AMC 10 ProblemsWord下载.docx
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AMC 10 ProblemsWord下载.docx
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ofthejellybeansthatwereinherjaratthebeginningofthatday.Attheendofthesecondday,
remained.Howmanyjellybeanswereinthejaroriginally?
Problem4
Chandrapaysanon-lineserviceproviderafixedmonthlyfeeplusanhourlychargeforconnecttime.HerDecemberbillwas
butinJanuaryherbillwas
becausesheusedtwiceasmuchconnecttimeasinDecember.Whatisthefixedmonthlyfee?
Problem5
Points
and
arethemidpointsofsides
of
.As
movesalongalinethatisparalleltoside
howmanyofthefourquantitieslistedbelowchange?
(a)thelengthofthesegment
(b)theperimeterof
(c)theareaof
(d)theareaoftrapezoid
Problem6
TheFibonaccisequence
startswithtwo
s,andeachtermafterwardsisthesumofitstwopredecessors.WhichoneofthetendigitsisthelasttoappearintheunitspositionofanumberintheFibonaccisequence?
Problem7
Inrectangle
ison
trisect
.Whatistheperimeterof
Problem8
AtOlympicHighSchool,
ofthefreshmenand
ofthesophomorestooktheAMC-10.Giventhatthenumberoffreshmenandsophomorecontestantswasthesame,whichofthefollowingmustbetrue?
Therearefivetimesasmanysophomoresasfreshmen.
Therearetwiceasmanysophomoresasfreshmen.
Thereareasmanyfreshmenassophomores.
Therearetwiceasmanyfreshmenassophomores.
Therearefivetimesasmanyfreshmenassophomores.
Problem9
If
where
then
Problem10
Thesidesofatrianglewithpositiveareahavelengths
.Thesidesofasecondtrianglewithpositiveareahavelengths
.Whatisthesmallestpositivenumberthatis
not
apossiblevalueof
Problem11
Twodifferentprimenumbersbetween
arechosen.Whentheirsumissubtractedfromtheirproduct,whichofthefollowingnumberscouldbeobtained?
Problem12
Figures
consistof
nonoverlappingunitsquares,respectively.Ifthepatternwerecontinued,howmanynonoverlappingunitsquareswouldtherebeinfigure100?
Problem13
Thereare5yellowpegs,4redpegs,3greenpegs,2bluepegs,and1orangepegtobeplacedonatriangularpegboard.Inhowmanywayscanthepegsbeplacedsothatno(horizontal)rowor(vertical)columncontainstwopegsofthesamecolor?
Problem14
Mrs.Waltergaveanexaminamathematicsclassoffivestudents.Sheenteredthescoresinrandomorderintoaspreadsheet,whichrecalculatedtheclassaverageaftereachscorewasentered.Mrs.Walternoticedthataftereachscorewasentered,theaveragewasalwaysaninteger.Thescores(listedinascendingorder)were
.WhatwasthelastscoreMrs.Walterentered?
Problem15
Twonon-zerorealnumbers,
satisfy
.Findapossiblevalueof
.
Problem16
Thediagramshows
latticepoints,eachoneunitfromitsnearestneighbors.Segment
meetssegment
at
.Findthelengthofsegment
Problem17
Borishasanincrediblecoinchangingmachine.Whenheputsinaquarter,itreturnsfivenickels;
whenheputsinanickel,itreturnsfivepennies;
andwhenheputsinapenny,itreturnsfivequarters.Borisstartswithjustonepenny.WhichofthefollowingamountscouldBorishaveafterusingthemachinerepeatedly?
Problem18
Charlynwalkscompletelyaroundtheboundaryofasquarewhosesidesareeach
kmlong.Fromanypointonherpathshecanseeexactly
kmhorizontallyinalldirections.WhatistheareaoftheregionconsistingofallpointsCharlyncanseeduringherwalk,expressedinsquarekilometersandroundedtothenearestwholenumber?
Problem19
Throughapointonthehypotenuseofarighttriangle,linesaredrawnparalleltothelegsofthetrianglesothatthetriangleisdividedintoasquareandtwosmallerrighttriangles.Theareaofoneofthetwosmallrighttrianglesis
timestheareaofthesquare.Theratiooftheareaoftheothersmallrighttriangletotheareaofthesquareis
Problem20
Let
benonnegativeintegerssuchthat
.Whatisthemaximumvalueof
Problem21
Ifallalligatorsareferociouscreaturesandsomecreepycrawlersarealligators,whichstatement(s)mustbetrue?
Problem22
OnemorningeachmemberofAngela'
sfamilydrankan8-ouncemixtureofcoffeewithmilk.Theamountsofcoffeeandmilkvariedfromcuptocup,butwereneverzero.Angeladrankaquarterofthetotalamountofmilkandasixthofthetotalamountofcoffee.Howmanypeopleareinthefamily?
Problem23
Whenthemean,median,andmodeofthelist
arearrangedinincreasingorder,theyformanon-constantarithmeticprogression.Whatisthesumofallpossiblerealvaluesof
Problem24
beafunctionforwhich
.Findthesumofallvaluesof
forwhich
Problem25
Inyear
the
dayoftheyearisaTuesday.Inyear
dayisalsoaTuesday.Onwhatdayoftheweekdidthe
dayofyear
occur?
Answerkey
1.(E)
2.(A)
3.(B)
4.(D)
5.(B)
6.(C)
7.(B)
8.(D)
9.(C)
10.(D)
11.(C)
12.(C)
13.(B)
14.(C)
15.(E)
16.(B)
17.(D)
18.(C)
19.(D)
20.(C)
21.(B)
22.(C)
23.(E)
24.(B)
25.(A)
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