2018AMC12B试题及答案

1、ProblemProblem1 1Kymbreascomicbookcollectioncurrentlyhas30comicbooksinit,andsheisaddingtohercollectionattherateof2comicbookspermonth.LaShawnscollectioncurrentlyhas10comicbooksinit,andheisaddingtohiscollectionattherateol6comrcbookspermonth.AfterhowmanymonthswillLaShawnscollectionhavetwiceasmanycomicb

2、ooksasKymbreaFs?(A)(A)1(B)(B)4(C)(C)5(D)(D)20(E)(E)25Problem2Problem2Realnumbers工，y,andzsatifytheinequalities0iVL1y0,and1s2.Whichofthefollowingnumbersisnecessarilypositive?(A)(A)y+(B)(B)y+xz(C)(C)y+y2(D)(D)y+2y2(E)(E)y+zProblem3Problem3-+3以Supposedthatxandwarenonzerorealnumberssuchthat-=-2.Whatisthe

3、valueof?x-Ayy(A)-3(B)(B)-1(C)1(D)2(E)3Problem4Problem4SamiasetoffonherbicycleIovisitherfriend,travelingatanaveragespeedof17kilometersperhourWhenshehadgonehalfthedistancetoherfriendshouse,atirewentflat,andshewalkedtherestofthewayat5kilometersperhourInallittookher14minutestoreachherfriendshouse.Inkilo

4、metersroundedtothenearesttenthrhowfardidSamiawalk?(A)2.0(B)2.2(C)2.8(D)3.4(E)4.4Problem5Problem5Thedataset|6,19.33.33,39,11H11/61(D)(E)(E)- -Jiri上Problem9Problem9Acirclehascenter(10T4)andradius13.Anothercfrclehascenter(3,9)andradius/65.Thelinepassingthroughthetwopointsofintersectionofthetwocirclesha

5、sequationxA-y=c.Whatisc?IyIy(A)(A)3 3(B)(B)3V(C)3V(C)44历(D)(D)6(E)6(E)Problem10Problem10AtTypicoHighSchool,60%ofthestudentslikedancing,andtherestdislikeitOfthosewholikedancing,80%saythattheylikeit,andtherestsaythattheydislikeit.Ofthosewhodislikedancing,90%saythattheydislikei、andtherestsaythattheylik

6、eit.Whatfractionofstudentswhosaytheydislikedancingactuallylikeit?(A)(A)10%10%(B)(B)12%12%(C)(C)20%20%(D)(D)25%25%(E)(E)3333：% %TjProblemProblem1111Callapositiveintegermonotonousifitisaone-digitnumberoritsdigits,whenreadfromlefttoright,formeitherastrictlyincreasingorastrictlydecreasingsequence.Forexa

7、mple,3+23578,and987620aremonotonous,but88,7434,and23557arenot.Howmanymonotonouspositiveintegersarethere?(A)(A)1024(13)(13)1524(C)(C)1533(D)(D)1536(E)(E)2048Problem12Problem12Whatisthesumoftherootsotzl=64thalhaveapositiverealpart?(A)2(B)4(C)e+2A(D)2v/2+(E)(1+/5)+(1+/5)iProblem13Problem13Inthefigurebe

8、low,3ofthe6disksaretobepaintedblue,2aretobepaintedred,andistobepaintedgreen.Twopaintingsthatcanbeobtainedfromoneanotherbyarotationorarejectionoftheentirefigureareconsideredthesame.Howmanydifferentpaintingsarepossible?(A)6(B)8(C)(A)6(B)8(C)9(D)12(E)(E)15Problem14Problem14Anice-creamnoveltyitemconsist

9、sofacupintheshapeofa4-inch-tallfrustumofarightcircularcone,wrtha2-inch-diameterbaseatthebottomanda4inchdiameterbaseatthetop,packedsolidwithicecream,togetherwithasolidconeoficecreamofheight4inches,whosebase,atthebottom,isthetopbaseofthefrustum.Whatisthetotalvolumeoftheicecream,incubicinches?447r(C)(C

