2015美国数学竞赛(
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• Problem6 TwoyearsagoPetewasthreetimesasoldashiscousinClaire.Twoyearsbeforethat,PetewasfourtimesasoldasClaire.Inhowmanyyearswilltheratiooftheiragesbe
smaller? Problem5 Amelianeedstoestimatethequantity,
whereandarelargepositiveintegers.Sheroundseachoftheintegerssothatthecalculationwillbeeasiertodomentally.Inwhi chofthesesituationswillheranswernecessarilybegreaterthantheexactvalueof?
•
Problem10Integersandwithsatisfy.Whatis
?Problem11 Onasheetofpaper,Isabelladrawsacircleofradius,acircleofradius,andallpossiblelinessimultaneouslytangenttobothcircl es.Isabellanoticesthatshehasdrawnexactlylines.Howmanydifferentvaluesofare
scores?Problem14 http://www.wendangxiazai.com/b-8f66dc3df61fb7360a4c656c-3.html
•
Whatisthevalueofforwhich
? Problem15 Whatistheminimumnumberofdigitstotherightofthedecimalpointneededtoexpressthe
stBiblioteka Baidund?Problem18 Thezerosofthe
function possiblevaluesof
?areintegers.Whatisthesumofthe Problem19
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
fractionasa
decimal? Problem16Tetrahedronhas.Whatisthevolumeofthe
tetrahedron?and
Problem17
Eightpeoplearesittingaroundacirculartable, eachholdingafaircoin.Alleightpeoplefliptheircoinsandthosewhoflipheadsstandwhilethosewhofliptailsremainseated.Whatistheprobabilitythatnotwoadjacentp eoplewill
possible?Problem12 The
parabolasandintersectthecoordinateaxesinexactly
.Whatis
?fourpoint http://www.wendangxiazai.com/b-8f66dc3df61fb7360a4c656c-3.html s,andthesefourpointsaretheverticesofakiteofarea Problem13 Aleaguewith12teamsholdsaroundrobintournament,witheachteamplayingeveryotherteamexactlyonce.Gameseitherendwithoneteamvictoriousorelseen dinadraw.Ateamscores2pointsforeverygameitwinsand1pointforeverygameitdraws.WhichofthefollowingisNOTatrues tatementaboutthelistof12
cylinders? Problem8 Theratioofthelengthtothe widthofarectangle
is:.Iftherectanglehasdiagonalof
length,thentheareamaybeexpressed
asforsome
constantWhatis
?. Problem9 Aboxcontains2redmarbles,2greenmarbles,and2yellowmarbles.Caroltakes2marblesfromtheboxatrandom;thenClaudiatakes2oftheremainingmarblesatrand om;andthenCheryltakesthelast2marbles.WhatistheprobabilitythatCherylgets2marblesofthesamecolor?
Forsomepositiveintegers,thereisa quadrilateral sidelengths,perimeter,rightangles at and , manydifferentvalues ofare possible?withpositiveinteger, and.How Problem20 Isoscelestriangles andarenotcongruentbuthavethesameareaandthesameperimeter.Thesides ofhavelengthsofand,whilethose ofhavelengthsofand.Whichofthefollowingnumbersisclosestto ? Problem21 Acircleofradius withequation What is ?passesthroughbothfociof,andexactlyfourpointson,theellipse.Thesetofallpossiblevaluesofisaninterval. Problem22 Foreachpositiveintegern,let consistingsolelyoftheletters morethanthreeandbethenumberofsequencesoflengthn,withnomorethanthreesinarowandnoisdividedby 12?sinarow.Whatistheremainderwhen Problem23 Letbeasquareofsidelength1.Twopointsarechosenindependentlyatrandomonthesidesof.Theprobabilitythatthestraight-linedistancebetweenthepointsisatleast is is?, whereandarepositiveintegers and.What •
2015美国数学竞赛(AMC12)试题
• of Problem2 Twoofthethreesidesofatriangleare20and15.Whichofthefollowingnumbersisnotapossibleperimeterofthe
triangle? Problem3 Mr.Patrickteachesmathto15students.Hewasgradingtestsandfoundthatwhenhegradedeveryone'stestexceptPayton's, theaveragegradefortheclasswas80.afterhegradedPayton'stest,theclassaveragebecame81.WhatwasPayton'sscoreo nthe test? Problem4 Thesumoftwopositivenumbersis5timestheirdifference.Whatistheratioofthelargernumbertothe
? Problem7 Tworightcircularcylindershavethesamevolume.Theradiusofthesecondcylinder
ismorethantheradiusofthefirst.Whatistherelationshipbetweentheheightsofthetwo