modul sbp 2014 perfect score add math

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Bahan Pecutan Akhir Add Math SPM

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  • 1. 1BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUHDAN SEKOLAH KECEMERLANGANMODUL PERFECT SCORESEKOLAH BERASRAMA PENUH TAHUN 2014Panel Penyedia:1. TN HJ MOHD RAHIMI BIN RAMLISEK MEN SAINS SULTAN MAHMUD .( SESMA)2. PN NORIZAH BINTI RAHMATSEKOLAH MENENGAH SAINS JOHOR (SMSJ)3. PN SARIPAH BINTI AHMADSM SAINS MUZAFFAR SYAH, MELAKA.(MOZAC)4. PN SABARIAH BINTI SAMADSM SAINS REMBAU ( SEMESRA)5. EN ABDUL RAHIM BIN BUJANGSEKOLAH TUN FATIMAH ( STF)6. EN ABDUL RAHIM BIN NAPIAHSM SAINS TUN SYED SHEH SHABUDIN (STSSS)ADDITIONAL MATHEMATICS

2. 2The following formulae may be helpful in answering the questions. The symbols given are the onescommonly used.ALGEBRA1. x =ab b ac24 2 8.abbccalogloglog 2. a a a m n mn 9. T n a (n 1)d3. a a a m n mn 10. [2 ( 1) ]2a n dnS n 4. a an mn ( m) 11. 1 nT n ar5. log a mn log a m log a n12.ra rra rSn nn1(1 )1( 1), r 16. log log log a a amm nn 13.raS 1, r < 17. m n a mnlog a logCALCULUS1. y = uv,dxduvdxdvudxdy 4 Area under a curve= bay dx or= bax dy2. y =vu,2 vdxdvudxduvdxdy5. Volume of revolution= bay dx 2 or= bax dy 2 3.dxdududydxdy GEOMETRY1. Distance = 22 12( x2 x1 ) ( y y )4. Area of triangle= 1 2 2 3 3 1 2 1 3 2 1 31( ) ( )2x y x y x y x y x y x y2. Mid point( x , y ) = 2,2x1 x2 y1 y25.2 2 r x y3. Division of line segment by a point( x , y ) = m nny mym nnx1 mx2 1 2 ,6.2 2xi yjrx y 3. 3STATISTICS1.Nxx 7ii iWW II2.ffxx 8( )!!n rnPrn3.N x x2 ( ) = 22xNx 9( )! !!n r rnCrn4. ff x x 2 ( ) = 22xffx10 P(AB) = P(A) + P(B) P(AB)11 P ( X = r ) =r n rrn C p q , p + q = 15. m = L + CfN Fm 2112 Mean , = np13 npq6. 1000 1 QQI 14 Z =X TRIGONOMETRY1. Arc length, s = r 8. sin ( A B ) = sin A cos B cos A sin B2. Area of sector, A = 221r9. cos ( A B ) = cos A cos B sin A sin B3. sin A + cos A = 110 tan ( A B ) =A BA B1 tan tantan tan4. sec A = 1 + tan A11 tan 2A =AA2 1 tan2tan5. cosec A = 1 + cot A12CcBbAasin sin sin 6. sin 2A = 2sin A cos A 13 a = b + c 2bc cos A7. cos 2A = cos A sin A= 2 cos A 1= 1 2 sin A14 Area of triangle =1sin2ab C 4. 4 5. 5ANALISIS KERTAS PEPERIKSAAN SIJIL PELAJARAN MALAYSIAMATEMATIK TAMBAHAN (2007 2013)Kertas / Paper 1 (3472/1)TAJUK 2007 2008 2009 2010 2011 2012 2013 Fungsi Functions1,2,31,2,31,2,31,2,31,2,31,2,31,2,3 Persamaan Kuadratik Quadratic Equations444544,54 Fungsi Kuadratik Quadratic Functions5,65,65,64,65,665,6 Indeks & Logaritma Indices & Logarithms7,87,87,87,87,87,87,8 Janjang Progressions9,10,119,10,119,10,119,10,119,10,119,10,119,10,11 Hukum Linear Linear Law1212-12121212 Koordinat Geometri Coordinate Geometry13,1413,141513,141313,1413,14 Vektor Vectors15,1615,1613,1415,1616,1715,1615,16 Sukatan Membulat Circular Measures18181217181817 Fungsi Trigonometri Trigonometry Functions171716,171814,151718 Pembezaan Differentiation19,2019,2019,20202019,2019,20 Pengamiran Integrations212118,2119,2119,212121 Statistik Statistics22222422222222Pilihatur & Gabungan Permutations & Combinations232322,2323232323 Kebarangkalian Probability2424-24242424 Taburan Kebarangkalian Probability Distributions25252525252525 6. 