AMC10B试题及答案精编版

最新资料推荐PAGE\*MERGEFORMAT#Problem1Katebakesa20-inchby18-inchpanofcornbread.Thecornbreadiscutintopiecesthatmeasure2inchesby2inches.Howmarrypiecesofcornbreaddoesthepancontain?(A)90(B)IOC(C)180(D)200(E)360Problem2Samdrove96milesin90minutes.Hisaveragespeedduringthefirst30minuteswas60mphSmilesperhour),andhisaveragespeedduringthesecond30minuteswas65nnph・Whatwaghisaveragespeed,inmphtduringthelast30minutes?(A)G4(B)65(C)66(D)67(E)68Problem3Intheexpression(X)十(X)eachblankistobefilledinwithoneofthedigils1,2,3Por4,Witheachdigitbeingusedonce.Howmanydifferentvaluescanbeobtained?(A)2(B)3(C)4(D)6(E)24Problem4Aihree-dimensioralrectangularboxwithdimensionsX*V,andZhasfaceswhosesurfaceareasare24,24,48,48,72tand72squareunits.WliatisX+V+Z?(A)18(B)22(C)24(D)：«1(E)36Problem5Howmanysubsetsof{2f3,4,5,6,7.8,9}containatleastoneprimenumber^(A)128(B)朗(C)224(D)240(E)256Problem6Aboxcontains5chips,numbered1.23t4$and5.Chipsaredrawnrardomlyoneatatimewithoutreplacementuntilthesumofthevaluesdrawnexceeds4Whatistheprobabili：ytha:3drawsarerequired?'业1亠"一址一皿.I⑷馬働莎©巨回管(EJJProblem7Inthefigurebelow,Ncongruentsemicirclesaredrawnalongadfameterofalargesemicircle,withtheirdiameterscoveringthediameteroflhelargesemicirclewithnooverlap.Let.1oe:heeerienedareao*thesmaIsemicircles甘rdBbethesreao*theregionfnsldethelargesemicirclebutoutsfdethesmallsemicirclesTheratfo>4:Bis1:18.WhatisTV?(A)16(E)17Problem3SnramakesastsircFseoutoftoolbpin<^assnown:Thisi&a3-stepstaircaseanduses18toothpicks.Howmanystepswouldboinastaircasethatused1的tgtftpfckS?(A}JO(E)11QU)12(O)21㈣別tProblem9Thelacesofeachof7standarddicearelabeledwiththeintegersfrom1to6.Letpbetheprobabilitythatwhenall7dicearerolled,thesumofthenumbersonihetopfacesis10.Whatothersumoccurswiththesameprobabilityp?(A)IS(B)2(i(C)32(D)39(E)d2Problem10Intherectangularparallelepipedshown,AB=3,13C—1FandCG=2*PointjfeffethemidpointofFGWhatisthevolumeofthercdangularpyramidwithtxsseBCHEandapexA/?435(Aji(B)|(O)-(D)-(E)2：Problem11Whichofthefollowicgexpressionsisneveraprimenumberwhenpisaprimenumber?(A)『(BJ/*24(C)/+邸(D)(E)护*96Problem12Linesegment_1£?isadiameterofacirclewithAB=2-I.PointCtnotequaltoAorB,liesonthecircle.AspointCmovesaroundthecirdetthecentroid(centerofmass)ofA4BCtracesoutaclosedcurvemissingtwopoints.Tothenearestpositiveinteger,whatistheareaoftheregionboundedbythiscurve?(A)25(B)38(C)50(D)63(E)75Problem13Howmanyofthefirst2018numherdInthesequence101^1001^10001,100001,・・・aredivisibleby101?(A)253(B)504(C)505(D)506(E)1009Problem14Aistof2018positiveintegershasauniquemode,whichoccursexadN^10times.Whatistheleastnumberofdistinctvaluesthatcanoccurinthelist?