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1、2015AMC12B竞赛真题Problem1Whatisthevalueof ?Problem2Mariedoesthreeequallytime-consumingtasksinarowwithouttakingbreaks.Shebeginsthefirsttaskat1:00PMandfinishesthesecondtaskat2:40PM.Whendoesshefinishthethirdtask?Problem3Isaachaswrittendownoneintegertwotimesandanotherintegerthreetimes.The
2、sumofthefivenumbersis100,andoneofthenumbersis28.Whatistheothernumber?Problem4David,Hikmet,Jack,Marta,Rand,andToddwereina12-personracewith6otherpeople.Randfinished6placesaheadofHikmet.Martafinished1placebehindJack.Davidfinished2placesbehindHikmet.Jackfinished2placesbehindTodd.Toddfi
3、nished1placebehindRand.Martafinishedin6thplace.Whofinishedin8thplace?Problem5TheTigersbeattheSharks2outofthe3timestheyplayed.Theythenplayedmoretimes,andtheSharksendedupwinningatleast95%ofallthegamesplayed.Whatistheminimumpossiblevaluefor?Problem6Backin1930,Tilliehadtomemorizehermul
4、tiplicationfactsfromto.Themultiplicationtableshewasgivenhadrowsandcolumnslabeledwiththefactors,andtheproductsformedthebodyofthetable.Tothenearesthundredth,whatfractionofthenumbersinthebodyofthetableareodd?Problem7Aregular15-gonhaslinesofsymmetry,andthesmallestpositiveangleforwhichi
5、thasrotationalsymmetryisdegrees.Whatis ?Problem8Whatisthevalueof ?Problem9LarryandJuliusareplayingagame,takingturnsthrowingaballatabottlesittingonaledge.Larrythrowsfirst.Thewinneristhefirstpersontoknockthebottleofftheledge.Ateachturntheprobabilitythataplayerknocksthebottleofftheled
6、geis,independentlyofwhathashappenedbefore.WhatistheprobabilitythatLarrywinsthegame?Problem10Howmanynoncongruentinteger-sidedtriangleswithpositiveareaandperimeterlessthan15areneitherequilateral,isosceles,norrighttriangles?Problem11Thelineformsatrianglewiththecoordinateaxes.Whatisthe
7、sumofthelengthsofthealtitudesofthistriangle?Problem12Let,,andbethreedistinctone-digitnumbers.Whatisthemaximumvalueofthesumoftherootsoftheequation ?Problem13Quadrilateralisinscribedinacirclewithand.Whatis?Problem14Acircleofradius2iscenteredat.Anequilateraltrianglewithside4hasavertex
8、at.Whatisthedifferencebetw
