AMC8考题和答案解析.docx

AMC8考题和答案解析.docx

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AMC8考题和答案解析

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2017AMC8考题及答案

Problem1

Whichofthefollowingvaluesislargest?

Problem2

Alicia,Brenda,andColbywerethecandidatesinarecentelectionfor

studentpresident.Thepiechartbelowshowshowthevoteswere

distributedamongthethreecandidates.IfBrendareceived36votes,

thenhowmanyvoteswerecastalltogether?

Problem3

Whatisthevalueoftheexpression?

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Problem4

When0.000315ismultipliedby7,928,564theproductisclosesttowhich

ofthefollowing?

Problem5

Whatisthevalueoftheexpression?

Problem6

Ifthedegreemeasuresoftheanglesofatriangleareintheratio

whatisthedegreemeasureofthelargestangleofthe

triangle?

Problem7

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Letbea6-digitpositiveinteger,suchas247247,whosefirstthree

digitsarethesameasitslastthreedigitstakeninthesameorder.Which

ofthefollowingnumbersmustalsobeafactorof?

Problem8

MalcolmwantstovisitIsabellaafterschooltodayandknowsthestreet

whereshelivesbutdoesn'tknowherhousenumber.Shetellshim,"My

housenumberhastwodigits,andexactlythreeofthefollowingfour

statementsaboutitaretrue."

（1）Itisprime.

（2）Itiseven.

（3）Itisdivisibleby7.

（4）Oneofitsdigitsis9.

ThisinformationallowsMalcolmtodetermineIsabella'shousenumber.

Whatisitsunitsdigit?

Problem9

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AllofMarcy'smarblesareblue,red,green,oryellow.Onethirdofher

marblesareblue,onefourthofthemarered,andsixofthemaregreen.

WhatisthesmallestnumberofyellowmarblesthatMarcycouldhave?

Problem10

Aboxcontainsfivecards,numbered1,2,3,4,and5.Threecardsare

selectedrandomlywithoutreplacementfromthebox.Whatisthe

probabilitythat4isthelargestvalueselected?

Problem11

Asquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotal

numberoftilesthatlieonthetwodiagonalsis37,howmanytilescover

thefloor?

Problem12

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Thesmallestpositiveintegergreaterthan1thatleavesaremainderof1

whendividedby4,5,and6liesbetweenwhichofthefollowingpairsof

numbers?

Problem13

Peter,Emma,andKylerplayedchesswitheachother.Peterwon4

gamesandlost2games.Emmawon3gamesandlost3games.IfKyler

lost3games,howmanygamesdidhewin?

Problem14

ChloeandZoearebothstudentsinMs.Demeanor'smathclass.Last

nighttheyeachsolvedhalfoftheproblemsintheirhomework

assignmentaloneandthensolvedtheotherhalftogether.Chloehad

correctanswerstoonlyoftheproblemsshesolvedalone,but

overallofheranswerswerecorrect.Zoehadcorrectanswersto

oftheproblemsshesolvedalone.WhatwasZoe'soverall

percentageofcorrectanswers?

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Problem15

Inthearrangementoflettersandnumeralsbelow,byhowmany

differentpathscanonespellAMC8?

BeginningattheAinthemiddle,a

pathallowsonlymovesfromonelettertoanadjacent（above,below,

left,orright,butnotdiagonal）letter.Oneexampleofsuchapathis

tracedinthepicture.

Problem16

Inthefigurebelow,choosepointonsothatand

haveequalperimeters.Whatistheareaof?

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Problem17

Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedto

put9goldcoinsineachtreasurechest,butthatleft2treasurechests

empty.SoinsteadIput6goldcoinsineachtreasurechest,butthenI

had3goldcoinsleftover.HowmanygoldcoinsdidIhave?

Problem18

Inthenon-convexquadrilateralshownbelow,isa

rightangle,,,,and.

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Whatistheareaofquadrilateral?

Problem19

Foranypositiveinteger,thenotationdenotestheproductof

theintegersthrough.Whatisthelargestintegerforwhichis

afactorofthesum?

Problem20

Anintegerbetweenand,inclusive,ischosenatrandom.

Whatistheprobabilitythatitisanoddintegerwhosedigitsareall

distinct?

Problem21

Suppose,,andarenonzerorealnumbers,and.

Whatarethepossiblevalue（s）for?

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Problem22

Intherighttriangle,,,andangleisaright

angle.Asemicircleisinscribedinthetriangleasshown.Whatisthe

radiusofthesemicircle?

Problem23

Eachdayforfourdays,Lindatraveledforonehourataspeedthat

resultedinhertravelingonemileinanintegernumberofminutes.Each

dayafterthefirst,herspeeddecreasedsothatthenumberofminutes

totravelonemileincreasedby5minutesovertheprecedingday.Each

ofthefourdays,herdistancetraveledwasalsoanintegernumberof

miles.Whatwasthetotalnumberofmilesforthefourtrips?

Problem24

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Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecalls

hereverythreedays,onecallshereveryfourdays,andonecallsher

everyfivedays.AllthreecalledheronDecember31,2016.Onhow

manydaysduringthenextyeardidshenotreceiveaphonecallfrom

anyofhergrandchildren?

Problem25

Inthefigureshown,andarelinesegmentseachoflength2,

and.Arcsandareeachone-sixthofacircle

withradius2.Whatistheareaoftheregionshown?

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2017AMC8AnswerKey

1.A

2.E

3.C

4.D

5.B

6.D

7.A

8.D

9.D

10.C

11.C

12.D

13.B

14.C

15.D

16.D

17.C

18.B

19.D

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20.B

21.A

22.D

23.C

24.D

25.B

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