(A)202(B)223(C)224(D)225(E)234Problem15Aclosedboxwithasquarebaseistobewrappedwithasquaresheetofwrappingpaper.Theboxiscenteredonthewrappingpaperwiththeverticesofthebaselyingonthemidlinesofthesquaresheetofpaper,asshowninthefigureontheleft*ThefourcomeraofthewrappingpaperaretobefoldedupoverthesidesandbroughttogethertomeetatthecenterofthetopoftheboxrpointAinthefigureontheright,Theboxhasbaseengthwandheighth.Whatistheareaofthesheetofwrappingpaper?♦(A)3(w+A)2(B)(2■专"L(C)2w24-4wh(D)2w2(E)w2h£Problem16Let<11,02,・■*aauisbeastricti/increasingsequenceofpositiveintegerssuchthatfliH-^24*■'■4*血ons=2018wlBtWhaiIstheremainderwhenu；十a；FIsdividedby6?(A)0(B)1(C)2(D)3(E)4Problem17InrectangleFQRS、PQ=8andQR=6.PointsAandBieonPQ、pointsCandDHeonQR.pofntsEandFlieonRS,andpointsGandHHeonSPsothat=I3Q<1andtheconvexoctagonABCDEEGHIsequilateralThelengthofasideofthisoctagoncanbeexpressedintheformk+my/ntwtierektm.andnareintegersandnisnotdivisiblebyth©squareofanyprime・Whatis+m亠n?(A)1(B)7(C)21(D)02(E)106Problem18Threeyoungbrother-sisterpairsfromdifferentfamiliesneedtotakeatripInavan.These3lxchildrenw(lioccupythesecondandthirdrowsinlhevan*eachofwhichtissthreeseats.Toavoiddisruptions,siblingsmaynotsitrightnexttoeachotherinthesamerow,andnochibmaysitdireGtlyinfrontofhisorhersibling.Howmanyseatingarrangementsarepossibleforthistrip?(A)60(B)72(C)92(D)96(E)120Problem19JoeyandChloeandtheirdaughterZoeallhavethesamebirthday*Joeyis1yearolderth占nChloe(andZoeisexactly1yearoldtoday.Todayisthefirstofthe9birthdaysonwNchCrioe'sagewillbeanIntegralmultipleofZoe'sage.WhatwllbethesumofthetwodigitsofJoey'sagethenexttimehisageisamultipleofZoe'sage?(A)7(B)8(C)9(D)10(E)11Problem20Afunction/isdefinedrecursivelyby/(1)=/(2)-1and/(n)=/(n—1)—/(n-2)+nforallintegersn>3,Whatis/(2018)?(A)2016(B)20L7(C)2018(D)2019(E)2020Problem21Marychoseaneven4-digitnumbertkShewrotedownallthedrvisorsofninincreasingnorderfromlefttoright1,2,—fn.AtsomemomentMarywrote323asadivisorof%£Whatisthesmallestpossiblevalueofthenextdivisorwrittentotherightof323?(A)324(B)330(C)340(D)361(E)646Problem22Realnumbersxandyarechosenindependentlyanduniformlyatrandomfromtheinterval[0,1].Whichofthefoflowingnumbersisclosesttotheprobabilitythaty.and1arethesidelengthsofanobtusetriangle?(A)0.21(B)0.25(C)0.29(D)0,50(E)0.79Problem23Howmanyorderedpairs(a,b)ofpositiveintegerssatisfytheequationa*&+63=20lcm&)+12•g)cd(Gfwheregcd(n,6)denotesthegreatestcommondivisorofaandbtandleTi)(o,ft)denotestheirleastcommonmultiple?(A)0(B)2(C)4(D)6(E)8Problem24LetABCDEFbearegularhexagon^withsidelengthLDenotebyXtY,andZthemidpointsofsidesXiJ,CDtandEF9respectively*WhatistheareaoftheconvexhexagonwhoseinterioristheintersectionoftheinteriorsofAACEand△XYN?(A)g(C)^v/3(D)-V^3(E)話箱Problem25Let［比」denotethegreatestintegerlessthanorequaltok.Hownnanyrealnumbersxsatisfytheequationx2+10,000=10,OOOx?(A)197(B)198(C)199(D)200(E)2012018AMC10BAnswerKey12345678910ADBBDDDCDE11121314151617181920CCCDAEBDEB2122232425CCBCC