2015-2019美國(guó)數(shù)學(xué)大聯(lián)盟杯賽Math League5年級(jí)及答案

2015-2016年度美田“數(shù)學(xué)大聯(lián)盟2015-2016年度美田“數(shù)學(xué)大聯(lián)盟杯賽”（中國(guó)賽區(qū)）（初賽時(shí)間；2015年11月14日，考試時(shí)間90分鐘，總分200分灼為我個(gè)人獨(dú)立完成的成果｀否則應(yīng)接受本次成續(xù)無(wú)效的處罰 如果怎同意遵守以上協(xié)議請(qǐng)?jiān)谘b訂線(xiàn)內(nèi)簽選擇題：每小題5分，答對(duì)加5分，答錯(cuò)不扣分，共200 B) 2.Eveiyprimehasexactly_J_positiveA) B)

4or3"IfIanswered34outof40questionsonmymathtestcorrectly,Ianswered_1_ofthequestion?120+3+4x120+3+4x B) C) D)曇10x20x30x4024)( B)10 C) D)IOOOOneofmyboxescontainsIpencilandtheotherseachcontain5pencils.thr,eare101pencilsinmyboxes,howmanyboxesdoIhave?／_`` B) ／_``Anelectricalcompanyimports2016lightbulbs.Unfortunately25%ofthosearedamaged.Howmanylightbulbsa「enot"damaged1 C) 50x(1.6+24)isthesquareB)-A)-B)- C) D)I0.'J:eopeoples1andinaline.Countingfromtheleft·,fonystandsatthe5thposition.CountingfromC)Tight,whichpositionisC)Onateamworkproject,Jackcontributed217ofthetotalamountofwork,Jillcontributed1/4ofLhework,Patcontributedl/5ofthework,andMauc0111ributedtherest.WhocontributedIhemosttowardthis B) C) D)Whichoftbefollowingnumbersisafactor B) D)A)22X4X8X16X)2XA)2

D2C)Onagameshow,AlwonfourtimesasmuchasBob,andBobwonfourtimesasmuchasCy.[fC)$1536,howrm1chdidAl,Bob,andCywin Thesumoftwocompositescannot B) C) D)Ifaandbarepositiveinlege『ssuch甘atalb517thena+b Whatisthegreatest(Jddfactorofthenumberofhomsinallthedaysoftheyear2015? B)365 C)1095 IfthecurrentmonthisFebmary,whatmonthwillitbel199999rnonthsfromJan B) C) Twoanglesarecomplemen.tary.Oneoftheseanglesis36°lessthantheother.Wl1atisthemeasureofthelargerangle? B) C) D)(Thesquarerootof16)+(thecuberootof64)+(the4throotof2561- B) D)21In兇BC,m乙A-1憶BIIILB-III乙CWhatis!hedegreemeasureof B) D)22,Forevery3mathbooksIbought,Tbought2biologybooks.Ibought55booksinall.Howmanyofthosearemathbooks?A) B) Johnwroteanumberwhosed.igitsconsistsentirelyofIs.Thisnt1mberwasacompositenumber_munbercouldcontain B) Flegs,then5Sels"'_J_Plegs. B) IfthelengthofarectangularprismwithvolumeVisdoubledwhilethewidthandtheheightarehalved,lbevolumeofthenewprismwillbe B) C) RickandRoyeachstandsatdifferent:endsofa、trnightroad!batis64mlongTheynmtowardeachother.Rick'sspeedis3m/sandRoy'sspeedis5mis.Theywi.11meetin? C) Iftheareaofacertaincircleis2016,itsradiusC)2016/兀

