2015年AMC8试题及答案.pdf

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1、2015AMC8Problems/Problem1Howmanysquareyardsofcarpetarerequiredtocoverarectangularfloorthatisfeetlongandfeetwide?(Thereare3feetinayard.)SolutionFirst,wemultiplytogetthatyouneedsquarefeetofcarpetyouneedtocover.Sincetherearesquarefeetinasquareyard,youdividebytogetsquareyards,soouranswer

2、is.Solution2Sincetherearefeetinayard,wedividebytoget,andbytoget.Tofindtheareaofthecarpet,wethenmultiplythesetwovaluestogethertoget.SeeAlso2015AMC8(Problems•AnswerKey•Resources(http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=2015))PrecededbyFollowedbyFirstProb

3、lemProblem21•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(http://www.maa.org)'sAmericanMathematicsCompetitions(http://amc.maa.org).Placement:EasyGeometryRetrie

4、vedfrom"http://artofproblemsolving.com/wiki/index.php?title=2015_AMC_8_Problems/Problem_1&oldid=80323"Copyright©2016ArtofProblemSolving2015AMC8Problems/Problem2Pointisthecenteroftheregularoctagon,andisthemidpointofthesideWhatfractionoftheareaoftheoctagonisshaded?Contents1Solution12So

5、lution23Solution34SeeAlsoSolution1Sinceoctagonisaregularoctagon,itissplitintoequalparts,suchastriangles,etc.Theseparts,sincetheyareallequal,areoftheoctagoneach.Theshadedregionconsistsofoftheseequalpartsplushalfofanother,sothefractionoftheoctagonthatisshadedisSolution2Theoctagonhasbee

6、ndividedupintoidenticaltriangles(andthustheyeachhaveequalarea).Sincetheshadedregionoccupiesoutofthetotaltriangles,theansweris.Solution3ForstarterswhatIfindhelpfulistodividethewholeoctagonupintotrianglesasshownhere:Nowitisjustamatterofcountingthelargertrianglesrememberthatandarenotful

7、ltrianglesandareonlyhalfforthesepurposes.Wecountitupandwegetatotalofoftheshapeshaded.Wethensimplifyittogetouranswerof.SeeAlso2015AMC8(Problems•AnswerKey•Resources(http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=2015))PrecededbyFollowedbyProblem1Problem31•2•3•

8、4•5•6•7•8•9•