2012美数学竞赛AMC8

Problem1Rachelleusespoundsofmeattomakehamburgersforherfamily.Howmanypoundsofmeatdoessheneedtomakehamburgersforaneighborhoodpicnic?Problem2InthecountryofEastWestmore,statisticiansestimatethereisababyborneveryhoursandadeatheveryday.Tothenearesthundred,howmanypeopleareaddedtothepopulationofEastWestmoreeachyear?Problem3OnFebruary13listedthelengthofdaylightas10hoursand24minutes,thesunrisewas,andthesunsetas.Thelengthofdaylightandsunrisewerecorrect,butthesunsetwaswrong.Whendidthesunreallyset?Problem4Peter'sfamilyordereda12-slicepizzafordinner.PeterateonesliceandsharedanothersliceequallywithhisbrotherPaul.WhatfractionofthepizzadidPetereat?Problem5Inthediagram,allanglesarerightanglesandthelengthsofthesidesaregivenincentimeters.Notethediagramisnotdrawntoscale.Whatis,incentimeters?Problem6Arectangularphotographisplacedinaframethatformsabordertwoincheswideonallsidesofthephotograph.Thephotographmeasures8incheshighand10incheswide.Whatistheareaoftheborder,insquareinches?Problem7Isabellamusttakefour100-pointtestsinhermathclass.Hergoalistoachieveanaveragegradeof95onthetests.Herfirsttwotestscoreswere97and91.Afterseeingherscoreonthethirdtest,sherealizedshecanstillreachhergoal.Whatisthelowestpossiblescoreshecouldhavemadeonthethirdtest?Problem8Ashopadvertiseseverythingishalfpriceintoday'ssale.Inaddition,acoupongivesa20%discountonsaleprices.Usingthecoupon,thepricetodayrepresentswhatpercentageofftheoriginalprice?Problem9TheFortWorthZoohasanumberoftwo-leggedbirdsandanumberoffour-leggedmammals.Ononevisittothezoo,Margiecounted200headsand522legs.HowmanyoftheanimalsthatMargiecountedweretwo-leggedbirds?Problem10Howmany4-digitnumbersgreaterthan1000aretherethatusethefourdigitsof2012?Problem11Themean,median,anduniquemodeofthepositiveintegers3,4,5,6,6,7,andareallequal.Whatisthevalueof?Problem12Whatistheunitsdigitof?Problem13Jamarboughtsomepencilscostingmorethanapennyeachattheschoolbookstoreandpaid.Sharonaboughtsomeofthesamepencilsandpaid.HowmanymorepencilsdidSharonabuythanJamar?Problem14IntheBIGN,amiddleschoolfootballconference,eachteamplayseveryotherteamexactlyonce.Ifatotalof21conferencegameswereplayedduringthe2012season,howmanyteamsweremembersoftheBIGNconference?Problem15Thesmallestnumbergreaterthan2thatleavesaremainderof2whendividedby3,4,5,or6liesbetweenwhatnumbers?Problem16Eachofthedigits0,1,2,3,4,5,6,7,8,and9isusedonlyoncetomaketwofive-digitnumberssothattheyhavethelargestpossiblesum.Whichofthefollowingcouldbeoneofthenumbers?Problem17Asquarewithintegersidelengthiscutinto10squares,allofwhichhaveintegersidelengthandatleast8ofwhichhavearea1.Whatisthesmallestpossiblevalueofthelengthofthesideoftheoriginalsquare?Problem18Whatisthesmallestpositiveintegerthatisneitherprimenorsquareandthathasnoprimefactorlessthan50?Problem19Inajarofred,green,andbluemarbles,allbut6areredmarbles,allbut8aregreen,andallbut4areblue.Howmanymarblesareinthejar?Problem20Whatisthecorrectorderingofthethreenumbers,,and,inincreasingorder?Problem21Marlahasalargewhitecubethathasanedgeof10feet.Shealsohasenoughgreenpainttocover300squarefeet.Marlausesallthepainttocreateawhitesquarecenteredoneachface,surroundedbyagreenborder.Whatistheareaofoneofthewhitesquares,insquarefeet?Problem22Letbeasetofninedistinctintegers.Sixoftheelementsare2,3,4,6,9,and14.Whatisthenumberofpossiblevaluesofthemedianof?Problem23Anequilateraltriangleandaregularhexagonhaveequalperimeters.Iftheareaofthetriangleis4,whatistheareaofthehexagon?Problem24Acircleofradius2iscutintofourcongruentarcs.Thefourarcsarejoinedtoformthestarfigureshown.Whatistheratiooftheareaofthestarfiguretotheareaoftheoriginalcircle?Problem25Asquarewitharea4isinscribedinasquarewitharea5,withonevertexofthesmallersquareoneachsideofthelargersquare.Avertexofthesmallersquaredividesasideofthelargersquareintotwosegments,oneoflength,andtheotheroflength.Whatisthevalueof?