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2021秋季AMC10A试题与答案Whatisthevalueof⑵微高219A7B21C49D64E91Answer:CMenkarahasa4x6indexcard.Ifsheshortensthelengthofonesideofthiscardby1inchthecardwouldhavearea18squareinches.Whatwouldtheareaofthecardbeinsquareinchesifinsteadsheshortensthelengthoftheothersideby1inchA16B17C18D19E20Answer:EWhatisthemaximumnumberofballsofclaywithradius2thatcancompletelyfitinsideacubeofsidelength6assumingthattheballscanbereshapedbutnotcompressedbeforetheyarepackedinthecubeA3B4C5D6E7Answer:DMr.Lopezhasachoiceoftworoutestogettowork.RouteAis6mileslongandhisaveragespeedalongthisrouteis30milesperhour.RouteBis5mileslongandhisaveragespeedalongthisrouteis40milesperhourexceptforaa-milestretchinaschoolzonewherehisaveragespeedis20milesperhour.ByhowmanyminutesisRouteBquickerthanRouteA3cl13B3-C4-D5-E6-Thesix-digitnumber20210AisprimeforonlyonedigitA.WhatisAA1B3C5D7E9Answer:EElmertheemutakes44equalstridestowalkbetweenconsecutivetelephonepolesonaruralroad.Oscartheostrichcancoverthesamedistancein12equalleaps.Thetelephonepolesareevenlyspacedandthe41stpolealongthisroadisexactlyonemile5280feetfromthefirstpole.HowmuchlongerinfeetisOscarsleapthanElmersstrideA6B8C10D11E15Answer:BAsshowninthefigurebelowpointEliesintheoppositehalf-planedeterminedbylineCDfrompointAsothat/.CDE=110°.PointFliesonADsothatDE=DFandABCDisasquare.WhatisthedegreemeasureofAAFEA160B164C166D170E174Answer:DAtwo-digitpositiveintegerissaidtobecuddlyifitisequaltothesumofitsnonzerotensdigitandthesquareofitsunitsdigit.Howmanytwo-digitpositiveintegersarecuddlyA0B1C2D3E4Whenacertainunfairdieisrolledanevennumberis3timesaslikelytoappearasanoddnumber.Thedieisrolledtwice.Whatistheprobabilitythatthesumofthenumbersrollediseven34595A8B9C9DT6E8Answer:EAschoolhas100studentsand5teachers.Inthefirstperiodeachstudentistakingoneclassandeachteacheristeachingoneclass.Theenrollmentsintheclassesare5020205and
5.Lettbetheaveragevalueobtainedifateacherispickedatrandomandthenumberofstudentsintheirclassisnoted.Letsbetheaveragevalueobtainedifastudentispickedatrandomandthenumberofstudentsintheirclassincludingthatstudentisnoted.WhatisZ—5A-
18.5B-
13.5C0D
13.5E
18.5Answer:BEmilyseesashiptravelingataconstantspeedalongastraightsectionofariver.Shewalksparalleltotheriverbankatauniformratefasterthantheship.Shecounts210equalstepswalkingfromthebackoftheshiptothefront.Walkingintheoppositedirectionshecounts42stepsofthesamesizefromthefrontoftheshiptotheback.IntermsofEmilysequalstepswhatisthelengthoftheshipA70B84C98D105E126Answer:AThebase-ninerepresentationofthenumberNis27006000052nine.WhatistheremainderwhenNisdividedby5Eachof6ballsisrandomlyandindependentlypaintedeitherblackorwhitewithequalprobability.Whatistheprobabilitythateveryballisdifferentincolorfrommorethanhalfoftheother5balls11151AB6Q4D16®2Answer:DHowmanyorderedpairsxyofrealnumberssatisfythefollowingsystemofequationsx2+=9|x|+|y|-42=1A1B2C3D5E7Answer:DIsoscelestriangleABChasAB=AC=3\/6andacirclewithradius5\/2istangenttolineABatBandtolineACatC.WhatistheareaofthecirclethatpassesthroughverticesABandCA247rB257rC267rD27兀E287rAnswer:CThegraphof/x=||_xj|—11_1—xj|issymmetricaboutwhichofthefollowingHere|_xjisthegreatestintegernotexceedingx.Athej-axisBthelinex=1CtheoriginDthepoint10Ethepoint10AnarchitectisbuildingastructurethatwillplaceverticalpillarsattheverticesofregularhexagonABCDEF.whichislyinghorizontallyontheground.Thesixpillarswillholdupaflatsolarpanelthatwillnotbeparalleltotheground.TheheightsofthepillarsatAB.andCare129and10metersrespectively.WhatistheheightinmetersofthepillaratEA9B673C873D17E1273Answer:DAfarmersrectangularfieldispartitionedintoa2by2gridof4rectangularsectionsasshowninthefigure.Ineachsectionthefarmerwillplantonecrop:cornwheatsoybeansorpotatoes.Thefarmerdoesnotwanttogrowcomandwheatinanytwosectionsthatshareaborderandthefarmerdoesnotwanttogrowsoybeansandpotatoesinanytwosectionsthatshareaborder.GiventheserestrictionsinhowmanywayscanthefarmerchoosecropstoplantineachofthefoursectionsofthefieldA12B64C84D90E144Answer:CAdiskofradius1rollsallthewayaroundtheinsideofasquareofsidelengths4andsweepsoutaregionofareaA.Aseconddiskofradius1rollsallthewayaroundtheoutsideofthesamesquareandsweepsoutaregionofarea2A.Thevalueofscanbewrittenas〃+等whereabandcarepositiveintegersandbandcarerelativelyprime.Whatis〃+/7+cA10B11C12D13E
1420.Forhowmanyorderedpairs/7cofpositiveintegersdoesneitherx2++c=0norx2+exh=0havetwodistinctrealsolutionsA4B6C8D12E16Answer:B
21.Eachof20ballsistossedindependentlyandatrandomintooneof5bins.Letpbetheprobabilitythatsomebinendsupwith3ballsanotherwith5ballsandtheotherthreewith4ballseach.Letqbetheprobabilitythateverybinendsupwith4balls.WhatisA1B4C8D12E16Answer:E
22.Insidearightcircularconewithbaseradius5andheight12arethreecongruentsphereseachwithradiusr.Eachsphereistangenttotheothertwospheresandalsotangenttothebaseandsideofthecone.Whatisr3A590—40-144-2573BC2D---E|Answer:BForeachpositiveintegern.letbetwicethenumberofpositiveintegerdivisorsofn.andfory2letForhowmanyvaluesofn50isfson=12A7B8C9D10E11Answer:DEachofthe12edgesofacubeislabeled0or
1.Twolabelingsareconsidereddifferentevenifonecanbeobtainedfromtheotherbyasequenceofoneormorerotationsand/orreflections.Forhowmanysuchlabelingsisthesumofthelabelsontheedgesofeachofthe6facesofthecubeequalto2A8B10C12D16E20Answer:EAquadraticpolynomialpxwithrealcoefficientsandleadingcoefficient1iscalleddisrespectfuliftheequationppx=0issatisfiedbyexactlythreerealnumbers.Amongallthedisrespectfulquadraticpolynomialsthereisauniquesuchpolynomial/xforwhichthesumoftherootsismaximized.Whatis/151-59A-B-C-D1E-lo2ooAnswer:A。