加拿大安大略省十年级数学试卷 英文

1of10GRADE10PRINCIPLESOFMATHEMATICS(ACADEMIC)MPM2DTotalMarks:INSTRUCTIONS:1.Calculatorsmaybeused.2.Readallinstructionscarefullyinordertomaximizeyourmark.A/C[K]PartA–MultipleChoice25Marks(25questions*1markeach)Foreachofthefollowingquestionsinthissection,circletheletterrepresentingthecorrectanswer.1.Alinearsystemoftwoequationsthathasonesolutionrepresentstwolinesthatare:a)parallelb)coincidentc)intersectingd)noneofthese2.ThemidpointofRSisM(8,-1).IfpointShascoordinates(11,4)whatarethecoordinatesofpointR?a)(3,-6)b)(15,-6)c)(5,-6)d)(3,9)3.ThemidpointofthelinesegmentwithendpointsA(-8,8)andB(6,4)is:a)(0,10)b)(1,2)c)(7,2)d)(-1,6)4.Theequationofahorizontallinepassingthroughthepoint(4,2)is:a)2xb)4yc)2yd)4x5.Theequationofalinewithaslopeof5mandayinterceptof8is:a)85xyb)85xyc)85xyd)58xyFeelfreetouseanyofthematerialinthisdocument.Marksareonlyguidelines.Wehavecategorizedeachquestionintooneofthe4achievementchart(A/C)categories:Knowledge/Understanding(K),ThinkingandInquiry(T),Application(A)andCommunication(C).Youcanchangeormodifythecategoriesasyouseefit.2of106.Theslopesof2linesare-7and71.Theselinesaresaidtobe:a)parallelb)perpendicularc)coincidentd)noneofthese7.Theslopeofalinesegmentpassingthrough2points(10,-4)and(-2,-16)is:a)1b)2c)-1d)-28.Thelengthofalinesegmentwithendpoints(-6,7)and(-1,-5)is:a)12b)5c)13d)1699.Thediameterofacirclewhoseequationis28922yxis:a)15b)16c)17d)noneofthese10.Theequationofacirclewithacentreof(0,0)thatalsopassesthroughthepoint(-8,-6)is:a)1022yxb)10022yxc)1422yxd)4822yx11.They-interceptoftheline01052yxis:a)2b)-2c)10d)512.Theslopeoftheline0124yxis:a)2b)-2c)1d)013.If(-3,y)isasolutiontotheequation132yx,whatisthevalueofy?a)3b)6c)5d)814.Theproductzyxzyx323243isequalto:a)2612zxyb)26412zyxc)2612zxyd)00412zyx15.Asimplifiedexpressionfornmnm52is:a)m7b)nm27c)m3d)nm273of1016.Asimplifiedexpressionfor242927abcbcais:a)ac3b)abc3c)23acd)223ca17.Theslopeoftheline,whichisperpendiculartotheline,084yxis:a)-4b)4c)1d)-118.Theshortestdistancefromthepoint(2,-3)totheline4xis:a)5b)3c)2d)619.Thevalueofthepolynomial8542aawhen3ais:a)59b)44c)13d)2920.Whichofthefollowingisnotafunction:a)7,6,5,4,3,2b)22xyc)22yxd)3,8,3,7,2,621.Therangeoftherelationwhoseequationis52xyis:a)5yb)5yc)5yd)5y22.Thevertexoftheparabola642xyis:a)6,4b)6,4c)4,6d)4,623.Theequationoftheaxisofsymmetryoftheparabola5242xyis:a)5xb)5xc)2xd)2x24.Aparabolawithavertexof3,2andastretchfactorof41(relativeto2xy)wouldhaveanequationof:a)32412xyb)32412xyc)23412xyd)23412xy25Theparabolakxy24passesthroughthepoint3,2.Thevalueofkis:4of10a)-19b)11c)13d)19A/CPartB–ShortAnswersForeachofthequestionsinthissection,writeyouranswersinthespacesprovided.Usethefoolscapprovidedforanyroughwork.Showdetailsofcalculationswhereverrequested.1.Intheaccompanyingdiagram,stateeachofthefollowing:(4Marks)[K]a)domain:__________(1Mark)[K]b)range:__________(1Mark)[C]c)Istherelationafunction?Justifyyouranswer.(2marks)[A]2.Thex-interceptsoftheparabola2892xyare:__________and__________.(Showyourwork)(2Marks)[A]3.Therootsofthequadraticequation0101732xxare:__________and__________.(Showyourwork)(3Marks)[A]4.Writetheequationoftheparabolawithavertexof(4,23)ifitpassesthroughthepoint(-1,-2):(Showyourwork)(3Marks)24-2-45of10x____________________[T]5.Alinepassesthrough2points(1,4)and(2,-4).Calculatetheslopeoftheline.Alsoshowtheequationofthelineintheform0CByAx.(Showyourwork)(4Marks)________________________________________SlopeEquation[K]6.TheTangentof45is:__________(1Mark)[A]7.a)Intheaccompanyingdiagram,thetwotrianglesaresimilar.Whatisthevalueofx?(Showyourwork)(2Marks)x__________[T]b)Iftheareaofthesmallertriangleis8cm2,whatistheareaofthelargertriangle?(Showyourwork)(2Marks)Area=__________[K]8GiventhatsinA=21,findA(tothenearestdegree)__________(1Mark)[A]9.Intheaccompanyingrighttriangle,findthevalueofxtoonedecimalplace.(Showyourwork)(2Marks)1218276of10x________[A]10.UsetheSINELAWtofindthevalueofsidextoonedecimalplace.(Showyourwork)(2Marks)x=________[A]11.UsetheCOSINELAWtofindthevalueofsidextoonedecimalplace.(Showyourwork)(2Marks)x=________[T]12.Factoreachofthefollowingtothefullestextentpossible:(4Questions*2markseach)a)yxmymx22________________________b)31142xx________________________c)2416916yx________________________3028x5642x30562030x7of10d)2225309srsr________________________A/CPartC–FullSolutionsRequiredForeachofthequestionsinthissection,fullsolutionsarerequired.Recordyouranswersinthespacesprovided.Usethefoolscapprovidedforanyroughwork.[A]1.Solvethelinearsystemusingtheeliminationmethod.Remembertofindvaluesforbothxandy.(5Marks)225yx2132yx[C]Explainwhatthesolutionaboverepresentsgeometrically.Howdoyouknowthatthesolutionyouarrivedatisthecorrectanswer?(2Marks)[A]2.Expandandsimplifythepolynomial21432xxx.(4Marks)[T]3.Findtheequationofthelineperpendiculartotheline088yxandpassingthroughthepoint(-4,1).(4Marks)8of10[T]4.Fromthewindowofonebuilding,am