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

2017AMC8考题及答案

Problem1

Whichofthefollowingvaluesislargest?

Problem2

Alicia,Brenda,andColbywerethecandidatesinarecentelectionforstudentpresident.Thepiechartbelowshowshowthevotesweredistributedamongthethreecandidates.IfBrendareceived36votes,thenhowmanyvoteswerecastalltogether?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_2

Problem3

Whatisthevalueoftheexpression

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_3

Problem4

When0.000315ismultipliedby7,928,564theproductisclosesttowhichofthefollowing?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_4

Problem5

Whatisthevalueoftheexpression

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_5

Problem6

Ifthedegreemeasuresoftheanglesofatriangleareintheratio

whatisthedegreemeasureofthelargestangleofthetriangle?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_6

Problem7

Let

bea6-digitpositiveinteger,suchas247247,whosefirstthreedigitsarethesameasitslastthreedigitstakeninthesameorder.Whichofthefollowingnumbersmustalsobeafactorof

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_7

Problem8

MalcolmwantstovisitIsabellaafterschooltodayandknowsthestreetwhereshelivesbutdoesn'tknowherhousenumber.Shetellshim,"Myhousenumberhastwodigits,andexactlythreeofthefollowingfourstatementsaboutitaretrue."

（1）Itisprime.

（2）Itiseven.

（3）Itisdivisibleby7.

（4）Oneofitsdigitsis9.

ThisinformationallowsMalcolmtodetermineIsabella'shousenumber.Whatisitsunitsdigit?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_8

Problem9

AllofMarcy'smarblesareblue,red,green,oryellow.Onethirdofhermarblesareblue,onefourthofthemarered,andsixofthemaregreen.WhatisthesmallestnumberofyellowmarblesthatMarcycouldhave?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_9

Problem10

Aboxcontainsfivecards,numbered1,2,3,4,and5.Threecardsareselectedrandomlywithoutreplacementfromthebox.Whatistheprobabilitythat4isthelargestvalueselected?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_10

Problem11

Asquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotalnumberoftilesthatlieonthetwodiagonalsis37,howmanytilescoverthefloor?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_11

Problem12

Thesmallestpositiveintegergreaterthan1thatleavesaremainderof1whendividedby4,5,and6liesbetweenwhichofthefollowingpairsofnumbers?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_12

Problem13

Peter,Emma,andKylerplayedchesswitheachother.Peterwon4gamesandlost2games.Emmawon3gamesandlost3games.IfKylerlost3games,howmanygamesdidhewin?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_13

Problem14

ChloeandZoearebothstudentsinMs.Demeanor'smathclass.Lastnighttheyeachsolvedhalfoftheproblemsintheirhomeworkassignmentaloneandthensolvedtheotherhalftogether.Chloehadcorrectanswerstoonly

oftheproblemsshesolvedalone,butoverall

ofheranswerswerecorrect.Zoehadcorrectanswersto

oftheproblemsshesolvedalone.WhatwasZoe'soverallpercentageofcorrectanswers?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_14

Problem15

Inthearrangementoflettersandnumeralsbelow,byhowmanydifferentpathscanonespellAMC8?

BeginningattheAinthemiddle,apathallowsonlymovesfromonelettertoanadjacent（above,below,left,orright,butnotdiagonal）letter.Oneexampleofsuchapathistracedinthepicture.

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_15

Problem16

Inthefigurebelow,choosepoint

on

sothat

and

haveequalperimeters.Whatistheareaof

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_16

Problem17

Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedtoput9goldcoinsineachtreasurechest,butthatleft2treasurechestsempty.SoinsteadIput6goldcoinsineachtreasurechest,butthenIhad3goldcoinsleftover.HowmanygoldcoinsdidIhave?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_17

Problem18

Inthenon-convexquadrilateral

shownbelow,

isarightangle,

and

.

Whatistheareaofquadrilateral

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_18

Problem19

Foranypositiveinteger

thenotation

denotestheproductoftheintegers

through

.Whatisthelargestinteger

forwhich

isafactorofthesum

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_19

Problem20

Anintegerbetween

and

inclusive,ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_20

Problem21

Suppose

and

arenonzerorealnumbers,and

.Whatarethepossiblevalue（s）for

?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_21

Problem22

Intherighttriangle

andangle

isarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicircle?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_22

Problem23

Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachdayafterthefirst,herspeeddecreasedsothatthenumberofminutestotravelonemileincreasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.Whatwasthetotalnumberofmilesforthefourtrips?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_23

Problem24

Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecallshereverythreedays,onecallshereveryfourdays,andonecallshereveryfivedays.AllthreecalledheronDecember31,2016.Onhowmanydaysduringthenextyeardidshenotreceiveaphonecallfromanyofhergrandchildren?

artofproblemsolving./wiki/index.php?

title=2017_AMC_8_Problems/Problem_24

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