s.q1t{4032爾Inatoyshop,thecostofaTeddyBea『is200%asmuchasthatofatoytn1inThecostofatoytrninis B) D)Intheseqnence20J6,225,14I,66.432,99,1458...,eachtermaftertheirsttermisthesumofthe C) D)Whatisthesumofall!hepositivedivigors2巾－ B)211- C)212- 0)213-3l.Ittakes4hoursforMikeandLucytofin.shatask.IttakesLucyandJerry5hou飛tofinishlhesameAndittakes6hoursforMikeandJe可tofinishthesametaskLucy沺dJerryfirstworkonthetaskforlhourand45minutes.ThenMiketakesoverthetaskonhisown.Howmanymorebou飛doesittakefor B) D)1fyousellaclothatitscurrentprice,youget$40profit.ThetotalprofityougetsellinglOclothesat70%ofitscurrentpriceis四uallothetotalprofityougetselling20clothesat$82percloth.Whatisthecurrentpriceofacloth? B) C) The1eare6ident:icalsquaresi11!hefigtireonthe1ightThesidelengthofeach.qae.sIOfallthetrianglescon斗trnt:tedbyconnectingthreeofthe18whichhasatleastoneverticalorhorizontalside? B) D)PickupNnumbe飛fromIto2015inclusively,suchthatthesm.ofanythreeoftheNm1mbersisdivisibleby24.WhatisthemaximumvalueofN? D)35湯如有一件花了64關(guān)金買(mǎi)來(lái)的襯衫，他打算以比原價(jià)高出25％的價(jià)格出售，他會(huì)賣(mài)出多少 B) C) D)滿(mǎn)足以下條件的最小整數(shù)是多少：除以3余2，除以5余4，除以7余6凸 37，飛人以每小時(shí)360 C) 38，設(shè)A為一個(gè)可整除11但不可整除10的正整數(shù)，若B為一個(gè)顛倒A數(shù)位的整數(shù)，那么B必須被幾 B) C) DA,B,C39珍妮花50美金買(mǎi)了一條圍巾。她一開(kāi)始準(zhǔn)備以60美金賣(mài)出，然后把價(jià)格增加25%,再把新的價(jià)格減少20％并且出售凸在這筆交易之中，她凸

