高二数学国际班试卷1

学校班级姓名学号A密封线内请不要答题2013——2014学年第一学期期末考试高二国际班数学命题人：王瑞1、Giventhreepoints,,,findtheequationoftheperpendicularbisectorof(a)AB,(b)BC.Hence,findthecoordinatesofthepointequidistantfromA,BandC.[10]2、Giventhat，findtheinversematrixofA，andthenuseyouranswertosolvethesimultaneousequations：[10]3、Thelineintersectsthecurveatpointand.Findthecoordinatesofand.[4]thelengthofAB.[4]4、(a)Expressinpartialfractions.[6](b)Factorisethecubicpolynomial.Hencesolvetheequation.[8]5、Thecoefficientofintheexpansionofis70,(a)Findthevalueofthepositiveconstant，[8](b)Hencecalculatethecoefficientofintheexpansionof.[6]6、Thefunction,areconstants,isexactlydivisibleby.Giventhatleavesaremainderof56whendividedby,findthevalueofandof,[7]determine,showingallnecessaryworking,thenumberofrealrootsoftheequation.[8]7、(a)Calculatetherangeofvaluesof.[4](b)Calculatetherangeofvaluesofforallrealvaluesof.[7](c)Findthevaluesoftheequationhas:[10](1)coincidentroots.(2)distinctrealroots.(3)onepositiverootandonenegativeroot.学校班级姓名学号A密封线内请不要答题8、(a)Twovariablesarerelatedbytheequation,Drawthegraphof.[6](b)Twovariablesarerelatedbytheequation.Showthat.[6]9、(a)Giventhatandthat,calculatethevalueofxandofy.[6](b)Solvetheequations:[10](1)(2)(c)Iffind[6](d)Solvethesimultaneousequations[8]10、Thediagrambelowshowslinesintersectingat.Linehasequationandhasequation.Thepointisthemidpointof.Thelineintersectsthey-axisatandthelineintersectsthex-axisat.Showthatangleis,[8]Findtheratiooftheareaoftriangletotheareaoftriangle.[8]