2015年美国“数学大联盟杯赛”(中国赛区)初赛七年级试卷

2014-2015年度美国“数学大联盟杯赛”(中国赛区)初赛(七年级)(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)301.2014+2015=1014+1015+?()A)200B)1000C)1200D)20002.Samhasdemolishedanumberofhousesequaltotheproductoftwoconsecutiveintegers.Hemayhavedemolished?houses.()A)54B)63C)72D)813.Theproductof8000000000and5000000000has?digits.()A)20B)19C)11D)104.Thesumofthelargestoddfactorof380andthelargestevenfactorof380is()A)759B)475C)285D)1715.Asquarehasaperimeterthatisthesquareofaninteger.Thelengthofonesideofthesquarecouldbe()A)1B)2C)3D)56.Mysandwichcost10quarters,10dimes,and10nickels,andIpaidforitwitha$20bill.HowmuchchangedidIgetback?()A)$8.00B)$10.00C)$12.00D)$16.007.Whenthetimeis600secondsaftermidnight,thetimeis()A)12:10P.M.B)10:00P.M.C)12:10A.M.D)10:00A.M.8.32÷2×4–6=()A)-8B)-2C)16D)589.Thesumofthefirst8primenumbersis()A)17B)59C)77D)8910.DeborahHarriedhasn’thadmuchfreetimetoday.Shehadonlytwobreaks,eachforawholenumberofminutes.Iftheproductofthetwowholenumbersisprime,shecouldhavehadatotalof?minutesofbreaktime.()A)5B)12C)13D)1911.555888?()A)0B)516C)58D)112.Themeasuresoftwoanglesinarighttriangledifferby40°.Whatistheleastpossiblemeasureofoneoftheanglesinthetriangle?()A)10°B)25°C)40°D)50°13.Ofthefollowing,whichisleast?()A)-1002B)(-49)2C)193D)(0.5)414.Mr.LupucutMerino’spayby20%lastyear,andthencutthislowerpayby20%lastweek!IfMerinonowearns$640perweek,Merino’sweeklypaywas$?beforethecuts.()A)896.00B)921.60C)1000.00D)1066.6715.Theaverageof66’sand312’sis()A)6B)8C)8.5D)916.Thesumofthetenthsandhundredsdigitsof321.123is()A)2B)3C)4D)517.Whatistheremainderwhen777+77+7isdividedby7?()A)0B)1C)3D)418.654321?543216720()A)-720B)-1C)1D)72019.Thesumofawholenumberanditsreciprocalcannotbe()A)2.0B)2.8C)4.25D)8.12520.Jenhasatotalof$2inpennies,nickels,dimes,andquarters.Shehasatleastsomeofeachtypeofcoin.Shehasatmost?dimes.()A)13B)14C)15D)1621.Tom’saveragedailynumberofhoursinthesunforthelast6daysistwicehisaveragedailynumberofhoursinthesunforthelast4days.Ifhespent12hoursinthesuninthelast4days,thenhespent?hoursinthesuninthelast6days.()A)12B)24C)36D)4822.20+40+60+80+100=(4+8+12+16+20)×?()A)4B)5C)25D)5523.Letxy=(2×x)–y.Then321()A)3B)5C)7D)9-1--2-城市区学校年级性别姓名（正楷）„„„„„„„„„„„„„„„„„„装„„„„„„„„„„„„„„„„„订„„„„„„„„„„„„„„„„„线„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„装„„„„„„„订„„„„„„„线„„„„„„„内„„„„„„„不„„„„„„„答„„„„„„„题„„„„„„„„„„„„„„„24.Eachlegofanisoscelesrighttriangleofarea60isaslongasthesideofasquarewitharea()A)30B)60C)120D)22525.Theproductofthreeprimeshasatmost?positivedivisors.()A)3B)6C)7D)826.AtworkIaskedeachpersonwhowantedicecreamtoraiseahand.If10%of100%of1000%ofthe30peopleatworkraisedhands,?peopleraisedtheirhands.()A)3B)10C)15D)3027.Thepositiveintegerxhas6whole-numberfactors.Theproductofthese6factorsis()A)x3B)x4C)x6D)x728.Thesumof8consecutiveintegerscouldbe()A)0B)2C)4D)829.Ifone-fourthofthesquareofanintegerislessthan1,thentheintegerisoneofexactly?possibilities.()A)1B)2C)3D)430.Whichofthefollowingcannotbethedegreemeasuresoftwooftheanglesinacertainisoscelestriangle?()A)40,80B)45,90C)50,65D)60,6031.Thedifferencebetweentwoprimesbetween110and130couldbe()A)2B)3C)8D)1432.3×296hasthesamevalueas()A)297+2B)297+296C)632+632D)69633.Igot90%ofmymathtestquestionsand90%ofmyhistorytestquestionscorrect.IfIgot18morequestionscorrectonmymathtestthanonmyhistorytest,mymathtesthad?morequestionsthanmyhistorytest.()A)18B)20C)36D)18034.Themaskedmathematiciantakesmeresecondstomultiplyeverymultipleof2from2to20byeverymultipleof3from3to30.Headdsalloftheproducts,andthetotalis()A)18150B)108900C)217800D)65340035.Twolinesareparallel,andeachofthemismarkedwith5differentdots.Howmanytrianglescanbeformedusingthesedotsasvertices?()A)80B)90C)100D)110二、填空题(每小题5分，答对加5分，答错不扣分，共25分)36.1261025255=___________.37.If3926Pxxx,whatistheminimumpossiblevalueofP?Answer:___________.38.Therearenballsinabox,eachwithadifferentnumberfrom1to100.Ifthesumofthetwonumbersonanytwoballscannotbe135,whatisthegreatestpossiblevalueofn?Answer:___________.39.Therearenorderedpairsofpositiveintegers(x,y)thatsatisfy2242015xy.Whatisthevalueof222nnn?Answer:___________.40.Therearetwopositivetwo-digitintegersaandbthatsatisfy(a+b)+ab=2014.Ifoneofthenumbersaandbisaperfectsquare,whatisthevalueof|a–b|=?Answer:___________.城市区学校年级性别姓名（正楷）„„„„„„„„„„„„„„„„„„装„„„„„„„„„„„„„„„„„订„„„„„„„„„„„„„„„„„线„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„„装„„„„„„„订„„„„„„„线„„„„„„„内„„„„„„„不„„„„„„„答„„„„„„„题„„„„„„„„„„„„„„„-3--4-