AMC8考题和答案解析Word格式.docx
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AMC8考题和答案解析Word格式.docx
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title=2017_AMC_8_Problems/Problem_4
Problem5
title=2017_AMC_8_Problems/Problem_5
Problem6
Ifthedegreemeasuresoftheanglesofatriangleareintheratio
whatisthedegreemeasureofthelargestangleofthetriangle?
title=2017_AMC_8_Problems/Problem_6
Problem7
Let
bea6-digitpositiveinteger,suchas247247,whosefirstthreedigitsarethesameasitslastthreedigitstakeninthesameorder.Whichofthefollowingnumbersmustalsobeafactorof
title=2017_AMC_8_Problems/Problem_7
Problem8
MalcolmwantstovisitIsabellaafterschooltodayandknowsthestreetwhereshelivesbutdoesn'
tknowherhousenumber.Shetellshim,"
Myhousenumberhastwodigits,andexactlythreeofthefollowingfourstatementsaboutitaretrue."
(1)Itisprime.
(2)Itiseven.
(3)Itisdivisibleby7.
(4)Oneofitsdigitsis9.
ThisinformationallowsMalcolmtodetermineIsabella'
shousenumber.Whatisitsunitsdigit?
title=2017_AMC_8_Problems/Problem_8
Problem9
AllofMarcy'
smarblesareblue,red,green,oryellow.Onethirdofhermarblesareblue,onefourthofthemarered,andsixofthemaregreen.WhatisthesmallestnumberofyellowmarblesthatMarcycouldhave?
title=2017_AMC_8_Problems/Problem_9
Problem10
Aboxcontainsfivecards,numbered1,2,3,4,and5.Threecardsareselectedrandomlywithoutreplacementfromthebox.Whatistheprobabilitythat4isthelargestvalueselected?
title=2017_AMC_8_Problems/Problem_10
Problem11
Asquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotalnumberoftilesthatlieonthetwodiagonalsis37,howmanytilescoverthefloor?
title=2017_AMC_8_Problems/Problem_11
Problem12
Thesmallestpositiveintegergreaterthan1thatleavesaremainderof1whendividedby4,5,and6liesbetweenwhichofthefollowingpairsofnumbers?
title=2017_AMC_8_Problems/Problem_12
Problem13
Peter,Emma,andKylerplayedchesswitheachother.Peterwon4gamesandlost2games.Emmawon3gamesandlost3games.IfKylerlost3games,howmanygamesdidhewin?
title=2017_AMC_8_Problems/Problem_13
Problem14
ChloeandZoearebothstudentsinMs.Demeanor'
smathclass.Lastnighttheyeachsolvedhalfoftheproblemsintheirhomeworkassignmentaloneandthensolvedtheotherhalftogether.Chloehadcorrectanswerstoonly
oftheproblemsshesolvedalone,butoverall
ofheranswerswerecorrect.Zoehadcorrectanswersto
oftheproblemsshesolvedalone.WhatwasZoe'
soverallpercentageofcorrectanswers?
title=2017_AMC_8_Problems/Problem_14
Problem15
Inthearrangementoflettersandnumeralsbelow,byhowmanydifferentpathscanonespellAMC8?
BeginningattheAinthemiddle,apathallowsonlymovesfromonelettertoanadjacent(above,below,left,orright,butnotdiagonal)letter.Oneexampleofsuchapathistracedinthepicture.
title=2017_AMC_8_Problems/Problem_15
Problem16
Inthefigurebelow,choosepoint
on
sothat
and
haveequalperimeters.Whatistheareaof
title=2017_AMC_8_Problems/Problem_16
Problem17
Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedtoput9goldcoinsineachtreasurechest,butthatleft2treasurechestsempty.SoinsteadIput6goldcoinsineachtreasurechest,butthenIhad3goldcoinsleftover.HowmanygoldcoinsdidIhave?
title=2017_AMC_8_Problems/Problem_17
Problem18
Inthenon-convexquadrilateral
shownbelow,
isarightangle,
and
.
Whatistheareaofquadrilateral
title=2017_AMC_8_Problems/Problem_18
Problem19
Foranypositiveinteger
thenotation
denotestheproductoftheintegers
through
.Whatisthelargestinteger
forwhich
isafactorofthesum
title=2017_AMC_8_Problems/Problem_19
Problem20
Anintegerbetween
inclusive,ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct?
title=2017_AMC_8_Problems/Problem_20
Problem21
Suppose
arenonzerorealnumbers,and
.Whatarethepossiblevalue(s)for
title=2017_AMC_8_Problems/Problem_21
Problem22
Intherighttriangle
andangle
isarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicircle?
title=2017_AMC_8_Problems/Problem_22
Problem23
Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachdayafterthefirst,herspeeddecreasedsothatthenumberofminutestotravelonemileincreasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.Whatwasthetotalnumberofmilesforthefourtrips?
title=2017_AMC_8_Problems/Problem_23
Problem24
Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecallshereverythreedays,onecallshereveryfourdays,andonecallshereveryfivedays.AllthreecalledheronDecember31,2016.Onhowmanydaysduringthenextyeardidshenotreceiveaphonecallfromanyofhergrandchildren?
title=2017_AMC_8_Problems/Problem_24
Problem25
Inthefigureshown,
arelinesegmentseachoflength2,and
.Arcs
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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