6Kertas / Paper 2 (3472/2) TAJUK 2007 2008 2009 2010 2011 2012 2013Section / Bahagian A Persamaan Serentak Simultaneous Equations1111111 Janjang Progressions63633-2 Fungsi Kuadratik Quadratic Functions-22--2- Indeks & Logaritma Indices & Logarithms----2-- Geometri Koordinat Coordinate Geometry2--55-- Vektor Vectors-65--53 Fungsi Trigonometri Trigonmetry Functions3442664 Pembezaan Differentiation4-3--35 Pengamiran Integration---4--- Statistik Statistics55-6446Section / Bahagian B Hukum Linear Linear Law7887777 Pembezaan Differentiation-778-8- Vektor Vectors8--910-- Pengamiran Integration10---8-8 Koordinat Geometri Geometry Coordinate-109--109 Probability Distributions Taburan Kebarangkalian11111110111110 Sukatan Membulat Circular Measures9910119911Section / Bahagian C Motion Along a Straight Line Gerakan Pada Garis Lurus12121512121212 Penyelesaian Segitiga Solutions of Triangles15141215131313 Nombor Indeks Number Index13131313141414 Pengaturcaraan Linear Linear Programming14151414151515 7. 7FORMAT OF QUESTION PAPER : ADDITIONAL MATHEMATICS PAPER 2 ; 3472/2 COMPONENT TOPICALGEBRAFunctionsQuadratic EquationsQuadratic FunctionsSimultaneous EquationsIndices and LogarithmsProgressionsLinear LawSTATISTICSStatisticsPermutations and CombinationsProbabilityProbability DistributionTRIGONOMETRICCircular MeasuresTrigonometric FunctionsCALCULUSDifferentiationIntegrationGEOMETRYCoordinate GeometryVectorsAPPLICATIONS OF SCIENCE AND TECNOLOGYSolution of TrianglesMotion Along a Straight LineAPPLICATION OF SOSIAL SCIENCEIndex NumberLinear Programming 8. 8NO. TOPIC NO TOPIC NO TOPIC1.Simultaneous Equations7Linear Law12.Motion Along a Straight Line2.8.13.Solution of Triangles3.9.14.Index Number4.10.Circular Measures15.Linear Programming5.Trigonometric Functions11.Probability Distributions6.40 marks40 marks20 marks 9. 9SENARAI SEMAK MENJELANG PEPERIKSAAN SPMPaper 1Topic Subtopic Concept CheckFUNCTIONS Relation Arrow diagram, ordered pairs, graph -Object, image, domain, codomain , range, type of range,Inverse ComparisonComposite function Comparison , find the function given the composite functionQUADRATICEQUATIONSRoot of QuadraticEquationFind the root using formulaEquation ofQuadratic EquationForm quadratic equation (i) given roots(ii) and Type of Rootsb2 4ac 0 , b2 4ac 0 , b2 4ac 0 ,QUADRATICFUNCTIONCompletingthe squareGraph , maximum / minimum values/point , axis of symmetryAnalysis of the graph (comparison with the CT2 )Inequalities Find the range oINDICES &LOGARITHMSIndices Solve the equations involving indices : same base, using log,factorisationLogarithm Solve the equation involving log : same base , different baseexpress express - laws of logPROGRESSIONS AP nth-term , sum of the termsGP nth-term, sum of terms, sum of infinity, decimal to fractionCOORDINATESGEOMETRYDistance , midpoint, division m:n, area, parallel, perpendicular,equation of straight line, locusLINEAR LAW Comparison linear equation with the graph (log/non log)VECTOR Resultant of Vectors Collinear, parallelVectors in CartesianPlaneState vectors in i and j , column vectors, parallel, collinear, unitvectorDIFFERENTIATION Differentiate Direct/expand, uv , u/v , find the value of the diff , rate , smallchange, minimum/maximumINTEGRATION How to integrate, properties of integration, area, volumeCIRCULARMEASUREFind the angle (SOH CAH TOA) , arc length (perimeter), area ,area of segmentTRIGO Equation , ratio (triangle)STAT Mean, mod, median (formula) , Q1 , Q3 , IR , variance, standarddeviation , effect of +/- or /PERMUTATIONS &COMBINATIONSPermutations and CombinationsPROBABILITY Simple ProbabilityPROBABILITYDISTRIBUTIONSBinomial : find the probability , np, npq 2 Normal : find the probability , standard scoreX, z .find variable if the probability given. 