2017AMC8考题及答案Problem1Whichofthefollowingvaluesislargest?Problem2Alicia,Brenda,andColbywerethecandidatesinarecentelectionforstudentpresident.Thepiechartbelowshowshowthevotesweredistributedamongthethreecandidates.IfBrendareceived36votes,thenhowmanyvoteswerecastalltogether?Problem3Whatisthevalueoftheexpression?Problem4When0.000315ismultipliedby7,928,564theproductisclosesttowhichofthefollowing?Problem5Whatisthevalueoftheexpression?Problem6Ifthedegreemeasuresoftheanglesofatriangleareintheratio,whatisthedegreemeasureofthelargestangleofthetriangle?Problem7Letbea6-digitpositiveinteger,suchas247247,whosefirstthreedigitsarethesameasitslastthreedigitstakeninthesameorder.Whichofthefollowingnumbersmustalsobeafactorof?Problem8MalcolmwantstovisitIsabellaafterschooltodayandknowsthestreetwhereshelivesbutdoesn'tknowherhousenumber.Shetellshim,"Myhousenumberhastwodigits,andexactlythreeofthefollowingfourstatementsaboutitaretrue."(1)Itisprime.(2)Itiseven.(3)Itisdivisibleby7.(4)Oneofitsdigitsis9.ThisinformationallowsMalcolmtodetermineIsabella'shousenumber.Whatisitsunitsdigit?Problem9AllofMarcy'smarblesareblue,red,green,oryellow.Onethirdofhermarblesareblue,onefourthofthemarered,andsixofthemaregreen.WhatisthesmallestnumberofyellowmarblesthatMarcycouldhave?Problem10Aboxcontainsfivecards,numbered1,2,3,4,and5.Threecardsareselectedrandomlywithoutreplacementfromthebox.Whatistheprobabilitythat4isthelargestvalueselected?Problem11Asquare-shapedflooriscoveredwithcongruentsquaretiles.Ifthetotalnumberoftilesthatlieonthetwodiagonalsis37,howmanytilescoverthefloor?Problem12Thesmallestpositiveintegergreaterthan1thatleavesaremainderof1whendividedby4,5,and6liesbetweenwhichofthefollowingpairsofnumbers?Problem13Peter,Emma,andKylerplayedchesswitheachother.Peterwon4gamesandlost2games.Emmawon3gamesandlost3games.IfKylerlost3games,howmanygamesdidhewin?Problem14ChloeandZoearebothstudentsinMs.Demeanor'smathclass.Lastnighttheyeachsolvedhalfoftheproblemsintheirhomeworkassignmentaloneandthensolvedtheotherhalftogether.Chloehadcorrectanswerstoonlyoftheproblemsshesolvedalone,butoverallofheranswerswerecorrect.Zoehadcorrectanswerstooftheproblemsshesolvedalone.WhatwasZoe'soverallpercentageofcorrectanswers?Problem15Inthearrangementoflettersandnumeralsbelow,byhowmanydifferentpathscanonespellAMC8?BeginningattheAinthemiddle,apathallowsonlymovesfromonelettertoanadjacent(above,below,left,orright,butnotdiagonal)letter.Oneexampleofsuchapathistracedinthepicture.Problem16Inthefigurebelow,choosepointonsothatandhaveequalperimeters.Whatistheareaof?Problem17Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedtoput9goldcoinsineachtreasurechest,butthatleft2treasurechestsempty.SoinsteadIput6goldcoinsineachtreasurechest,butthenIhad3goldcoinsleftover.HowmanygoldcoinsdidIhave?Problem18Inthenon-convexquadrilateralshownbelow,isarightangle,,,,and.Whatistheareaofquadrilateral?Problem19Foranypositiveinteger,thenotationdenotestheproductoftheintegersthrough.Whatisthelargestintegerforwhichisafactorofthesum?Problem20Anintegerbetweenand,inclusive,ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct?Problem21Suppose,,andarenonzerorealnumbers,and.Whatarethepossiblevalue(s)for?Problem22Intherighttriangle,,,andangleisarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicircle?Problem23Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachdayafterthefirst,herspeeddecreasedsothatthenumberofminutestotravelonemileincreasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.Whatwasthetotalnumberofmilesforthefourtrips?Problem24Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecallshereverythreedays,onecallshereveryfourdays,andonecallshereveryfivedays.AllthreecalledheronDecember31,2016.Onhowmanydaysduringthenextyeardidshenotreceiveaphonecallfromanyofhergrandchildren?Problem25Inthefigureshown,andarelinesegmentseachoflength2,and.Arcsandareeachone-sixthofacirclewithradius2.Whatistheareaoftheregionshown?2017AMC8AnswerKey1.A2.E3.C4.D5.B6.D7.A8.D9.D10.C11.C12.D13.14.B15.16.C17.18.D19.20.D21.22.C23.24.B25.D26.B27.28.A29.30.D31.32.C33.D34.35.B
