2017年美國數(shù)學(xué)競賽8年級AMC8真題附答案電腦版

2017年美國數(shù)學(xué)競賽8年級(AMC8)真題(附答案)AMC系列的全稱AmericanMathematicsCompetitions是由美國數(shù)學(xué)協(xié)會舉辦的，是美國最老的(1950年開始舉辦)的和最負(fù)盛名的初高中生數(shù)學(xué)競賽。2017年AMC8競賽于2017年11月15日下午結(jié)束。AMC系列比賽一共有以下幾個比賽：AmericanMathematicsCompetition8-AMC8AmericanMathematicsCompetition10/12-AMC10/12AmericanInvitationalMathematicsExam-AIMEUnitedStatesMathematicalOlympiadandJuniorMathematicalOlympiad-USA(J)MOLWhichofthefollowingvaluesisthelargest?(A)2+0+1+7(B)2xOH-1+7 (C)2+0x1^7(D)2+Q+1x7(E)2x0x1x7Solution.(A)Alicia.Brenda,andColbvwerethecandidatesinarecentelectionforstudentpresident.Thepiechartshowshowthevoteswereciistributedamongthethreecandidates.IfDrcndareceived36votes,thenhowinanyvoteswerecastalltojietlicr?BrendaBrenda30%(A)70(B)84(C)100(D)106(E)120Solution.(E);拓330%=120Whatist.hcvalueoftheexpressiuu\/L6M8v^?(A)4(B)472(C)S(D)8V欠 (E)16Solution.(C)Wlien0.000315ismultipliedby7,928,564theproductisclosesttowliichofthefollowing?(A)210(B)240 (C)2JOO(D)2,400(E)24.Q00Solution.(D) 口Wiiatisthevalueoftheexpression卜J卜紀(jì)二篙*十二?(A)1020(B)1120(C)1220(D)2240(E)3360Solution.(B)l+2+--+8=2x：3x6,4x5x7x8=l120. □Ifthedegreemeasuresoftheanglesofatrianglearcintheratio3:3:4.whatisthedegreemeasureofthelargestangleofthetriangle?(A)18(B)36 (C)60(D)72 (E)9()Solution,(D)180+(3+3+4)=72. □Let.Zbea6-digitpositiveinteger,suchas247247,whosefirstthreedigitsarethesameasitslastthreedigitstakeninthesameorder.WhichofthefollowingnumbersmustbeafactorofZ?(A)11(B)19 (C)101(D)111 (E)1111Solution.(A)ll|100kMalcolmwantstovisitIsabellaafterschooltodayandknowsthestreetwheresholivesbutdoesn'tknowherhousenumber.Shetellshim,"Myhousenumberhastwodigits,andexactlythreeofthefollowingfourstatementsaboutitaretrue?(L)Itisprime,(2)Itiseven.(J)Itisdivisibleby7.Oneofitsdigitsis9ThisinformationallowsMalcolmtodetermineIsabella'shousenumber.Whatisitsunitdigit?(A)4(B)6(C)7(D)8(E)9Solution,(D}98. □AllofMarcy^smarblesareblue,red,green,oryellow.Onethirdofhermarblesarcblue,onefourthofthemarcred,andsixofthemarcgreen.WhatisthesmallestuurnberofyellowmarblesthatMarcycouldhave?(A)1(B)2(C)3(D)4(E)5Solution.(D)Thetotalnumberofmarblesshouldbethemultipleof12,Aboxcontainsfivecards,inimbcr<?d1,2,3,4.and5,Threecardsareselectedrandomwithoutreplacementfromthebox.Whatistheprobabilitythat4isthelargestvalueselected?(A)L(B)l(C)后(D)I(E)iSolution.(C)ILAsquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotalnumberoftilesthatlieonthetwodiagonalsis37：howmanytilescoverthefloor?(A)118(B)324(C)361(D)1296(E)1369Solution.(C)(37-1)-?2+1=19,192=361.ThesmanoRtpositiveintegergreaterthan1thatleavesaremainderof1whendividedby4.5、and6liesbetweenwhichofthefollowingpairsofnumbers?(A)2and19(B)20and39(C)40and59(D)60and79 (E)80and124Solution.(D)卜1,5,6]—60,sothatnumberisGl. □Pct.oi\Emma,andKylorplayedchesswitheachother.Peterwen4gamesandlost2games,E)nniawon3gamesandlost3games.TfKylerlost3games,bowmanygamesdidhewin?(A)0(B)1 (C)2(D)3(E)4Solution,(B)Totalnumberofwins=Totalnumberofdefeats.ChloeandZoearebothstudentsinMs.Demeanor'smathclass.Lastnightthey68chsolvedhalfoftheproblemsintheirliorneworkassignmentaloneandthensolvedtheotherhalftogether.Chloehadcorrectanswerstoonly80%oftheproblemsshesolvedalone,butoverall88%ofheranswerswerecorrect.Zoehadcorrectanswersto90%oftheproblemsshesolvedalone.IVhalwasZoe'soverallpei,centa志eofcollectanswers?(A)89(B)92(C)93(D)96 (E)98Solution.(C)88x2-80=96,(96+90)子2=93. □Inth(?iirriiiigenioitoflettersantinnnicralsl)elow\byhowinmiydiffeniiipathscanonspellAMCS?BeginningattheAinthemiddle,apahlallow?onlymovesfromonelettertoanadjacent(-bovi?below,left,orrigiit.butnotdiagonal)letter.Oneexampleofsuchapathistracedinthepicture.TOC\o"1-5"\h\z8 C 88 C M C 8\o"CurrentDocument"C Al A Z C8 C M C 88 C 8(A)8(B)9(C)12(D)24(E)36Solution.(D)Intliefigureshownbelow,choosepointDonsideBCsothat/\ACDand△AB。haveequalperimeters.WhatistheareofAABD?(A)t(13)|(C)2(D)f(E-)fSoluti(m.(D) □Startingwithsomegoldcoinsandsomeemptytreasuresliests,Itriedtoput9goldcoinshieachtreasurechest,butthatleft2treasureehestsempty.SoinsteadIput.6goldcoinsineachtreasurechestybutthenIhad3goldcoinsleft.over.HowmanygoldcoinsdidIhave?(A)9(B)27(C)45(D)63(E)81Solution.(C)6x2+3=15,15+3x9=45.Inthenon-covexquadrilateralABCDshownbelow,/BCDisarightangle,AB—12,BC=4,CD=3,andAD=13.WhatistheareaofquadrilateralABCD?(A)12(B)24(C)26(D)3()(E)36Solution.(B) □ForanypositiveintegerM.thenotationMldenotesIheproductoftheintegers1throughtM,Whatisthelargestintegernforwhicli5"isafactorofthesum98!十99!+10()!?(A)23(B)24(C)25(D)26(E)27Solution.(D)98!+99!+100!=98!x10000"陰+[||]+4=26.Anintegerbetween1000and9999、inclusive.ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct?(A)堯(B)<(C)源(D)扇(E)iSolution.(B)Mo_一而,Supposea.b,andcarenonzerorealnumbers,andq*b+e=ChWhatarethepossiblevalue(s)fbr京+向+病+儡？(A)0(B)1and-1 (C)2and-2(D)0,2,and-2(E)0,1,and-1Solution,(A) □IntherighttriangleABC.AC=12,BC=5andangleGisarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicinde?(A)I(B)號(C)|(D)f(E)患Solution.(D)Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachday泣fterthefirst,herspeeddecreasedsothatthenumberofiniuutcstotravelonemileiiicicasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.WhatwasthetotalnumberHillerforthefourtrips?(A)10(B)1