10. 10Paper 2TopicSubtopicConceptCheckSECTION ASIMULTANEOUS EQUATIONFactorisation / using the formulaQUADRATIC EQUATION / FUNCTIONCT2 : express to the form of a(x+b)2 + c ; maximum/ minimum value/points , axis of symmetry , sketch the graph, the new equation when reflected x-axis/y-axisPROGRESSIONSAP , GPn-term, sum of the terms, sum to the infinitySTATISTICS- Mean, variance, standard deviation using formula,- Median (Formula) , Q1 and Q3 (using formula) , IR(using formula)- Histogram (find the mod)TRIGONOMETRIFUNCTION- prove- graph sine/cosine/tangent ; equation of straight line , noof solution(s)DIFFERENTATIONGradient function , turning point, equation of tangent/normal , equation of the curve by integrationSECTION BLINEAR LAWwith log / without logINTEGRATIONArea and volume by integrationCOORDINAT GEOMETRYEquation of straight line , parallel, perpendicular, area, midpoint, division m:n, equation of locusCIRCULARMEASUREAngle in radians (SOH CAH TOA or SOT) , arc length , perimeter and areaVECTORparallel, collinear , resultant of the vectors , find the variablesPROBABILITYDISTRIBUTIONSBinomial and NormalSECTION CINDEX NUMBERIndex, composite index , find the price using the index , three years caseSOLUTION OF TRIANGLEsine rule, cosine rule, area , ambiguous caseLINEAR PROGRAMMINGInequalities, graph, maximum/minimumINGAT ADD , INGAT A+ 11. 1111Answer all questionsJawab semua soalan1. Diagram 1 shows the graph of the function : 1myx , where m is a constant.Rajah 1 menunjukkan graf bagi fungsi : 1myx , dengan m ialah pemalar.Diagram 1 /Rajah 1Find the value of m.Cari nilai m.[2 marks]Answer/Jawapan:_______________________________________________________________________________2. The function f is defined by f (x) = 2x + 1 and fg(x) = 6x + 5, find 1g (x) .Fungsi f ditakrifkan oleh f (x) = 2x + 1 dan fg(x) = 6x + 5, cari 1g (x) .[3 marks]Answer/Jawapan :_______________________________________________________________________________yx (2,5)SET 1 12. 123. Given the function h : x ax b, where a and b are positive constants and the composite functionh : x 124x . Find the values of a and b.Diberi fungsi h : x ax b, dengan a dan b ialah pemalar positif dan fungsi gubahanh : x 124x . Cari nilai a dan nilai b.[3 marks]Answer/Jawapan:_______________________________________________________________________________4. Given that the roots of the quadratic equation x2 hx + 8 = 0 are p and 2p, find the values of h.Diberi punca-punca persamaan kuadratik x2 hx + 8 = 0 ialah p dan 2p, cari nilai-nilai h.[3 marks]Answer/Jawapan :_______________________________________________________________________________ 13. 135. Diagram 5 shows the graph of a quadratic function y = f (x). The straight line y = 16 is a tangentto the curve.Rajah 5 menunjukkan graf fungsi kuadratik y = f (x). Garis lurus y = 16 ialah tangen kepadalengkung.Diagram 5 / Rajah 5(a) Express f (x) in the form (x + b)2 + c, where b and c are constant.Ungkapkan f (x) dalam bentuk (x + b)2 + c, dengan keadaan b dan c adalah pemalar.(b) The curve, y = f (x) is reflected to the y-