2008 AMC 12B Problems

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1、2008AMC12BProblemsProblem1Abasketballplayermadebasketsduringagame.Eachbasketwaswortheitherorpoints.Howmanydifferentnumberscouldrepresentthetotalpointsscoredbytheplayer?Problem2Ablockofcalendardatesisshown.Theorderofthenumbersinthesecondrowistobereversed

2、.Thentheorderofthenumbersinthefourthrowistobereversed.Finally,thenumbersoneachdiagonalaretobeadded.Whatwillbethepositivedifferencebetweenthetwodiagonalsums?Problem3Asemiprobaseballleaguehasteamswithplayerseach.Leaguerulesstatethataplayermustbepaidatleas

3、tdollars,andthatthetotalofallplayers'salariesforeachteamcannotexceeddollars.Whatisthemaximumpossibllesalary,indollars,forasingleplayer?Problem4Oncircle,pointsandareonthesamesideofdiameter,,and.Whatistheratiooftheareaofthesmallersectortotheareaofthecircl

4、e?Problem5Aclasscollectsdollarstobuyflowersforaclassmatewhoisinthehospital.Rosescostdollarseach,andcarnationscostdollarseach.Nootherflowersaretobeused.Howmanydifferentbouquetscouldbepurchasedforexactlydollars?Problem6PostmanPetehasapedometertocounthisst

5、eps.Thepedometerrecordsuptosteps,thenflipsovertoonthenextstep.Peteplanstodeterminehismileageforayear.OnJanuaryPetesetsthepedometerto.Duringtheyear,thepedometerflipsfromtoforty-fourtimes.OnDecemberthepedometerreads.Petetakesstepspermile.Whichofthefollowi

6、ngisclosesttothenumberofmilesPetewalkedduringtheyear?Problem7Forrealnumbersand,define.Whatis?Problem8Pointsandlieon.Thelengthofistimesthelengthof,andthelengthofistimesthelengthof.Thelengthofiswhatfractionofthelengthof?Problem9Pointsandareonacircleofradi

7、usand.Pointisthemidpointoftheminorarc.Whatisthelengthofthelinesegment?Problem10BricklayerBrendawouldtakehourstobuildachimneyalone,andbricklayerBrandonwouldtakehourstobuilditalone.Whentheyworktogethertheytalkalot,andtheircombinedoutputisdecreasedbybricks

8、perhour.Workingtogether,theybuildthechimneyinhours.Howmanybricksareinthechimney?Problem11Acone-shapedmountainhasitsbaseontheoceanfloorandhasaheightof8000feet.Thetopofthevolumeofthemountainisabovewater.Whatisthedepthoftheoceanatth