KCPSS 2023 Prelim Paper 1

KUOCHUANPRESBYTERIANSECONDARYSCHOOL2023PreliminaryExaminationSecondary4Express/ 5NormalAcademic NAME CLASS INDEXNUMBER ADDITIONALMATHEMATICSPaper1 CandidatesanswerontheQuestionPaper.NoAdditionalMaterialsarerequired.Setter:Mr. WilsonSitoh 4049/01 28August2023 2hours15minutes READTHESEINSTRUCTIONSFIRSTWriteyourname,classandindexnumberinthespacesatthetopofthispage.Writeindarkblueorblackpen.YoumayuseanHBpencilforanydiagramsorgraphs.Donotusestaples,paperclips,highlighters,glueorcorrectionfluid. Answerallthequestions.Givenon-exactnumericalanswerscorrecttothreesignificantfiguresor1decimalplaceinthecaseofanglesindegrees,unlessadifferentdegreeofaccuracyisspecifiedinthequestion.Theuseofanapprovedscientificcalculatorisexpected,whereappropriate. Thenumberofmarksisgiveninbrackets[ ] attheendofeachquestionorpartquestion. Parent’sSignatureForExaminer’sUse Paper1(50%) / 90m Paper2(50%) / 90m TOTAL% / 100 Thetotalnumberofmarksforthispaperis90. AreastoNoteAccuracy Presentation

2 Pencil Units Thisdocumentconsistsof19printedpagesand1blankpage. MathematicalFormulae 1. ALGEBRA QuadraticEquationFortheequationax 2 +bx+c=0, . Binomialexpansion wherenisapositiveintegerand 2. TRIGONOMETRY Identities sin 2 A+cos 2 A=1.sec 2 A=1+tan 2 A.cosec 2 A=1+cot 2 A.sin( A±B)= sinAcosB±cosAsinBcos( A±B)= cosAcosB sinAsinB KCPSS2023/Sec4Exp/5NAPrelimAMathP1

3 sin2A=2sinAcosAcos2A= cos 2 A– sin 2 A=2cos 2 A–1=1–2sin 2 A FormulaeofΔABC KCPSS2023/Sec4Exp/5NAPrelimAmathP1 [TurnOver

4 1 (a)Express intheform wherea, and areconstants.− 2𝑥 2 + 3𝑥 + 2 𝑎 𝑥 + 𝑏( ) 2 + 𝑐 𝑏 𝑐[2] (b)Useyouranswerfrompart(a)toexplainwhythecurveswithequations and willnotintersect.𝑦 =− 2𝑥 2 + 3𝑥 + 2 𝑥 − 9( ) 2 + 𝑦 − 15( ) 2 = 25[4] KCPSS2023/Sec4Exp/5NAPrelimAMathP1

5 2 Thetableshowsexperimentalvaluesoftwovariables,xandy,whichareconnectedbyan equationoftheform , wherenandkareconstants. 𝑦 = 𝑘𝑥 𝑛 x 1.58 2.00 5.01 13.80 y 20.89 15.14 4.37 1.10 (a) Plotlgyagainstlgxanddrawastraightlinegraphtoillustratethisinformation. [2] KCPSS2023/Sec4Exp/5NAPrelimAmathP1 [TurnOver

6 (b) Useyourgraphtoestimatethevalueof kandn. [3] (c) Bydrawinganotherstraightlineonthesameaxes,estimatethevalueofxforwhich . [2] KCPSS2023/Sec4Exp/5NAPrelimAMathP1

7 3 Express inpartialfractions. [6] 4𝑥 3 −𝑥 2 +37𝑥−50(𝑥 2 +9)(𝑥−1) KCPSS2023/Sec4Exp/5NAPrelimAmathP1 [TurnOver

8 4 Acurvehasequation . PointsAandBlieonthecurveandhave 𝑦 =𝑥 2 − 𝑥 − 12xcoordinatesofkand2krespectively.– (a) FindtherangeofvaluesofkforwhichtheycoordinateofBislesserthan–ycoordinateofA. [3]– (b) ExplainwhythegradientofthecurveatAisalwayslesserthanthegradientofthecurveatB. [2] KCPSS2023/Sec4Exp/5NAPrelimAMathP1

9 5 (a) Findthefirst4termsintheexpansionof indescendingpowersof x,(2 − 3𝑥 2 ) 7 simplifyingeachterm. [3] (b) Hence,findthecoefficientofxintheexpansionof . [2](5𝑥 − 4𝑥 3 )(2 − 3𝑥 2 ) 7 KCPSS2023/Sec4Exp/5NAPrelimAmathP1 [TurnOver

10 (c) Giventhattheconstantterminthebinomialexpansionof is61236,findthe valueofthepositiveconstantk. [4] KCPSS2023/Sec4Exp/5NAPrelimAMathP1