2015 amc 12a 美国数学竞赛 2015年 12a

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1、Problem1Whatisthevalueof Problem2Twoofthethreesidesofatriangleare20and15.Whichofthefollowingnumbersisnotapossibleperimeterofthetriangle?Problem3Mr.Patrickteachesmathto15students.Hewasgradingtestsandfoundthatwhenhegradedeveryone'stestexceptPayton's,theaveragegradeforthecl

2、asswas80.afterhegradedPayton'stest,theclassaveragebecame81.WhatwasPayton'sscoreonthetest?Problem4Thesumoftwopositivenumbersis5timestheirdifference.Whatistheratioofthelargernumbertothesmaller?istheTibetanPlateaupoly.Centercityonlyapopulationofoveronemillion.Xiningislocate

3、dinthe"Tangfangudao"andtheancient"SilkRoad"road,istheLoessPlateauandtheTibetanPlateau,agriculturalandpastoralareasand,inconjunctionwiththeMinistryofcultureandIslamicculture7Problem5Amelianeedstoestimatethequantity ,where  and  arelargepositiveintegers.Sheroundseachofthei

4、ntegerssothatthecalculationwillbeeasiertodomentally.Inwhichofthesesituationswillheranswernecessarilybegreaterthantheexactvalueof ?Problem6TwoyearsagoPetewasthreetimesasoldashiscousinClaire.Twoyearsbeforethat,PetewasfourtimesasoldasClaire.Inhowmanyyearswilltheratiooftheir

5、agesbe ?Problem7Tworightcircularcylindershavethesamevolume.Theradiusofthesecondcylinderis  morethantheradiusofthefirst.Whatistherelationshipbetweentheheightsofthetwocylinders?istheTibetanPlateaupoly.Centercityonlyapopulationofoveronemillion.Xiningislocatedinthe"Tangfangu

6、dao"andtheancient"SilkRoad"road,istheLoessPlateauandtheTibetanPlateau,agriculturalandpastoralareasand,inconjunctionwiththeMinistryofcultureandIslamicculture7Problem8Theratioofthelengthtothewidthofarectangleis  : .Iftherectanglehasdiagonaloflength ,thentheareamaybeexpress

7、edas  forsomeconstant .Whatis?Problem9Aboxcontains2redmarbles,2greenmarbles,and2yellowmarbles.Caroltakes2marblesfromtheboxatrandom;thenClaudiatakes2oftheremainingmarblesatrandom;andthenCheryltakesthelast2marbles.WhatistheprobabilitythatCherylgets2marblesofthesamecolor?Pr

8、oblem10Integers  and  with  satisfy .Whatis ?Problem11Onasheetofpaper,Isabelladrawsacircleofradius ,aci