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秋季2021AMC10A试题与答案
1.What isthe value of⑵微高219A7B21C49D64E91Answer:C
2.Menkara hasa4x6index card.If she shortens the length of one sideof thiscardby1inch,the cardwould havearea18square inches.What wouldthe areaof thecardbe insquare inchesif insteadsheshortensthe lengthof theother sideby1inchA16B17C18D19E20Answer:E
3.What isthe maximumnumber ofballs ofclay with radius2that cancompletely fitinsidea cubeof sidelength6assuming that the balls can bereshaped butnotcompressed beforethey arepacked in the cubeA3B4C5D6E7Answer:D
4.Mr.Lopez hasa choiceof tworoutes toget towork.Route A is6miles long,andhis average speed along this route is30miles perhour.Route Bis5miles long,and his averagespeed along thisrouteis40miles perhour,except fora a-milestretch ina schoolzone wherehis averagespeed is20miles perhour.By howmanyminutes isRoute Bquicker thanRoute A3cl13B3-C4-D5-E6-
5.The six-digit number20210Aisprime foronly onedigit A.What isAA1B3C5D7E9Answer:E
6.Elmer theemu takes44equal stridesto walkbetween consecutivetelephone polesona ruralroad.Oscar theostrich cancover the same distancein12equal leaps.The telephonepoles areevenly spaced,and the41st polealongthisroad isexactlyone mile5280feet from the firstpole.How muchlonger,in feet,is Oscarsleapthan ElmersstrideA6B8C10D11E15Answer:B
7.As shown in the figure below,point Elies inthe oppositehalf-plane determinedbyline CDfrom pointA sothat/.CDE=110°.Point Flies onAD sothat DE=DF,and ABCDisa square.What isthe degreemeasure ofAAFE A160B164C166D170E174Answer:D
8.A two-digit positive integer issaid tobe cuddlyif itis equal to the sum of itsnonzero tensdigit and the squareofitsunits digit.How many two-digit positiveintegersare cuddlyA0B1C2D3E
49.When acertain unfairdie is rolled,an evennumber is3times aslikely toappear asanodd number.The dieisrolledtwice.What isthe probability that thesum of thenumbers rolledis even34595A8B9C9D T6E8Answer:E
10.A schoolhas100students and5teachers.In thefirst period,each student is takingoneclass,and eachteacher isteaching oneclass.The enrollmentsintheclassesare50,20,20,5,and
5.Let tbe theaverage valueobtained if a teacheris pickedatrandom andthe number of studentsin theirclass is noted.Let sbe theaveragevalue obtainedifastudentispicked atrandom andthe numberof studentsin theirclass,including thatstudent,isnoted.What isZ—5A-
18.5B-
13.5C0D
13.5E
18.5Answer:B
11.Emily seesa shiptraveling at a constantspeedalonga straightsection ofa river.She walksparallel to the riverbankatauniform ratefaster thanthe ship.Shecounts210equal stepswalking fromthe backof theship to the front.Walking intheopposite direction,she counts42steps of thesamesize fromthe frontof theshipto theback.In termsof Emilysequal steps,what isthelengthof theshipA70B84C98D105E126Answer:A
12.The base-nine representationof thenumber N is27,006,000,
052.What isthenineremainder whenNisdivided by
513.Each of6balls israndomly andindependently paintedeither blackor whitewithequal probability.What isthe probabilitythat everyball isdifferent incolor frommorethan halfof theother5balls11151A B6Q4D16®2Answer:DHow many ordered pairsx,y ofreal numberssatisfy thefollowing systemofequationsx2+=9|x|+|y|-42=1A1B2C3D5E7Answer:D
14.Isosceles triangleABC hasAB=AC=3\/6,and acircle withradius5\/2is tangenttoline ABat Band toline ACat C.What isthe areaof thecircle thatpassesthrough verticesA,B,and C兀A247rB257rC267rD27E287rAnswer:C
15.The graphof/x=||_xj|—11_1—xj|is symmetricabout whichof thefollowingHere|_xj isthe greatestinteger notexceeding x.A thej-axis Btheline x=1C theoriginD thepoint1,0E thepoint1,0An architectis buildinga structurethat willplacevertical pillars atthevertices ofregular hexagonABCDEF.which islyinghorizontally on the ground.The sixpillars willhold upa flatsolar panelthat willnotbe paralleltotheground.The heightsof thepillarsatA,B.and Care12,9,and10meters,respectively.What isthe height,in meters,of thepillar atE A9B673C873D17E1273Answer:D
16.A farmersrectangular fieldis partitionedinto a2by2grid of4rectangularsections asshowninthefigure.In eachsection thefarmer willplant onecrop:corn,wheat,soybeans,or potatoes.The farmer does not want togrow comandwheat in anytwo sections that share a border,andthefarmerdoesnotwanttogrow soybeansand potatoesinanytwosectionsthatshareaborder.Given theserestrictions,in howmany wayscan thefarmer choosecrops toplant ineach of thefour sectionsofthefieldAnswer:CA disk of radius1rolls allthe wayaround theinside ofasquareof sidelengths4and sweepsout aregion ofarea A.A seconddiskofradius1rolls alltheway aroundthe outsideofthesame squareand sweepsout aregion ofarea2A.The等,〃valueofscanbe writtenas+where a,b,and c are positive integers andb and〃carerelatively prime.What is+/7+c A10B11C12D13E
1420.For howmanyorderedpairs/7,c ofpositive integersdoes neitherx2++c=0nor x2+ex h=0have twodistinct realsolutionsA4B6C8D12E16Answer:B
21.Each of20balls istossed independentlyand atrandom intoone of5bins.Let pbethe probabilitythat somebin ends up with3balls,another with5balls,and theotherthree with4balls each.Let qbe theprobabilitythatevery binendsupwith4balls.What isA1B4C8D12E16Answer:E
22.Inside aright circularcone withbase radius5and height12are threecongruentspheres eachwithradiusr.Each sphereis tangent totheother twospheres andalsotangenttothe baseand sideofthecone.What isr-3A590—40144-2573B C2D---E|Answer:B
23.For eachpositiveintegern.let betwice thenumberofpositiveintegerdivisors ofn.and fory2,letFor howmanyvalues ofn50is fson=12A7B8C9D10E11Answer:D
24.Each ofthe12edges ofa cubeis labeled0or
1.Two labelingsare considereddifferenteven ifone canbe obtainedfromtheother bya sequenceofoneormore rotationsand/or reflections.For howmany suchlabelings isthesum of thelabelsontheedges ofeach ofthe6faces ofthe cubeequalto2A8B10C12D16E20Answer:E
25.A quadraticpolynomial pxwith realcoefficients andleading coefficient1iscalled disrespectfulif theequation ppx=0is satisfiedby exactlythree realnumbers.Among allthe disrespectfulquadratic polynomials,there isa uniquesuchpolynomial/x forwhich thesumofthe rootsis maximized.What is/151-59A-B-C-D1E-lo2o Answer:Ao。