2023年MathLeague美国大联盟六年级思维探索第一阶段活动.docx
2022-2023年度美国MathLeagUe思维探索第一阶段活动（六年级）（答题时间：75分钟，总分：175分）学生诚信协议：答题期间，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，我确定我所填写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。选择题：每小题5分，答对加5分，答错不扣分，共175分。1.Afarmerhas36morepigsthansheep.Ifhehas10timesasmanypigsassheep,howmanypigsdoesthefarmerhave?A)40B)44C)45D)46Ifthecostofadozenbagelsincreasesby$1.80,theaveragecostofeachbagelwillincreasebyA)10¢B)150C)180D)3003. Theinteger2equals?timesthereciprocalof2.A)2B)4C)6D)84. Whichofthefollowingcouldbetheperimeterofarectanglewithbothoddandevenwhole-numberside-lengths?A)12B)13C)14D)165. Howmanypositivedivisorsof122aremultiplesof12?A)2B)6C)12D)246. Whatisthedifferencebetween23.456roundedtothenearesttenthand23.456roundedtothenearesthundredth?A)0B)0.04C)0.05D)0.17. Theareaofasquareis36m2.TheperimeterofthesquareincmisA)900cmB)2400cmC)3600cmD)360(MM)cm8. Whatisthegreatestodddivisorof2×4×6×8×10×12?A)9B)15C)45D)1359. Roypainted100houses.IfRoypainted40%ofthehousesgrayand20%oftheremaininghousesyellow,howmanyhousesdidRoypaintyellow?A)8B)12C)20D)4010. Whichofthefollowingexpressionshasthegreatestvalue?11. Thetemperatureofapotofsoupincreasesby3oevery40seconds.Howmuchwillthetemperatureincreasein30minutes?A)135oB)450oC)750oD)1800o12.1countedfrom1to100outloud,skippingeverymultipleof3.HowmanynumbersdidIsayoutloud?A)66B)67C)76D)77A)2022B) 2023 C) 2027 D) 203213. Whatisthedifferencebetween2primeswhoseproductis10135?14. Apileof1003penniescanbedividedequallyintoexactly?equalpilesworth$4each.z>-A)25B)250C)2500D)2500015. In2022Iranon101moredaysthanthenumberofdaysIdidnotrun.ThesumofthedigitsofthenumberofdaysIranin2022isB) 6D) 11A)5C)86.2999+2999A)2+9"B)2lx999C)22+9"D)22x9"17. If80%ofAri'ssavingsequals20%ofAri,sandBev,ssavingscombined,Bevmusthave2_timesasmuchsavingsasAri.A)2B)3C)4D)618. Whatisthegreatestpowerof2thatisafactoroftheproductofthe6smallestpositive2-digitintegers?A)23B)24C)26D)2819. Asquareposterconsistsofan8cm-wideborderaroundtheperimeterofasquarephoto.Iftheareaoftheentireposteris6400cm2,whatistheareaofthephotoportionoftheposter?A)4096cm2B)4608cm2C)5120cm2D)5184cm220. Atriangle,sangleshavemeasuresthatareconsecutivemultiplesof15o.Whatistheaveragemeasureofthe2smallestangles?A)37.5oB)52.5oC)67.5oD)82.5o1.1 1dividedamultipleof5byasmallermultipleof5andgotaremainderof15.Whatisthesmallestpossiblesumofthemultiples?A)30B)45C)55D)6522. Everythirdgumballdispensedhascracks,buttherestdonot.IfIkeepevery4thgumballdispensedanddiscardtherest,howmanyofthe72gumballsIkeepwillhavecracks?A) 6B)12C) 18D)24A) IOlB)102C)201D)20223. Howmanyfactorsgreaterthanorequalto5does2×5,01have?24. Eachoftheintegersfrom1through50waswrittenonaseparatetag,then3consecutivelynumberedtagswerelost.Ifthesumoftheintegersonthe47remainingtagsis1221,whatisthesumofthedigitsoftheintegersonthelosttags?A)13B)17C)27D)3025. Ifthemedianof6consecutiveintegersis4.5,whatisthemedianoftheirreciprocals?2499A)-B)-C)D)99204026. Myridetoschooltakesfrom10to18minutes,dependingontraffic.Icannotarrivebefore8:10AMorafter8:30AM.WhatisthedifferencebetweentheearliestandlatesttimesIcouldstartridingtoensurethatIarriveontime?A)8minutesB)12minutesC)20minutesD)28minutes27. Whatistheaverageof2100and2,°1?A)2,5B)2×2"C)2×2lD)3×2"28. If(0,0)and(3,4)aretwoverticesofaparallelograminacoordinateplane,whichofthefollowingcouldnotbeanothervertexofthisparallelogram?A)(4,3)B)(-1,7)C)(-3,-4)D)(-4,3)29. Onaclasstest,theaveragescoreoftheboysandgirlscombinedwas88.Iftheaveragescoreoftheboyswas80,andtheaveragescoreofthegirlswas100,whichofthefollowingnumberscouldbethetotalnumberoftheboysandgirlscombined?A)105B)63C)48D)noneofabove30. Aclockthatuniformlyloses4minutesevery24hourswascorrectlysetat6A.M.onJanuary1.Whatisthecorrecttimewhentheclockreads11:39AMonJanuary6ofthesameyear?A)11:54AM,January6B)12:00PM,January6C) 12:30 PM, January 6D) 11:00 AM, January 731. Ifwegetabullseyehalfthetimethatweplaydarts,isitmostlikelythatweA) missabullseyeinanysingletry,B) getabullseyeatleast1timein2tries,orC) getabullseye2or3timesin3tries?32. Whatisthequotientoftheleastcommonmultipleofthefirst40positiveintegersdividedbytheleastcommonmultipleofthefirst30positiveintegers?A)1209B)1147C)2294D)noneofabove33. Howmanypointsdoesonehavetoplaceona1inchby3inchesrectangletoguaranteethattwoofthemarestrictlylessthan1inchapart?(Therectanglehereincludesitscompleteinterior.)A)8B)10C)12D)noneofabove34. Onesquarehastwicetheareaofanothersquare.Isitpossibleforbothsquarestohavesidelengthsthatarewholenumbers?A)YesB)No35. Whatistheradiusofthecircleinscribedinatrianglewithsidelengths7,24,and25?Note:Thefigurebelowshowsthecircleinscribedinatriangle.A)3B)4.5C)6D)noneofabove2022-2023年度美国MathLeague思维探索第一阶段活动六年级试卷答案题号12345678910答案ABBCBBBCBB题号11121314151617181920
