2015年AMC8试题及答案

Copyright©2016ArtofProblemSolvingHowmanysquareyardsofcarpetarerequiredtocoverarectangularfloorthatisfeetlongandfeetwide?(Thereare3feetinayard.)First,wemultiplytogetthatyouneedsquarefeetofcarpetyouneedtocover.Sincetherearesquarefeetinasquareyard,youdividebytogetsquareyards,soouransweris.Sincetherearefeetinayard,wedividebytoget,andbytoget.Tofindtheareaofthecarpet,wethenmultiplythesetwovaluestogethertoget.2015AMC8(Problems•AnswerKey•Resources(=182&cid=42&year=2015))Preceded byFirstProblemFollowed byProblem21•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica()'sAmericanMathematicsCompetitions().Placement:EasyGeometryRetrievedfrom=2015_AMC_8_Problems/Problem_1&oldid=803232015AMC8Problems/Problem1SolutionSolution2SeeAlsoPointisthecenteroftheregularoctagon,andisthemidpointofthesideWhatfractionoftheareaoftheoctagonisshaded?1Solution12Solution23Solution34SeeAlsoSinceoctagonisaregularoctagon,itissplitintoequalparts,suchastriangles,etc.Theseparts,sincetheyareallequal,areoftheoctagoneach.Theshadedregionconsistsofoftheseequalpartsplushalfofanother,sothefractionoftheoctagonthatisshadedis2015AMC8Problems/Problem2ContentsSolution1Solution2Theoctagonhasbeendividedupintoidenticaltriangles(andthustheyeachhaveequalarea).Sincetheshadedregionoccupiesoutofthetotaltriangles,theansweris.ForstarterswhatIfindhelpfulistodividethewholeoctagonupintotrianglesasshownhere:Nowitisjustamatterofcountingthelargertrianglesrememberthatandarenotfulltrianglesandareonlyhalfforthesepurposes.Wecountitupandwegetatotalofoftheshapeshaded.Wethensimplifyittogetouranswerof.2015AMC8(Problems•AnswerKey•Resources(=182&cid=42&year=2015))Preceded byProblem1Followed byProblem31•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25AllAJHSME/AMC8ProblemsandSolutionsSolution3SeeAlsoCopyright©2016ArtofProblemSolvingJackandJillaregoingswimmingatapoolthatisonemilefromtheirhouse.Theyleavehomesimultaneously.Jillridesherbicycletothepoolataconstantspeedofmilesperhour.Jackwalkstothepoolataconstantspeedofmilesperhour.HowmanyminutesbeforeJackdoesJillarrive?Using,wecansetupanequationforwhenJillarrivesattheswimmingpool:Solvingfor,wegetthatJillgetstothepoolinofanhour,whichisminutes.DoingthesameforJack,wegetthatJackarrivesatthepoolinofanhour,whichinturnisminutes.Thus,JillhastowaitminutesforJacktoarriveatthepool.2015AMC8(Problems•AnswerKey•Resources(=182&cid=42&year=2015))Preceded byProblem2Followed byProblem41•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica()'sAmericanMathematicsCompetitions().Retrievedfrom=2015_AMC_8_Problems/Problem_3&oldid=810642015AMC8Problems/Problem3SolutionSeeAlsoCopyright©2016ArtofProblemSolvingTheCentervilleMiddleSchoolchessteamconsistsoftwoboysandthreegirls.Aphotographerwantstotakeapictureoftheteamtoappearinthelocalnewspaper.Shedecidestohavethemsitinarowwithaboyateachendandthethreegirlsinthemiddle.Howmanysucharrangementsarepossible?Therearewaystoordertheboysontheend,andtherearewaystoorderthegirlsinthemiddle.Wegettheanswertobe.2015AMC8(Problems•AnswerKey•Resources(=182&cid=42&year=2015))Preceded byProblem3Followed byProblem51•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica()'sAmericanMathematicsCompetitions().Retrievedfrom=2015_AMC_8_Problems/Problem_4&oldid=732242015AMC8Problems/Problem4SolutionSeeAlsoCopyright©2016ArtofProblemSolvingBilly'sbasketballteamscoredthefollowingpointsoverthecourseofthefirst11gamesoftheseason:Ifhisteamscores40inthe12thgame,whichofthefollowingstatisticswillshowanincrease?Whentheyscoreaonthenextgame,therangeincreasesfromto.Thismeanstheincreased.Becauseislessthanthescoreofeverygamethey'veplayedsofar,themeasuresofcenterwillneverrise.Onlymeasuresofspread,suchasthe,mayincrease.2015AMC8(Problems•AnswerKey•Resources(=182&cid=42&year=2015))Preceded byProblem4Followed byProblem61•2•3•4•5•6•7•8•9•10•11•12•13•14•15•16•17•18•19•20•21•22•23•24•25AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica()'sAmericanMathematicsCompetitions().Retrievedfrom=2015_AMC_8_Problems/Problem_5&oldid=808252015AMC8Problems