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1、2016AMC12AProblem1Whatisthevalueof ?SolutionProblem2Forwhatvalueof does ?SolutionProblem3Theremaindercanbedefinedforallrealnumbers and with bywhere denotesthegreatestintegerlessthanorequalto .Whatisthevalueof ?SolutionProblem4Themean,median,andmodeofthe datavalues areallequalto .What
2、isthevalueof ?SolutionProblem5Goldbach'sconjecturestatesthateveryevenintegergreaterthan2canbewrittenasthesumoftwoprimenumbers(forexample, ).Sofar,noonehasbeenabletoprovethattheconjectureistrue,andnoonehasfoundacounterexampletoshowthattheconjectureisfalse.Whatwouldacounterexampleconsistof?So
3、lutionProblem6Atriangulararrayof coinshas coininthefirstrow, coinsinthesecondrow, coinsinthethirdrow,andsoonupto coinsinthe throw.Whatisthesumofthedigitsof ?SolutionProblem7Whichofthesedescribesthegraphof ?SolutionProblem8Whatistheareaoftheshadedregionofthegiven rectangle?SolutionPr
4、oblem9Thefivesmallshadedsquaresinsidethisunitsquarearecongruentandhavedisjointinteriors.Themidpointofeachsideofthemiddlesquarecoincideswithoneoftheverticesoftheotherfoursmallsquaresasshown.Thecommonsidelengthis ,where and arepositiveintegers.Whatis ?SolutionProblem10Fivefriendssatinamovi
5、etheaterinarowcontaining seats,numbered to fromlefttoright.(Thedirections"left"and"right"arefromthepointofviewofthepeopleastheysitintheseats.)DuringthemovieAdawenttothelobbytogetsomepopcorn.Whenshereturned,shefoundthatBeahadmovedtwoseatstotheright,Cecihadmovedoneseattotheleft,andDeeandEd
6、iehadswitchedseats,leavinganendseatforAda.InwhichseathadAdabeensittingbeforeshegotup?SolutionProblem11Eachofthe studentsinacertainsummercampcaneithersing,dance,oract.Somestudentshavemorethanonetalent,butnostudenthasallthreetalents.Thereare studentswhocannotsing, studentswhocannotdance,an
7、d studentswhocannotact.Howmanystudentshavetwoofthesetalents?SolutionProblem12In , , ,and .Point lieson ,and bisects .Point lieson ,and bisects .Thebisectorsintersectat .Whatistheratio : ?SolutionProblem13Let beapositivemultipleof .Oneredballand gr
