2015年AMC12B竞赛真题和答案解析

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1、...2015AMC12B竞赛真题Problem1Whatisthevalueof ?Problem2Mariedoesthreeequallytime-consumingtasksinarowwithouttakingbreaks.Shebeginsthefirsttaskat1:00PMandfinishesthesecondtaskat2:40PM.Whendoesshefinishthethirdtask?Problem3Isaachaswrittendownoneintegertwotimesandanotherintegerthreetimes.Thesu

2、mofthefivenumbersis100,andoneofthenumbersis28.Whatistheothernumber?Problem4David,Hikmet,Jack,Marta,Rand,andToddwereina12-personracewith6otherpeople.Randfinished6placesaheadofHikmet.Martafinished1placebehindJack.Davidfinished2placesbehindHikmet.Jackfinished2placesbehindTodd.Toddfinished1

3、placebehindRand.Martafinishedin6thplace.Whofinishedin8thplace?Problem5参考学习...TheTigersbeattheSharks2outofthe3timestheyplayed.Theythenplayedmoretimes,andtheSharksendedupwinningatleast95%ofallthegamesplayed.Whatistheminimumpossiblevaluefor?Problem6Backin1930,Tilliehadtomemorizehermultipli

4、cationfactsfromto.Themultiplicationtableshewasgivenhadrowsandcolumnslabeledwiththefactors,andtheproductsformedthebodyofthetable.Tothenearesthundredth,whatfractionofthenumbersinthebodyofthetableareodd?Problem7Aregular15-gonhaslinesofsymmetry,andthesmallestpositiveangleforwhichithasrotati

5、onalsymmetryisdegrees.Whatis ?Problem8Whatisthevalueof ?Problem9LarryandJuliusareplayingagame,takingturnsthrowingaballatabottlesittingonaledge.Larrythrowsfirst.Thewinneristhefirstpersontoknockthebottleofftheledge.Ateachturntheprobabilitythataplayerknocksthebottleofftheledgeis,independen

6、tlyofwhathashappenedbefore.WhatistheprobabilitythatLarrywinsthegame?参考学习...Problem10Howmanynoncongruentinteger-sidedtriangleswithpositiveareaandperimeterlessthan15areneitherequilateral,isosceles,norrighttriangles?Problem11Thelineformsatrianglewiththecoordinateaxes.Whatisthesumofthelengt

7、hsofthealtitudesofthistriangle?Problem12Let,,andbethreedistinctone-digitnumbers.Whatisthemaximumvalueofthesumoftherootsoftheequation ?Problem13Quadrilateralisinscribedinacirclewithand.Whatis?Problem14Acircleofradius2iscenteredat.Anequilateraltrianglewithside4hasavertexat.Whatis