D)虧了10關(guān)40,A,B兩袋子里分有若I個(gè)，袋B袋數(shù)比是4：巨A袋中取個(gè)A袋球和B袋球的數(shù)呈之比變?yōu)?:3;再?gòu)腂袋中取出若l-·個(gè)球放入A袋后，A袋球和B袋球的奻噩之比變?yōu)?:2。兩個(gè)袋子里最少一？A) B) C) 2015-2016年度美國(guó)“數(shù)學(xué)大聯(lián)2015-2016年度美國(guó)“數(shù)學(xué)大聯(lián)盟杯（中國(guó)賽區(qū)）初賽選擇題；每小題5分，答對(duì)加5分，答錯(cuò)不扣分，共200分，答案請(qǐng)?zhí)钔吭诖鹪缚ㄉ希?4orIO000D)lOOOA)-D)lO.B)B)IL22ID)C)32CC)33sqrt(2016爾D)1008/210-2ll-212-ID)D)D)A,B,CB2016-數(shù)學(xué)大聯(lián)盟杯（五年級(jí)2016-數(shù)學(xué)大聯(lián)盟杯學(xué)生誠(chéng)信協(xié)議：考試期間，我確定沒(méi)有就所涉及的問(wèn)題或結(jié)論，與任何人、用任何方式交流或討論，我確定以下的答案選擇題：每小題55200Whichofthefollowinghasthegreatest 8) C)20 D)20+ 8)20I ABizz-Numberisapositiveintegerthateithercontainsthedigit3orisamultipleof3.Whatisthevalueofthe10thBizz-Number? Theperimeterofanisoscelestrianglewithside-lengthsIandI008 8) Howmanyintegerslessthan2017aredivisibleby16butnotby Jonhasacertainnumberofpens.Ifhedistributedthemevenlyamong4students,hewouldhave3leftJoncouldhaveis C) Whichofthefollowingnumbersisnotdivisibleby 8) Whichofthefollowingisbothaperfectsquareandaperfect36 B)36 C)36xS D)39xS 8) themgot4's,25%ofthemgot3's,and15%ofthemgot2's.Howmanystudentsgotl's?ooox52011=looox52011=l8)8)I%of1/10of10000is_1_percentgreaterthanI sideofSareequal?兀： B)兀： C)兀： D)兀： Ifthesumofthreeprimenumbersis30,whatisthelargestpossiblevalueofanyofthethree dollars,didIspendintotal? 8) Howmanypos山veoddfactorsdoes25x35x55 Thenumberofscalenetriangleswithperimeter15andintegralside-lengths and3460,respectively? 8) Eachtennafterthe1stterminthesequenceI,5,9,...is4morethanthepreviousterm.Thegreatestterminthissequencethatis<1000andthatleavesaremainderof1whendividedby6is writeareprime? Ifapaintingmachinepaintsataspeedof1m2/sec,itsspeedis600 8)600060000 D)600000ofSquareCisthreetimesthatofSquareB.TheareaofSquareCis..1_timesthatofSquareA Ifthetime17minutesagowas19:43,whatwillbethetime17minutesfrom 28和ckanyintegergreaterthanI00andsubtractthesumofitsdigitsfromtheintegerThelargestintegerthatmustdividetheresultisA) roomborninthesamemonthis. IfM,A,T,andHaredifferentdigitssuchthatMATH+HTAM=12221,whatisthevalueofM+A+T+ If10forks,20knives,and30spoonscost$360,and30forks,20knives,and10spoonscost$240,what Write,insimplestreducedform,thevalue hissixopponentsexactlyonce.Sofar,AlhasplayedImatch.Barbhasplayed2matches.CalhasplayedmanymatcheshasGregplayedatthispoint? nothreeoftheseintegerscouldbethelengthsofthesidesofthesame D)lquarters)withoutbeingabletogivesomeoneexactchangeforaone-dollar 36小羅星期一工作了2個(gè)小時(shí)。在那之后的每一天，他的工作時(shí)間是前一一 37蘇珊花了一天中的－的時(shí)間做英語(yǔ)作業(yè)，－的時(shí)間做數(shù)學(xué)作業(yè)，請(qǐng)問(wèn)她這一 38下面哪個(gè)數(shù)是11,111,111和llllll,111,111的公約數(shù) 39設(shè)n是一任意自然數(shù)。若將n的各位數(shù)字反向排列所得自然數(shù)n1與n相等，則稱(chēng)n為一回文數(shù)。例如，若n1234321,則稱(chēng)n為一回文數(shù)；但若n1234567,則n不是回文數(shù)。請(qǐng)問(wèn)在10000 8) C)40湯姆建了兩個(gè)塔。塔A發(fā)射5次能最波5秒。B發(fā)射l0次能量波需要正好l0秒。能量波是間隔發(fā)送的，間隔是相同的。假設(shè)塔A發(fā)射l2次能暈波需要t1秒，塔B發(fā)射l2次能量波需要t2秒。t,<l2B)t1 C)t1

D)“數(shù)學(xué)大聯(lián)盟杯賽”（中國(guó)賽區(qū)）初賽答（五年級(jí) 20xD)20+D)36X36X36X539x5C)冗D)兀600600060000600000A)t1<t,=t1>（五年級(jí)選擇題：每小題5分，答對(duì)加5分，答錯(cuò)不扣分，共200Thesmallestpossiblesumoftwodifferentprimenumbers Thegreatestcommonfactoroftwonumbersis3.Theproductofthesetwonumbersmustbedivisible Thesumof5consecutiveone-digitintegersisat Howmanytwo-digitmultiplesof10arealsomultiplesof12 D)exactly

eachchapterhasthesamewholenumberofpages,thenthetotalnumberofchaptersIhaveleftcouldbe Whatisthegreatestoddfactorof44x55x63 35X55 D)36X55

Whatisthesumofthefactorsof D)Theleastcommonmultipleof8and12isthegreatestcommonfactorof120 JanuaryhasthegreatestpossiblenumberofSaturdayswhenJanuaryIoccursonanyofthefollowingdaysoftheweekexcept B) C) D)Thenumberthatisl0%ofl000islOmorethanl0% B)222 C)444 D)8885hours?35 B)40 C)42 D)45displayedonmywatch65minuteslater?7:20C)8:20(2018x2017)+(2018xI)=

B)7:25D)8:25atmosthowmanydaysthatweekdidthebirdlayexactly2eggs?

