2014成都国际学校初升高数学试题

ENTRYEXAMINATIONFORTHEYEAROF2011TheInternationalCurriculumProgramEntryExam(Mathematics,Grade10),2011CandidateName6¶µCandidateNumberÒ:PAPERCODE11/2011READTHESEINSTRUCTIONSFIRST1.Thereare30questions.Eachquestionisfollowedby5optionsmarkedA,B,C,D,E.Onlyoneoftheseiscorrect.EntertheletterA-EcorrespondingtothecorrectanswerinthecorrespondingboxontheAnswerSheet.2.Timeallowed:60minutes.3.Calculatorsareforbidden.4.Scoringrules:0marksareawardedforeachquestionleftunanswered;2.5marksareawardedforeachcorrectanswer;0.5marksisdeductedforeachincorrectanswer.`²µ1.Áò
30K,þüÀK¶2.Ážm60©¨§ØU¦^OŽì;3.zKÀ˜‡Z‰Y:‰é2©§‰†ž0.5©§Ø‰0©;4.‰Y3‰Yò£˜¤þ§Á(å¤kÁò£iP“;1ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF20115.3=©ÁK¥§\ŒU¬^±eêÆ;’c®.midpoint¥:linesegment‚ãgradientÇevaluateOŽpositiveconstant~êvalueŠequalrootƒŠexpandÐminequalityتpercentz©'graphã”side(õ/)set8Ünumberêminimumfunction¼êinterval«mpoint:vertexº:sumÚanglerightangle†distinctØÓquadrilateralo/integerêarea¡ÈlengthÝintersectƒequation§trianglen/plane²¡realnumber¢êslopeǧ†gradientƒÓaltitude(n/)pline†‚joinëvertices(pl.)º:primenumberƒê£Ÿê¤maximumŒperfectsquare²square/cubeáNremainder{êtrapeziumF/diagonalé‚inscribeScircleprismcÎplane²¡surfaceareaL¡Èrhombus!/shadedÒKhexagon8/median¥ êregularhexagon8/positivesemicircleŒcentre¥%!%two-digitnumberü êprobabilityVÇmean²þêrandom‘Ådiameter†»overlap­UpentagonÊ/evennumberóêoddnumberÛêpolygonõ/hypotenuseperimeter±Thereare8printedpages
82ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF20111.Themidpointofthelinesegmentjoining(4;5)to(8;5)isA(2;4)B(1;4)C(2;5)D(1;5)Enoneoftheabove2.Thegradientofthelinejoining(3,-4)and(-1,8)isA3B3C13D13E13.Thetwolinesx+y=0and2xy+6=0intersectatthepointA1;12
B(1;1)C(3;4)D(2;1)E(2;2)4.Evaluate12sin3p22(1)30sin90A14Bp23Cp34Dp38ENoneofthese5.Thelengthofthelinesegmentjoining(1;4)to(7;2)isA6B7C8D9E106.Thevaluesofxforwhich(2x+1)(x3)0,areAx3Bx12Cx3orx12D12x3Ex37.Ifx2+x+p=0hasequalrootsandp0,pisA:p48B:p6C:4D:14E28.Solvingtheequation1x2=1x2x3givesAx=0Bx=1Cx=2DnosolutionEnoneoftheabove3ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF20119.Theline2x+3y=1isperpendiculartotheline2y+mx=2,thenm=Am=3Bm=3Cm=43Dm=43E.m=110.Ifaballisrandomlychosenfromaboxwhichcontains4redballs,5blackballsand7yellowballs,thenwhatistheprobabilitythattherandomlychosenballisblack?A17B13C14D516.E.71611.Thevertexoftheparabolay=x24x+hhascoordinates(2;5),whatisthevalueofh?A©9B.8C.2D.3E.noneofthese12.TheentriestotheFunprogramgrewfrom500in2010to701in2011.Approximatelywhatpercentageincreasedoesthisrepresent?A.30%B.40%C.50%D.60%.E.80%13.Solvingtheinequalities(2x+23x+3x13x422,givesA.2x1B.1x2Cx2Dx1Ex214.Inamagazine,10pagesofthe80pagesaredevotedtosports.WhatpercentofthemagazineisNOTdevotedtosports?A.27%B.37.5%C.47.5%D.62.5%E.87.5%15.Theminimumvalueofthefunctiony=x2+2x+3overtheinterval[2;1]isA-2B-3C0D2E316.Whichofthefollowingnumberisaperfectsquare?A.445566B.446665.C.455466.D.465465E.465564.17.Whatisthevalueofq126+162?A.110B.19C.13D.524E.7244ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF201118.200T-shirtshavebeenboughtforaFunRunatacostof$400plustaxat1712%.Thecostofentryfortherunis$5perperson.WhatistheminimumnumberofentriesneededinordertocoverthetotalcostoftheT-shirts?A.40B.47C.80D.84E.9419.Inthe…gureshown,AB=AFandABC,AFD,BFE,andCDEareallstraightlines.Whichofthefollowingexpressionsgiveszintermsofxandy?A.yx2B.yx2C.yx3D.yx3E.yx20.Thesymbolrisde…nedbyxry=xy2xy.Whatisthevalueof(1r0)r4?A.-9B.7C.5D.0.E.3:21.Inthexy-plane,pointR(2;3)andpointS(5;6)aretwoverticesoftriangleRST.Ifthesumoftheslopesofthesidesofthetriangleis1,whichofthefollowinganglescouldbearightangle?I\RII\SIII\TANoneBIonlyCIIIonlyDIIandIIIonlyEI,IIandIII22.Thereare10girlsinamixedclass.IftwopupilsfromtheclassareselectedatrandomtorepresenttheclassontheSchoolCouncil,thentheprobabilitythatbotharegirlsis0.15.Howmanyboysareintheclass?A.10B.12.C.15D.18E.noneofthese23.Whichoneofthefollowingrationalnumberscannotbeexpressedas1m+1n,wherem;naredi¤erentpositiveintegers?A.34B.35C.36D.37E.385ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF201124.Thediagramshowsanequilateraltriangletouchingtwostraightlines.Whatisthesumofthefourmarkedangles?A.120.B.180.C.240.D.300.E.36025.Deanrunsupamountainroadat8kmperhour.Ittakeshimonehourtogettothetop.Herunsdownthesameroadat12kmperhour.Howmanyminutesdoesittakehimtorundownthemountain?A.30B.40C.45D.50E.9026.Whichofthefollowingisequivalentto(x+y+z)(xyz)?A.x2y2z2.B.x2y2+z2.C.x2xyxzz2.D.x2(y+z)2.E.x2(yz)2.27.Thenumbersx;yandzsatisfytheequationsx+y+2z=850;x+2y+z=950;2x+y+z=1200whatistheirmean?A.250B.10003C.750D.1000Emoreinformationisneeded.28.Expanding3+p2
3givesA15+26p3B29p2+45C45p2+29D26+15p3Enoneoftheabove6ALLRIGHTSRESERVEDENTRYEXAMINATIONFORTHEYEAROF201129.Thedistancebetweentwoneighboringdotsinthedotlatticeis1unit.What,insquareunits,istheareaoftheregionwherethetworectanglesoverlap?A.6B.614C.612D.7E.71230.Fivetouchingcircleseachhaveradius1andtheircentersareatthever