2015年AMC12B竞赛真题及答案

2015年AMC12B竞赛真题及答案

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时间:2019-10-03

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1、2015AMC12B竞赛真题Problem1Whatisthevalueof ?Problem2Mariedoesthreeequallytime-consumingtasksinarowwithouttakingbreaks.Shebeginsthefirsttaskat1:00PMandfinishesthesecondtaskat2:40PM.Whendoesshefinishthethirdtask?Problem3Isaachaswrittendownoneintegertwotimesandanotherintegerthree

2、times.Thesumofthefivenumbersis100,andoneofthenumbersis28.Whatistheothernumber?Problem4David,Hikmet,Jack,Marta,Rand,andToddwereina12-personracewith6otherpeople.Randfinished6placesaheadofHikmet.Martafinished1placebehindJack.Davidfinished2placesbehindHikmet.Jackfinished2place

3、sbehindTodd.Toddfinished1placebehindRand.Martafinishedin6thplace.Whofinishedin8thplace?Problem58/82015年AMC12BTheTigersbeattheSharks2outofthe3timestheyplayed.Theythenplayedmoretimes,andtheSharksendedupwinningatleast95%ofallthegamesplayed.Whatistheminimumpossiblevaluefor?Pro

4、blem6Backin1930,Tilliehadtomemorizehermultiplicationfactsfromto.Themultiplicationtableshewasgivenhadrowsandcolumnslabeledwiththefactors,andtheproductsformedthebodyofthetable.Tothenearesthundredth,whatfractionofthenumbersinthebodyofthetableareodd?Problem7Aregular15-gonhasli

5、nesofsymmetry,andthesmallestpositiveangleforwhichithasrotationalsymmetryisdegrees.Whatis ?Problem8Whatisthevalueof ?Problem9LarryandJuliusareplayingagame,takingturnsthrowingaballatabottlesittingonaledge.Larrythrowsfirst.Thewinneristhefirstpersontoknockthebottleofftheledge.

6、Ateachturntheprobabilitythataplayerknocksthebottleofftheledgeis,independentlyofwhathashappenedbefore.WhatistheprobabilitythatLarrywinsthegame?8/82015年AMC12BProblem10Howmanynoncongruentinteger-sidedtriangleswithpositiveareaandperimeterlessthan15areneitherequilateral,isoscel

7、es,norrighttriangles?Problem11Thelineformsatrianglewiththecoordinateaxes.Whatisthesumofthelengthsofthealtitudesofthistriangle?Problem12Let,,andbethreedistinctone-digitnumbers.Whatisthemaximumvalueofthesumoftherootsoftheequation ?Problem13Quadrilateralisinscribedinacirclewi

8、thand.Whatis?Problem14Acircleofradius2iscenteredat.Anequilateraltrianglewithside4hasavert

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