10、)12vr(D)(D)147r(E)(E)(A)(A)8TT(B)120140120(E)3?ProblemProblem1515LetABCbeanequilateraltriangle.ExtendsideABbeyondBtoapointBfsothatBB!=3/1RSimilarly,extendsideBCbeyondCtoapointC1sothatCCf=3BCtandextendsideCAbeyondAtoapointA!sothatAAf=3cAWhatistheratiooftheareaofBfCrtotheareaofABC?(A)(A)9:1(B)16:1(C)(

11、C)25:1(D)36:1(E)(E)37:1Problem16Problem16Thenumber21=51,090,942,171.709,440,(MJOhasover60,000positiveintegerdivisors.Oneofthemischosenatrandom.Whatistheprobabilitythatitisodd?5白表(D)iProblem17Problem17AcoinisbiasedinsuchawaythatoneachtosstheprobabilityAheadsis-andtheprobabilityoftailsisTheoutcomesoft

12、hetossesareindependent.AplayerhasthechoiceofplayingGameAorGameB.InGameAshetossesthecointhreetimesandwinsifallthreeoutcomesarethesame.InGameBshetossesIhecoinfourtimesandwinsifbo1htheoutcomesofthefirstandsecondtossesarethesameandtheoutcomesofthethirdandfourthtossesarethesame.HowdothechancesofwinningGa

13、meAcomparetothechancesofwinningGameB?4(A)(A)TheprobabilityofwinningGameAis-lessIhantheprobabilityofwinningGameB.ol2(B)(B)TheprobabilityofwinningGameAislessthantheprobabilityofwinningGameB.81(C)(C)Theprobabilitiesarethesame.2(D)(D)TheprobabilityofwinningGameAisgreaterthantheprobabilityofwinningGameB.

14、814(E)(E)TheprobabilityofwinningGameAisgreaterthantheprobabilityofwinningGameB.olProblem18Problem18ThediameterABofacircleofradius2isextendedtoapointDoutsidethecirclesothatBD=3.PointEischosensothatED=5andlineEDisperpendiculartolineAD.SegmentAEintersectsthecircleatapointCbetweenAandE.WhatistheareaotA4

15、/?C?ProblemProblem1919LetN=123456789LOI112.4344bethe79-digitnumberthatIsformedbywritingtheintegersfrom1to44inorder,oneaftertheotherWhatistheremainderwhenNisdividedby43?(A)1(A)1(13)(13)1(C)9(D)(D)18(E)(E)44Problem20Problem20Realnumbers工andyarechosenindependentlyanduniformlyatrandomfromtheinterval(0.1

16、).Whatistheprobabilitythatlog2=lug.where|rdenotesthegreatestintegerlessthanorequaltotherealnumberr?(A)(B)；(C)3(D)(D)1(E)i(E)iProblem21Problem21LastyearIsabellatook7mathtestsandeGeived7differentscores,eachanintegerbetween9land100,inclusive.Aftereachtestshenoticedthattheaverageofhertestscoreswasaninte

17、ger.Herscoreontheseventhtestwas95,Whatwasherscoreonthesixthtest?(A)92(B)(B)91(C)96(D)98(E)(E)100Problem22Problem22Abb儿Bernardo.CarltandDebraplayagameinwhicheachofthemstartswithfourcoins.Thegameconsistsoffourrounds.3neachround,fourballsareplacedinanum-onegreen,onered,andtwowhite.Theplayerseachdrawaba

18、llatrandomwithoutreplacementWhoevergetsthegreenballgivesonecointowhoevergetstheredball.Whatistheprobabilitythat,attheendofthefourthround,eachoftheplayershasfourcoins?7(E)(E)48Problem23Problem23Thegraphofy=f(琦wheref(T)isapolynomialofdegree3,containspoints/I(2,4),/?(3.and0(4J6),LinesABtAC：andBCinterse

19、ctthegraphagainatpointsDtE,andFtrespectively,andthesumofthecoordinatesofI)tE、and产is24.Whatis/(0)?(A)(A)-2-2(B)0(C)2(C)2(D)(E)(D)(E)8 85(D)(D)17144ProblemProblem2424QuadrilateralABCDhasrightanglesatBandC.AABCABCD,andA13BC.ThereisapointEintheinteriorofABCDsuchthatZXABC/CEBandtheareaofAEDis17timestheareaofACERWhatis黑？BC(A)1+x/2(B)2+(C)