AMC考题和答案解析.docx
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AMC考题和答案解析.docx
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AMC考题和答案解析
Documentserialnumber【NL89WT-NY98YT-NC8CB-NNUUT-NUT108】
AMC考题和答案解析
2017AMC8考题及答案
Problem1
Whichofthefollowingvaluesislargest
Problem2
Alicia,Brenda,andColbywerethecandidatesinarecentelectionforstudentpresident.Thepiechartbelowshowshowthevotesweredistributedamongthethreecandidates.IfBrendareceived36votes,thenhowmanyvoteswerecastalltogether
Problem3
Whatisthevalueoftheexpression
Problem4
Whenismultipliedby7,928,564theproductisclosesttowhichofthefollowing
Problem5
Whatisthevalueoftheexpression
Problem6
Ifthedegreemeasuresoftheanglesofatriangleareintheratio
whatisthedegreemeasureofthelargestangleofthetriangle
Problem7
Let
bea6-digitpositiveinteger,suchas247247,whosefirstthreedigitsarethesameasitslastthreedigitstakeninthesameorder.Whichofthefollowingnumbersmustalsobeafactorof
Problem8
MalcolmwantstovisitIsabellaafterschooltodayandknowsthestreetwhereshelivesbutdoesn'tknowherhousenumber.Shetellshim,"Myhousenumberhastwodigits,andexactlythreeofthefollowingfourstatementsaboutitaretrue."
(1)Itisprime.
(2)Itiseven.
(3)Itisdivisibleby7.
(4)Oneofitsdigitsis9.
ThisinformationallowsMalcolmtodetermineIsabella'shousenumber.Whatisitsunitsdigit
Problem9
AllofMarcy'smarblesareblue,red,green,oryellow.Onethirdofhermarblesareblue,onefourthofthemarered,andsixofthemaregreen.WhatisthesmallestnumberofyellowmarblesthatMarcycouldhave
Problem10
Aboxcontainsfivecards,numbered1,2,3,4,and5.Threecardsareselectedrandomlywithoutreplacementfromthebox.Whatistheprobabilitythat4isthelargestvalueselected
Problem11
Asquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotalnumberoftilesthatlieonthetwodiagonalsis37,howmanytilescoverthefloor
Problem12
Thesmallestpositiveintegergreaterthan1thatleavesaremainderof1whendividedby4,5,and6liesbetweenwhichofthefollowingpairsofnumbers
Problem13
Peter,Emma,andKylerplayedchesswitheachother.Peterwon4gamesandlost2games.Emmawon3gamesandlost3games.IfKylerlost3games,howmanygamesdidhewin
Problem14
ChloeandZoearebothstudentsinMs.Demeanor'smathclass.Lastnighttheyeachsolvedhalfoftheproblemsintheirhomeworkassignmentaloneandthensolvedtheotherhalftogether.Chloehadcorrectanswerstoonly
oftheproblemsshesolvedalone,butoverall
ofheranswerswerecorrect.Zoehadcorrectanswersto
oftheproblemsshesolvedalone.WhatwasZoe'soverallpercentageofcorrectanswers
Problem15
Inthearrangementoflettersandnumeralsbelow,byhowmanydifferentpathscanonespellAMC8BeginningattheAinthemiddle,apathallowsonlymovesfromonelettertoanadjacent(above,below,left,orright,butnotdiagonal)letter.Oneexampleofsuchapathistracedinthepicture.
Problem16
Inthefigurebelow,choosepoint
on
sothat
and
haveequalperimeters.Whatistheareaof
Problem17
Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedtoput9goldcoinsineachtreasurechest,butthatleft2treasurechestsempty.SoinsteadIput6goldcoinsineachtreasurechest,butthenIhad3goldcoinsleftover.HowmanygoldcoinsdidIhave
Problem18
Inthenon-convexquadrilateral
shownbelow,
isarightangle,
and
.
Whatistheareaofquadrilateral
Problem19
Foranypositiveinteger
thenotation
denotestheproductoftheintegers
through
.Whatisthelargestinteger
forwhich
isafactorofthesum
Problem20
Anintegerbetween
and
inclusive,ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct
Problem21
Suppose
and
arenonzerorealnumbers,and
.Whatarethepossiblevalue(s)for
Problem22
Intherighttriangle
andangle
isarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicircle
Problem23
Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachdayafterthefirst,herspeeddecreasedsothatthenumberofminutestotravelonemileincreasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.Whatwasthetotalnumberofmilesforthefourtrips
Problem24
Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecallshereverythreedays,onecallshereveryfourdays,andonecallshereveryfivedays.AllthreecalledheronDecember31,2016.Onhowmanydaysduringthenextyeardidshenotreceiveaphonecallfromanyofhergrandchildren
Problem25
Inthefigureshown,
and
arelinesegmentseachoflength2,and
.Arcs
and
areeachone-sixthofacirclewithradius2.Whatistheareaoftheregionshown
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
20.B
21.A
22.D
23.C
24.D
25.B
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