10 B)22 C)34 D)58eachcoin)is circumferenceofthedrum?12060兀

8)80兀40Ofthefollowing,whichexpressionhasthegreatestnumberoffactorsthataremultiplesof2018x Whenthesumofthefactorsofaprimenumberisdividedbythatprimenumber,theremainder B) Forhowmanydifferentpairsofunequalpos山veintegerslessthan10istheleastcommonmultipleofthenumberslessthantheirproduct? Exactly—ofthestudentsinmyclasshaveatleastonebrother,and-=-haveatleastonesister. l-chavenosiblings,whatfractionofthestudentsinmyclasshaveatleastonebrotherandatleastonel-c3）D4-5、丿B6、?AEachday,SalswimsalapIsecondfasterthanonthedaybefore.IfSalswimsalapin60minutesonthe1stday,onwhatdaydoesheswimalapinI3）D4-5、丿B6、?AC)36lC)36l

20I72018X20172019=20I7LX20I7' BotharcsABandADarequartercirclesofradius5,figureontheright.ArcBCDisasemi-circleofradius5.WhatistheareaoftheregionABCD?

B)105D)50+Forevery$5IearnfrommyjobIsave$2Forevery$4Isavefrommy」ob,Iamgivenanadditional$1frommyparentstoaddtomysavingsHowmuchmustIearninordertohave$40insavings?

$l20cDarefoursemi-circles.EachsideofsquareABCDistangenttooneofthecDsemi-circles.TheareaofABCD

RAAmillionisalargenumber,a"I"followedby6zeros.Agoogolisalargenumber,a"I"followedbyonehundredzeros.Agoogolplexisalargenumber,a"l"followedbyagoogolofzeros.Agoogolplexianisalargenumber,a"l"followedbyagoogolplexofzeros.AgoogolplexianisRA10 B)

Anintegraltriangleisatrianglewithpositiveintegralside-lengthsandapos山vearea.Suchatrianglecanhaveaperimeterassmallas3Whatisthenextsmallestpossibleperimeterofanintegraltriangle? 2literof2%fatmilk+3literof3%fatmilk=5literof_J_fat Oneday,amotoristcametoahillthatwasten-miledriveuponesideandaten-miledrivedowntheother.Hedroveupthehillatanaveragespeedof30milesperhour.Howfastwillhehavetodrivedowntheothersidetoaverage60milesperhourfortheentire20-miledistance?30milesper90milesper

60milesperD)NoneoftheWhatistheweightofafish們tweighstenpoundsplushalfits B) Withoutusingpennies,howmanydifferentcombinationsofcoins(nickels,dimes,quarters)willmake30cents? Amanonceboughtafinesuitforwhichhepaid$30morethan-:-ofitsprice.Howmuchdidheforthe Afatherisfivetimesasoldashisson.Infifteenyearshewillbeonlytwiceasold.Howoldisthefatheratpresent? Ittakes30minutestocompletelyfillatank.If,however,aholeallows—ofthewaterthatisthetanktoescape,howlongwillitthentaketofillthe “數(shù)學(xué)大聯(lián)盟杯賽”（中國(guó)賽區(qū)）（五年級(jí)選擇題：每小題55200I.D)35X36XIll222444888354042457:207:258:208:25D)(2018+10223458120806040113） ） ）DABCD．62B)B)79、丿）79、丿））） ．）D BCD．52B)105兀D)50+5cRDAcRDA8)（五年級(jí)（活動(dòng)日期：2018年11月25日，答題時(shí)間：90分鐘，總分：200分答案均為我個(gè)人獨(dú)立完成的成果，否則愿接受本次成績(jī)無(wú)效的處罰。選擇題：每小題5分，答對(duì)加5分，答錯(cuò)不扣分，共2002018+2019=20+18+20+19+ If1/3ofmyhatsarered,and36arenotred,Ihave_.1_87）87）A2）CThesumofthemeasuresofthe2smallestanglesofatrianglecould B)135 C)121 D)612018=2QX_J_+18xA) A)EveryEnglishletterappearsinmy2018-letterpasswordatleastonce.TheletterAappearsatmost_J__ Whichofthefollowingistheproductof2consecutive Theleastintegerwithaprimenumberofdifferentprimefactors Ihave5coinsconsistingofpennies,nickels,anddimes.IfIhaveatleastIofeachtypeofcoin,theleastpossiblevalueofmy5coinsisExactly...1_different3-digitareacodescanbemadeusingonly2sand3s,withatleastone2andone3ineachareacode.Howmanymultiplesof10arefactorsof10

