14-15美国“数学大联盟杯赛”( 中国赛区)初赛六年级试卷

2014-2015年度美国“数学大联盟杯赛”(中国赛区)初赛(六年级)(初赛时间：2015年1月3日，考试时间90分钟，总分200分)学生诚信协议：考试期间，我确定没有就所涉及的问题或结论，与任何人、用任何方式交流或讨论，我确定以下的答案均为我个人独立完成的成果，否则愿接受本次成绩无效的处罚。一、选择题(每小题5分，答对加5分，答错不扣分，共175分，请将正确答案A、B、C或者D写在每题后面的圆括号内。)正确答案填写示例如下：20−5×2=2×?(A)A)5B)15C)25D)301.2×0+1×4–2×0+1×5=()A)0B)5C)9D)152.Thereare84beaversinacolony.Yesterdaytheyallwentoutinteamsof6tocollectlogs.Todaytheyareallgoingoutinteamsof4.Therewillbe?moreteamstodaythantherewereyesterday.()A)2B)7C)14D)213.12345+54321=11111×?()A)66666B)666C)66D)64.Mybrotherisexactlytwicemyage,andheis192monthsold.Iam?yearsold.()A)8B)16C)32D)965.Applecost$1.25each,or3for$3.IfIwanttobuy11apples,Ineedatleasthowmuchmoney?()A)$11.00B)$11.50C)$12.00D)$13.756.Multiplyinganumberby23isthesameasdividingitby()A)0.667B)0.75C)1.5D)1.6677.Howmanyprimefactorsof120aremultiplesof4?()A)0B)6C)7D)88.Ihavetestscoresof80,84,and94,andIwantmyaveragetestscoretobe86aftermynexttest.WhatscoremustIgetonthenexttest?()A)0B)86C)87D)889.Thelengthsofthesidesofatriangleareconsecutiveevenintegers.Whichofthefollowingcannotbethelengthofthelongestside?()A)6B)10C)12D)1610.Nigelhasthevolumesetat8,butitgoesto10.Hecouldincreasethevolumebyatmost?.()A)2%B)10%C)20%D)25%11.752×25=252×?()A)32B)52C)75D)15212.Thesumoftwodifferentprimescannotbe()A)oddB)evenC)123D)aperfectsquare13.Theproductofacircle’scircumferenceandradiusdividedbyitsareais()A)2B)πC)2πD)2π214.Mr.Wellsisbecominginvisible.Todayheis100%visible,buteachmorningfromtomorrowonhewillwaketofindhimself80%asvisibleashehadbeenthedaybefore.Hewillfirstbelessthan50%visiblein?days.()A)3B)4C)5D)615.111111345()A)2B)3C)116D)116016.Thelargestprimefactorof1000000000is()A)1B)2C)5D)1017.999999×999998=9999992–?()A)1B)999997C)999998D)99999918.Thecombinedvalueofmyquartersandnickelsistentimesthecombinedvalueofmypenniesandnickels.IfIhavethesamenumberofpenniesasnickels,myratioofquarterstopenniesis()A)1:1B)2:1C)10:3D)11:519.500is?%greaterthan200.()A)50B)150C)250D)30020.Between100and1000,?numbersaresquaresofoddintegers.()A)11B)16C)21D)3121.Asquareofperimeter360consistsofexactly?squaresofarea9.()A)40B)400C)900D)160022.Thelargestoddfactorof66×1010is()A)65×109B)63×105C)36×510D)33×5523.Gregfinishedsenioryearwithoutlearninghowtotype!HisfriendOrichargedhim$4perpagethefirsttimeapagewastyped,and$2eachtimeapagewasredone.Orityped150pages,thenredid30pages,andfinallyredid15pagesa2ndtime.ThetotalcosttoGregwas()A)$660B)$690C)$720D)$760-1--2-城市区学校年级性别姓名（正楷）„„„„„„„„„„„„„„„„„„装„„„„„„„„„„„„„„„„„订„„„„„„„„„„„„„„„„„线„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„装„„„„„„„订„„„„„„„线„„„„„„„内„„„„„„„不„„„„„„„答„„„„„„„题„„„„„„„„„„„„„„„0215ABDCP24.Whatfractionofthefactorsof102arefactorsof10?()A)110B)49C)59D)91025.Whichofthefollowingsumsisequaltoaprimenumber?()A)292+662B)422+452C)222+642D)322+54226.Ifthesquareshownisrotated1890°counterclockwise,side?willbeatthetop.()A)AB)BC)CD)D27.Theleastcommonmultipleof22,42,62,82,and102is()A)3840B)14400C)57600D)23040028.Asnailcrawls2400mmperhour.Ittakes?secondstocrawl1mm.()A)13B)23C)1.5D)329.Acirclecanintersectaquadrilateralat?points.()A)0,2or8onlyB)0,2,4,6or8onlyC)1,2,3,4,6,or8onlyD)0,1,2,3,4,5,6,7,or830.Carlalovesshells!Shecollectsthem,labellingeachwitha1-,2-,or3-lettercode.Ifthesamelettersareusedinadifferentorder,itisadifferentcode.Shehasusedeverysuchcode,soshehas?shells.()A)156B)17576C)18278D)2088831.Ifthesumof50consecutiveintegersis1525,whatisthesumofthenext50consecutiveintegers?()A)1575B)2775C)4025D)7625032.Of4pairsoftwins,3studentsarechosentodoareporttogether.Thereare?possiblegroupsof3thatdon’tincludebothtwinsfromapair.()A)16B)24C)28D)3233.八年后我的年龄是两年前我的年龄的两倍。请问两年后我是几岁？()A)14B)16C)18D)2034.将0.75转换为分数，这些分数的分子和分母都是小于100的正整数。这样的分数共有多少个？()A)3B)24C)25D)3335.船长们划船5个小时。从第二个小时开始，每个小时行驶的距离比前一个小时少了2千米。如果5个小时的平均行驶速度是6千米/小时，那么前2个小时行驶了多少千米？()A)6B)12C)16D)18二、填空题(每小题5分，答对加5分，答错不扣分，共25分)36.Calculatethenumberofdigitswhichareequalto0intheproductof826446281,11and11.Answer:___________.37.Inthisproblemasshownontheright,eachsquarerepresentsadigitfrom0to9.Whatisthefinalproduct?Answer:___________.38.Forsomeintegern,thesumofallofthedigitsofnisamultipleof8andthesumofallofthedigitsofn+1isalsoamultipleof8.Ifn=2015,whatisthegreatestpossiblevalueofn?Answer:___________.39.IntriangleABContheright,BD:DC=1:2.IftheareaoftriangleABPis7andtheareaoftriangleACPis5,whatistheareaoftriangleADP?Answer:___________.40.地球表面由陆地和海洋构成，其中陆地面积占29%，并且陆地的四分之三在北半球，那么北半球的海洋面积占所有海洋面积的___________%。（结果四舍五入保留整数）-3--4-城市区学校年级性别姓名（正楷）„„„„„„„„„„„„„„„„„„装„„„„„„„„„„„„„„„„„订„„„„„„„„„„„„„„„„„线„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„装„„„„„„„订„„„„„„„线„„„„„„„内„„„„„„„不„„„„„„„答„„„„„„„题„„„„„„„„„„„„„„„