2019 AMC 8 考题及答案

2019AMC8考题及答案 Problem1 Whichofthefollowingvaluesislargest? Problem2 Alicia,Brenda,andColbywerethecandidatesinarecentelectionforstudentpresident.Thepiechartbelowshowshowthevotesweredistributedamongthethreecandidates.IfBrendareceived36votes,thenhowmanyvoteswerecastalltogether? Problem3 Whatisthevalueoftheexpression? Problem4 When0.000315ismultipliedby7,928,564theproductisclosesttowhichofthefollowing? Problem5 Whatisthevalueoftheexpression? Problem6 Ifthedegreemeasuresoftheanglesofatriangleareintheratio,whatisthedegreemeasureofthelargestangleofthetriangle? Problem7 Letbea6-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.Chloehadcorrectanswerstoonlyoftheproblemsshesolvedalone,butoverallofheranswerswerecorrect.Zoehadcorrectanswerstooftheproblemsshesolvedalone.WhatwasZoe'soverallpercentageofcorrectanswers? Problem15 Inthearrangementoflettersandnumeralsbelow,byhowmanydifferentpathscanonespellAMC8?BeginningattheAinthemiddle,apathallowsonlymovesfromonelettertoanadjacent(above,below,left,orright,butnotdiagonal)letter.Oneexampleofsuchapathistracedinthepicture. Problem16 Inthefigurebelow,choosepointonsothatandhaveequalperimeters.Whatistheareaof? Problem17 Startingwithsomegoldcoinsandsomeemptytreasurechests,Itriedtoput9goldcoinsineachtreasurechest,butthatleft2treasurechestsempty.SoinsteadIput6goldcoinsineachtreasurechest,butthenIhad3goldcoinsleftover.HowmanygoldcoinsdidIhave? Problem18 Inthenon-convexquadrilateralshownbelow,isarightangle,,,,and. Whatistheareaofquadrilateral? Problem19 Foranypositiveinteger,thenotationdenotestheproductoftheintegersthrough.Whatisthelargestintegerforwhichisafactorofthesum? Problem20 Anintegerbetweenand,inclusive,ischosenatrandom.Whatistheprobabilitythatitisanoddintegerwhosedigitsarealldistinct? Problem21 Suppose,,andarenonzerorealnumbers,and.Whatarethepossiblevalue(s)for? Problem22 Intherighttriangle,,,andangleisarightangle.Asemicircleisinscribedinthetriangleasshown.Whatistheradiusofthesemicircle? Problem23 Eachdayforfourdays,Lindatraveledforonehourataspeedthatresultedinhertravelingonemileinanintegernumberofminutes.Eachdayafterthefirst,herspeeddecreasedsothatthenumberofminutestotravelonemileincreasedby5minutesovertheprecedingday.Eachofthefourdays,herdistancetraveledwasalsoanintegernumberofmiles.Whatwasthetotalnumberofmilesforthefourtrips? Problem24 Mrs.Sandershasthreegrandchildren,whocallherregularly.Onecallshereverythreedays,onecallshereveryfourdays,andonecallshereveryfivedays.AllthreecalledheronDecember31,2019.Onhowmanydaysduringthenextyeardidshenotreceiveaphonecallfromanyofhergrandchildren? Problem25 Inthefigureshown,andarelinesegmentseachoflength2,and.Arcsandareeachone-sixthofacirclewithradius2.Whatistheareaoftheregionshown? 2019AMC8AnswerKey 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 - 1 -