2023年Math League美国大联盟六年级思维探索第一阶段活动

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.hehas10timesmanypigsassheep,howmanypigsdoesthehave?A)4044C)45D)462.thecostofadozenbagelsincreasesby$1.80,theaveragecostofeachbagelwillincreasebyA)10¢.Theinteger2equals?timesthereciprocalof2.A)24C)615¢C)18¢D)30¢34D)8.Whichofthefollowingcouldbetheperimeterofarectanglewithbothoddandwhole-numberside-lengths?12.Howmanypositivedivisorsof122aremultiplesof12?A)26C)12D)2413C)14D)1656.Whatisthedifferencebetween23.456roundedtothenearesttenthand23.456roundedtothenearesthundredth?A)00.04C)0.05D)0.178.Theareaofasquareis36m2.TheperimeterofthesquareinisA)9002400C)3600D)360000.Whatisthegreatestodddivisorof2×4×6×8×10×12?A)915C)45D)1359.Roypainted100houses.Roypainted40%ofthehousesgrayand20%oftheremaininghouseshowmanyhousesdidRoypaintA)812C)20D)40110.Whichofthefollowingexpressionshasthegreatestvalue?12212A)C)D)2222221.Thetemperatureofapotofsoupincreasesby3°every40seconds.Howmuchwillthetemperatureincreasein30minutes?A)135°2.Icountedfrom1to100outloud,skippingeverymultipleof3.HowmanynumbersdidIsayoutloud?A)6667C)76D)773.Whatisthebetween2primeswhoseproductis10A)20222023C)2027D)20324.Apileof1003penniescanbedividedequallyintoexactly?equalpilesworth$4each.A)25250C)2500D)25000450°C)750°D)1800°11115.2022Ion101moredaysthanthenumberofdaysIdidnotrun.ThesumofthedigitsofthenumberofdaysIin2022isA)56C)8D)16.2999+2=A)21+9991×C)22+D)22×99917.80%ofAri’ssavingsequals20%ofAri’sandBev’ssavingscombined,musthave?timesmuchAri.A)28.Whatisthegreatestpowerof2thatisafactoroftheproductofthe6smallestpositive2-digitintegers?A)234C)26D)283C)4D)6119.Asquareposterconsistsof8cm-wideborderaroundtheperimeterofasquarephoto.theareaoftheentireposteris6400cm2,whatistheofthephotoportionoftheposter?A)4096cm24608cm2C)5120cm2D)5184cm220.Atriangle’sangleshavemeasuresthatareconsecutivemultiplesof15°.istheaveragemeasureofthe2smallestangles?A)37.5°52.5°C)67.5°D)82.5°21.Idividedamultipleof5byasmallermultipleof5andaremainderof15.Whatisthesmallestpossiblesumofthemultiples?A)3045C)55D)6522.Everythirdgumballdispensedhascracks,butthedonot.Ikeepevery4thgumballdispensedanddiscardtherest,howmanyofthe72gumballsIkeepwillhavecracks?A)63.Howmanyfactorsgreaterthanorequalto5does2×5101have?A)101102C)201D)20212C)18D)24224.oftheintegersfrom1through50waswrittenonaseparatetag,then3consecutivelynumberedwerelost.thesumoftheintegersonthe47remainingtagsis1221,whatisthesumofthedigitsoftheintegersonthelostA)1317C)27D)30225.themedianof6consecutiveintegersis4.5,whatisthemedianoftheirreciprocals?294999A)C)D)6.Myridetoschooltakesfrom10to18minutes,dependingontraffic.Icannotarrivebefore8:10AMor8:30AM.WhatisthebetweentheearliestandlatesttimesIcouldstartridingtoensurethatIarriveontime?A)8minutes7.Whatistheof2100and101?A)2100.52×29912minutesC)20minutesD)28minutes22C)2×2100D)3×2998.(0,0)and(3,4)aretwoverticesofaparallelograminacoordinateplane,whichofthefollowingcouldnotbeanothervertexofthisparallelogram?A)(4,3)(-1,7)C)-4)D)(-4,3)29.Onaclasstest,theaveragescoreoftheboysandcombinedwas88.theaveragescoreofthewas80,andtheaveragescoreofthewas100,whichofthefollowingnumberscouldbethetotalnumberoftheboysandcombined?A)10563C)48D)noneofabove30.Aclockthatuniformlyloses4minutesevery24hourscorrectlyset6A.M.onJanuary1.WhatisthecorrecttimetheclockreadsAMonJanuary6ofthesameA)AM,January612:00PM,January6C)12:30PM,January6D)AM,January731.wegetabullseyehalfthetimethatweplaydarts,isitmostlikelythatweA)missabullseyeinanysingleabullseyeleast1timein2tries,orC)abullseye2or3timesin332.Whatisthequotientofleastcommonmultipleofthefirst40positiveintegersdividedbytheleastcommonmultipleofthefirst30positiveintegers?A)1209C)2294D)noneofabove33.Howmanypointsdoesonehavetoplaceona1inchby3inchesrectangletoguaranteethattwoofthemarestrictlylessthan1inchapart?(TherectanglehereincludesitscompleteA)810C)12D)noneofabove34.Onesquarehastwicetheofanothersquare.Isitpossibleforbothsquarestohavesidelengthsthatarewholenumbers?A)35.Whatistheradiusofthecircleinscribedinatrianglewithsidelengths7