2003A年AMC10

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1、Problem1Whatisthedifferencebetweenthesumofthefirst  evencountingnumbersandthesumofthefirst  oddcountingnumbers?SolutionProblem2MembersoftheRockhamSoccerLeaguebuysocksandT-shirts.Sockscost$4perpairandeachT-shirtcosts$5morethanapairofsocks.Eachmemberneedsonepairofsock

2、sandashirtforhomegamesandanotherpairofsocksandashirtforawaygames.Ifthetotalcostis$2366,howmanymembersareintheLeague?SolutionProblem3Asolidboxis  cmby  cmby  cm.Anewsolidisformedbyremovingacube  cmonasidefromeachcornerofthisbox.Whatpercentoftheoriginalvolumeisremoved

3、?SolutionProblem4IttakesMary  minutestowalkuphill  kmfromherhometoschool,butittakesheronly  minutestowalkfromschooltoherhomealongthesameroute.Whatisheraveragespeed,inkm/hr,fortheroundtrip?SolutionProblem5Let  and  denotethesolutionsof .Whatisthevalueof ?SolutionProb

4、lem6Define  tobe  forallrealnumbers  and .Whichofthefollowingstatementsisnottrue? forall  and  forall  and  forall  forall  if SolutionProblem7Howmanynon-congruenttriangleswithperimeter  haveintegersidelengths?SolutionProblem8Whatistheprobabilitythatarandomlydrawnpo

5、sitivefactorof  islessthan SolutionProblem9Simplify.SolutionProblem10Thepolygonenclosedbythesolidlinesinthefigureconsistsof4congruentsquaresjoinededge-to-edge.Onemorecongruentsquareisattatchedtoanedgeatoneoftheninepositionsindicated.Howmanyofthenineresultingpolygons

6、canbefoldedtoformacubewithonefacemissing?SolutionProblem11Thesumofthetwo5-digitnumbers  and  is .Whatis ?SolutionProblem12Apoint  israndomlypickedfrominsidetherectanglewithvertices , , ,and .Whatistheprobabilitythat ?SolutionProblem13Thesumofthreenumbersis .Thefirst

7、isfourtimesthesumoftheothertwo.Thesecondisseventimesthethird.Whatistheproductofallthree?SolutionProblem14Let  bethelargestintegerthatistheproductofexactly3distinctprimenumbers , ,and ,where  and  aresingledigits.Whatisthesumofthedigitsof ?SolutionProblem15Whatisthep

8、robabilitythatanintegerintheset  isdivisibleby  andnotdivisibleby ?SolutionProblem16Whatistheunitsdigitof ?SolutionProblem17Thenumberofinc