英数题练习(附答案)

2016南外冲刺群2840662111冲南外英数题练习1.Withthesameenginepower,ifaferryisrunningfor60kmwiththecurrent,ittakes5hoursfewerthanwhenitreturns.Whentheenginepowerisdoubled,thatmeansthespeedofferryinstillwaterisdoubled,ittakes1hourfewerwhentheferryisrunningfor60kmwiththecurrentthanitisagainstthecurrent.Findthespeedofthecurrentinkm/h.2.InΔABC,linesaredrawnfromverticesA,BandCtotheiroppositesidessothatthetriangleisdividedinto6parts.Theareasofsomepartsareshowninthefigure.FindtheareaofΔABC.3.EquilateraltriangleABPwithsideABoflength1cmisplacedoutsidesquareAXYZwithsideoflength2cmsothatBisonsideAX.Thetriangleisrotatedanti-clockwiseaboutB,thenP,andsoonalongthesidesofthesquareuntilP,AandBallreturntotheiroriginalpositions.FindthelengthofthepathincmtravelledbyvertexP.4.Therearefivepositiveintegers.Takenfouratatime,theysumtofourdistinctvalues,namely,14,15,19,20.Findthefivepositiveintegers.5.Inthefigure,ABCDisasquare.AP=AQ=CR=CS=2cm.EisapointinsidethesquaresuchthatareasofthequadrilateralsAPEQandCRESare7cm2and9cm2respectively.WhatistheareaofthesquareABCD?2016南外冲刺群28406621126.Itisknownthatthesumoftwopositiveintegersis45andtheirL.C.M.is168,findthesetwointegers.7.Agroupofworkmentakessomebricksfromoneplacetoanother.Ifeachworkmantakesybricks,therewillbe12bricksleft.Ifeachofthemtakes8bricks,thelastworkmanjustneedstotake7bricks.Whatisthenumberofthisgroupofworkmen?8.Mingwenttoschoolwhenitwas12:00shownattheclockathome.Onhiswaytoschool,helookedattheclockinthechurchanditwas12:20pm.Whenhereachedschool,henotedthatthetimeshownattheclockintheschoolhallwas12:32pm.Afterstayingfor10minutesatschool,hewentbackhome.Onhiswayback,helookedatthechurchclockagainanditwas12:52pmandthattheclockathomewas1:16pmwhenhearrivedhome.Mingwastoldthatonlythetimeshownattheclockinhishomewascorrect,andifweassumethatthespeedofMingremainedconstantduringhisjourney,findthedifferencebetweenbothtimesshownatthechurchclockandtheschoolhallclockandthetimeshownattheclockathomerespectively.9.AnumberAwhichisdivisibleby9has2005digits.Thesumofallitsdigitsisa,thesumofalldigitsofaisbandthesumofalldigitsofbisc.Findthevalueofc.10.Thediagramshowsthenetofadodecahedron（十二面体）.Whichofthelabeledvertices(BtoK)willcometoAwhenthenetisfoldedtomakethedodecahedron?2016南外冲刺群2840662113答案：1.82.3154.1,2,5,6,75.646.21,247.138.22,339.910.D