandsarerelativelyprimepositiveintegers.Finds
r?
s.
14.Positiveintegersa,b,canddsatisfya?
d,a?
d?
201X,anda2?
b2?
c2?
d2?
201X.Findthenumberofpossiblevaluesofa.
15.LetP(x)beaquadraticpolynomialwithrealcoefficientssatisfying
2x?
2?
P(x)?
2x2?
4x?
forallrealnumbersx,andsupposeP(11)?
181.FindP(16).
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