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1、冲南外英数题练习1.Withthesameenginepower,ifaferryisrunningfor60kmwiththecurrent,ittakes5hoursfewerthanwhenitreturns.Whentheenginepowerisdoubled,thatmeansthespeedofferryinstillwaterisdoubled,ittakes1hourfewerwhentheferryisrunningfor60kmwiththecurrentthanitisagai
2、nstthecurrent.Findthespeedofthecurrentinkm/h.2.InΔABC,linesaredrawnfromverticesA,BandCtotheiroppositesidessothatthetriangleisdividedinto6parts.Theareasofsomepartsareshowninthefigure.FindtheareaofΔABC.3.EquilateraltriangleABPwithsideABoflength1cmisplaced
3、outsidesquareAXYZwithsideoflength2cmsothatBisonsideAX.Thetriangleisrotatedanti-clockwiseaboutB,thenP,andsoonalongthesidesofthesquareuntilP,AandBallreturntotheiroriginalpositions.FindthelengthofthepathincmtravelledbyvertexP.4.Therearefivepositiveintegers
4、.Takenfouratatime,theysumtofourdistinctvalues,namely,14,15,19,20.Findthefivepositiveintegers.5.Inthefigure,ABCDisasquare.AP=AQ=CR=CS=2cm.EisapointinsidethesquaresuchthatareasofthequadrilateralsAPEQandCRESare7cm2and9cm2respectively.Whatistheareaofthesqua
5、reABCD?32016南外冲刺群2840662116.Itisknownthatthesumoftwopositiveintegersis45andtheirL.C.M.is168,findthesetwointegers.7.Agroupofworkmentakessomebricksfromoneplacetoanother.Ifeachworkmantakesybricks,therewillbe12bricksleft.Ifeachofthemtakes8bricks,thelastwork
6、manjustneedstotake7bricks.Whatisthenumberofthisgroupofworkmen?8.Mingwenttoschoolwhenitwas12:00shownattheclockathome.Onhiswaytoschool,helookedattheclockinthechurchanditwas12:20pm.Whenhereachedschool,henotedthatthetimeshownattheclockintheschoolhallwas12:3
7、2pm.Afterstayingfor10minutesatschool,hewentbackhome.Onhiswayback,helookedatthechurchclockagainanditwas12:52pmandthattheclockathomewas1:16pmwhenhearrivedhome.Mingwastoldthatonlythetimeshownattheclockinhishomewascorrect,andifweassumethatthespeedofMingrema
8、inedconstantduringhisjourney,findthedifferencebetweenbothtimesshownatthechurchclockandtheschoolhallclockandthetimeshownattheclockathomerespectively.9.AnumberAwhichisdivisibleby9has2005digits.Thesumofallitsdigitsisa,thesumofalldig
