2012美国数学竞赛AMC8

华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，2012AMC8ProblemsProblem1Rachelleusespoundsofmeattomakehamburgersforherfamily.Howmanypoundsofmeatdoessheneedtomakehamburgersforaneighborhoodpicnic?SolutionProblem2InthecountryofEastWestmore,statisticiansestimatethereisababyborneveryhoursandadeatheveryday.Tothenearesthundred,howmanypeopleareaddedtothepopulationofEastWestmoreeachyear?SolutionProblem3OnFebruary13listedthelengthofdaylightas10hoursand24minutes,thesunrisewas,andthesunsetas.Thelengthofdaylightandsunrisewerecorrect,butthesunsetwaswrong.Whendidthesunreallyset?SolutionProblem4Peter'sfamilyordereda12-slicepizzafordinner.PeterateonesliceandsharedanothersliceequallywithhisbrotherPaul.WhatfractionofthepizzadidPetereat?Solution华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，Problem5Inthediagram,allanglesarerightanglesandthelengthsofthesidesaregivenincentimeters.Notethediagramisnotdrawntoscale.Whatis,incentimeters?SolutionProblem6Arectangularphotographisplacedinaframethatformsabordertwoincheswideonallsidesofthephotograph.Thephotographmeasures8incheshighand10incheswide.Whatistheareaoftheborder,insquareinches?SolutionProblem7Isabellamusttakefour100-pointtestsinhermathclass.Hergoalistoachieveanaveragegradeof95onthetests.Herfirsttwotestscoreswere97and91.Afterseeingherscoreonthethirdtest,sherealizedshecanstillreachhergoal.Whatisthelowestpossiblescoreshecouldhavemadeonthethirdtest?Solution华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，Problem8Ashopadvertiseseverythingishalfpriceintoday'ssale.Inaddition,acoupongivesa20%discountonsaleprices.Usingthecoupon,thepricetodayrepresentswhatpercentageofftheoriginalprice?SolutionProblem9TheFortWorthZoohasanumberoftwo-leggedbirdsandanumberoffour-leggedmammals.Ononevisittothezoo,Margiecounted200headsand522legs.HowmanyoftheanimalsthatMargiecountedweretwo-leggedbirds?SolutionProblem10Howmany4-digitnumbersgreaterthan1000aretherethatusethefourdigitsof2012?SolutionProblem11Themean,median,anduniquemodeofthepositiveintegers3,4,5,6,6,7,areallequal.Whatisthevalueof?SolutionProblem12Whatistheunitsdigitof?华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，SolutionProblem13Jamarboughtsomepencilscostingmorethanapennyeachattheschoolbookstoreandpaid.Sharonaboughtsomeofthesamepencilsandpaid.HowmanymorepencilsdidSharonabuythanJamar?SolutionProblem14IntheBIGN,amiddleschoolfootballconference,eachteamplayseveryotherteamexactlyonce.Ifatotalof21conferencegameswereplayedduringthe2012season,howmanyteamsweremembersoftheBIGNconference?SolutionProblem15Thesmallestnumbergreaterthan2thatleavesaremainderof2whendividedby3,4,5,or6liesbetweenwhatnumbers?SolutionProblem16Eachofthedigits0,1,2,3,4,5,6,7,8,and9isusedonlyoncetomaketwofive-digitnumberssothattheyhavethelargestpossiblesum.Whichofthefollowingcouldbeoneofthenumbers?Solution华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，Problem17Asquarewithintegersidelengthiscutinto10squares,allofwhichhaveintegersidelengthandatleast8ofwhichhavearea1.Whatisthesmallestpossiblevalueofthelengthofthesideoftheoriginalsquare?SolutionProblem18Whatisthesmallestpositiveintegerthatisneitherprimenorsquareandthathasnoprimefactorlessthan50?SolutionProblem19Inajarofred,green,andbluemarbles,allbut6areredmarbles,allbut8aregreen,andallbut4areblue.Howmanymarblesareinthejar?SolutionProblem20Whatisthecorrectorderingofthethreenumbers,,and,inincreasingorder?Solution华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，Problem21Marlahasalargewhitecubethathasanedgeof10feet.Shealsohasenoughgreenpainttocover300squarefeet.Marlausesallthepainttocreateawhitesquarecenteredoneachface,surroundedbyagreenborder.Whatistheareaofoneofthewhitesquares,insquarefeet?SolutionProblem22Letbeasetofninedistinctintegers.Sixoftheelementsare2,3,4,6,9,and14.Whatisthenumberofpossiblevaluesofthemedianof?SolutionProblem23Anequilateraltriangleandaregularhexagonhaveequalperimeters.Iftheareaofthetriangleis4,whatistheareaofthehexagon?SolutionProblem24Acircleofradius2iscutintofourcongruentarcs.Thefourarcsarejoinedtoformthestarfigureshown.Whatistheratiooftheareaofthestarfiguretotheareaoftheoriginalcircle?华数教育专业中小学奥数辅导，专注美国数学竞赛AMC8、10、12，美国数学邀请赛AIME，美国普林斯顿数学竞赛PUMAC，13524602295，SolutionProblem25Asquarewitharea4isinscribedinasquarewitharea5,withonevertexofthesmallersquareoneachsideofthelargersquare.Avertexofthesmallersquaredividesasideofthelargersquareintotwosegments,oneoflength,andtheotheroflength.Whatisthevalueof?Solution