A) A)Myteamhadtowinacertainnumberofgamestomakeittothefinals,andwewonhowmanywinsdidweneed? Whatisthegreatestcommonfactorof1x3x5x7x9and2x4x6x8x The2ndactofa3-actplayis1/3thelengthoftheentireplay.Ifthe1stactistwiceaslongasthe3rd,whatfractionoftheplayisthe3rdact?

Ifldoublemyspeedof12000m/hr.,mynewspeedwill200 B)400C)600 D)2400Whichofthefollowingcouldbetheperimeterofanequilateraltrianglewithintegralside- ThegreatestofIOconsecutivepositiveintegersisaprimenumber.Whatistheleastpossiblesumof One-fourthofEd'sballoonspopped,with2balloonspoppingevery3minutes

Whatisthegreatestcommonfactorof68and8Theexpression1002018canbewrittenastheproductofexactly二＿primeC)2x

Howmanyintegershaveasquarerootgreaterthan15andlessthan 8)22＝霾

Eachdayforamonth,Sullywakesup5minutesearlierthanhedidthedaybefore.IfSullywokeupat Theproductofallfactorsof21equals (1234+0+1234+1+1234+2+1234+3+1234+4)—5 B)1234+ C)1234+ D)1234+Onanumberline,twodifferentintegersareeachthesamedistancefrommyfavoriteintegerandhaveasumof144.Whatismyfavoriteinteger? LastyearIspent$180for80pairsofshades.ThisyearIspent$180for5fewerpairsofthesameshades.HowmuchdidthepriceperpairincreasesinceIboughtthemlastyear? Idroveataconstantspeedof60km/hr.withoutstopping.Atexactly5:00p.m.Ihadtraveled318km.AtwhattimedidIstartdriving?10:42C)12:42

11:42D)1:42wasoneofthese9numbers.Whenmysumwasdividedby11,theremaindercouldnothave ofthelast4digitsonthefirstline? Theproductofallthefactorsofanintegergreaterthanlequalsthecubeofthatinteger.Whatistheleastintegerforwhichthisistrue? Xi0;-(iX23X25XXi0;-(iX23X25X...X297X bothlanes? Icountedbackwardsoutloudfrom2018byones.WhenIsaidmy50thmultipleof8,howmanynumbershadIcounted? D)1+7=18.Howmanyluckyyearsaretherebetween2018and2108? 3.0C)4.5

4.0D)9.0thepatternwouldbe 2018-2019年度美國(guó)“大聯(lián)盟”(MathLeague)（五年級(jí)選擇題：每小題5分，答對(duì)加5分，答錯(cuò)不扣分，共200 (2018-20-18)+2019-20-19=1980+1980=3960.8)ThenumberofredhatsishalfthenumberthatarenotIfthemeasuresofthe2smallestanglesofatrianglewere30and31degrees,thelargestanglewouldbe119degreesfeveryEnglishletterexceptAappearedexactlyonce,thenAwouldappear2018-25=1993Thenumber6hastwoprimefactors,2and3.pennies,1nickel,and1dime.Thecommonfactorsare1,3,5,and15.Thegreatestis15Since2400=16100,itistheproductofexactly100sixteens.Iftheplayis90mins.,the2ndactis30mins.Thatleaves60mins.forthe1stand3rdacts.The1stactw