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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