AMC8试题及答案.pdf

AMC8试题及答案.pdf

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Copyright2016ArtofProblemSolvingHowmanysquareyardsofcarpetarerequiredtocoverarectangularfloorthatisfeetlongandfeetwide?

（Thereare3feetinayard.）First,wemultiplytogetthatyouneedsquarefeetofcarpetyouneedtocover.Sincetherearesquarefeetinasquareyard,youdividebytogetsquareyards,soouransweris.Sincetherearefeetinayard,wedividebytoget,andbytoget.Tofindtheareaofthecarpet,wethenmultiplythesetwovaluestogethertoget.2015AMC8（ProblemsAnswerKeyResources（http:

/FirstProblemFollowedbyProblem212345678910111213141516171819202122232425AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica（http:

/www.maa.org）sAmericanMathematicsCompetitions（http:

/amc.maa.org）.Placement:

EasyGeometryRetrievedfromhttp:

/AMC8Problems/Problem1SolutionSolution2SeeAlsoPointisthecenteroftheregularoctagon,andisthemidpointofthesideWhatfractionoftheareaoftheoctagonisshaded?

1Solution12Solution23Solution34SeeAlsoSinceoctagonisaregularoctagon,itissplitintoequalparts,suchastriangles,etc.Theseparts,sincetheyareallequal,areoftheoctagoneach.Theshadedregionconsistsofoftheseequalpartsplushalfofanother,sothefractionoftheoctagonthatisshadedis2015AMC8Problems/Problem2ContentsSolution1Solution2Theoctagonhasbeendividedupintoidenticaltriangles（andthustheyeachhaveequalarea）.Sincetheshadedregionoccupiesoutofthetotaltriangles,theansweris.ForstarterswhatIfindhelpfulistodividethewholeoctagonupintotrianglesasshownhere:

Nowitisjustamatterofcountingthelargertrianglesrememberthatandarenotfulltrianglesandareonlyhalfforthesepurposes.Wecountitupandwegetatotalofoftheshapeshaded.Wethensimplifyittogetouranswerof.2015AMC8（ProblemsAnswerKeyResources（http:

/Problem1FollowedbyProblem312345678910111213141516171819202122232425AllAJHSME/AMC8ProblemsandSolutionsSolution3SeeAlsoCopyright2016ArtofProblemSolvingJackandJillaregoingswimmingatapoolthatisonemilefromtheirhouse.Theyleavehomesimultaneously.Jillridesherbicycletothepoolataconstantspeedofmilesperhour.Jackwalkstothepoolataconstantspeedofmilesperhour.HowmanyminutesbeforeJackdoesJillarrive?

Using,wecansetupanequationforwhenJillarrivesattheswimmingpool:

Solvingfor,wegetthatJillgetstothepoolinofanhour,whichisminutes.DoingthesameforJack,wegetthatJackarrivesatthepoolinofanhour,whichinturnisminutes.Thus,JillhastowaitminutesforJacktoarriveatthepool.2015AMC8（ProblemsAnswerKeyResources（http:

/Problem2FollowedbyProblem412345678910111213141516171819202122232425AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica（http:

/www.maa.org）sAmericanMathematicsCompetitions（http:

/amc.maa.org）.Retrievedfromhttp:

/AMC8Problems/Problem3SolutionSeeAlsoCopyright2016ArtofProblemSolvingTheCentervilleMiddleSchoolchessteamconsistsoftwoboysandthreegirls.Aphotographerwantstotakeapictureoftheteamtoappearinthelocalnewspaper.Shedecidestohavethemsitinarowwithaboyateachendandthethreegirlsinthemiddle.Howmanysucharrangementsarepossible?

Therearewaystoordertheboysontheend,andtherearewaystoorderthegirlsinthemiddle.Wegettheanswertobe.2015AMC8（ProblemsAnswerKeyResources（http:

/Problem3FollowedbyProblem512345678910111213141516171819202122232425AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica（http:

/www.maa.org）sAmericanMathematicsCompetitions（http:

/amc.maa.org）.Retrievedfromhttp:

/AMC8Problems/Problem4SolutionSeeAlsoCopyright2016ArtofProblemSolvingBillysbasketballteamscoredthefollowingpointsoverthecourseofthefirst11gamesoftheseason:

Ifhisteamscores40inthe12thgame,whichofthefollowingstatisticswillshowanincrease?

Whentheyscoreaonthenextgame,therangeincreasesfromto.Thismeanstheincreased.Becauseislessthanthescoreofeverygametheyveplayedsofar,themeasuresofcenterwillneverrise.Onlymeasuresofspread,suchasthe,mayincrease.2015AMC8（ProblemsAnswerKeyResources（http:

/Problem4FollowedbyProblem612345678910111213141516171819202122232425AllAJHSME/AMC8ProblemsandSolutionsTheproblemsonthispagearecopyrightedbytheMathematicalAssociationofAmerica（http:

/www.maa.org）sAmericanMathematicsCompetitions（http:

/amc.maa.org）.Retrievedfromhttp:

/AMC8Problems/Problem5SolutionSolution2Copyright2016ArtofProblemSolvingIn,and.Whatistheareaof?

Weknowthesemi-perimeterofis.Next,weuseHeronsFormul