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  • 1

    BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN

    MODUL PERFECT SCORE

    SEKOLAH BERASRAMA PENUH TAHUN 2012

    Panel Penyedia:

    1. EN ABDUL RAHIM BIN BUJANG SEK TUN FATIMAH JOHOR BAHARU JOHOR (STF)

    2. TN HJ MOHD RAHIMI BIN RAMLI SEK MEN SAINS SULTAN MAHMUD .( SESMA)

    3. PN ROHANI MD NOR SEKOLAH SULTAN ALAM SHAH, PUTRAJAYA (SAS)

    4. PN AZIZAH BINTI KAMAR SBPI SABAK BERNAM (SBPISB)

    5. PN SARIPAH BINTI AHMAD

    SM SAINS MUZAFFAR SYAH, MELAKA.(MOZAC)

    6. PN SITI AZLINA BINTI KHAIRUDIN SMS TUANKU MUNAWIR

    7. PN NOTERZAM BINTI JAAFAR SMS TENGKU MUHAMMAD FARIS PETRA

    8. CHE RUS BINTI HASHIM SM SULTAN ABDUL HALIM KEDAH

    9. EN LIM YU TEONG SMS KUCHING

    10. EN JUPRI BIN BASARI SMS LAHAD DATU

    ADDITIONAL MATHEMATICS

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  • 2

    The following formulae may be helpful in answering the questions. The symbols given are the ones

    commonly used.

    ALGEBRA

    1. x = a

    acbb

    2

    42 8.

    a

    bb

    c

    ca log

    loglog

    2. aaanmnm 9. dnaT n )1(

    3. aaanmnm 10. ])1(2[

    2dna

    nS n

    4. aamnnm )( 11.

    1 nn arT

    5. nmmn aaa logloglog 12.

    r

    ra

    r

    raS

    nn

    n

    1

    )1(

    1

    )1(, r 1

    6. log log loga a am

    m nn 13.

    r

    aS

    1

    , r < 1

    7. mnm an

    a loglog

    CALCULUS

    1. y = uv, dx

    duv

    dx

    dvu

    dx

    dy

    4 Area under a curve

    = b

    adxy or

    = b

    adyx

    2. y = v

    u ,

    2v

    dx

    dvu

    dx

    duv

    dx

    dy

    5. Volume of revolution

    = b

    adxy2 or

    = b

    adyx2

    3. dx

    du

    du

    dy

    dx

    dy

    GEOMETRY

    1. Distance = 2122

    12 )()( yyxx 4. Area of triangle

    = 1 2 2 3 3 1 2 1 3 2 1 31

    ( ) ( )2

    x y x y x y x y x y x y

    2. Mid point

    ( x , y ) =

    2,

    22121 yyxx

    5. 22 yxr

    3. Division of line segment by a point

    ( x , y ) =

    nm

    myny

    nm

    mxnx 2121 , 6.

    2 2

    xi yjr

    x y

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  • 3

    STATISTICS

    1. N

    xx

    7

    i

    ii

    W

    IWI

    2.

    f

    fxx 8

    )!(

    !

    rn

    nPr

    n

    3. N

    xx

    2)( = 2

    2

    xN

    x

    9 !)!(

    !

    rrn

    nCr

    n

    4.

    f

    xxf 2)( = 2

    2

    xf

    fx

    10 P(AB) = P(A) + P(B) P(AB)

    11 P ( X = r ) = rnrrn qpC , p + q = 1

    5. m = L + Cf

    FN

    m

    21

    12 Mean , = np

    13 npq

    6. 1000

    1 Q

    QI 14 Z =

    X

    TRIGONOMETRY

    1. Arc length, s = r 8. sin ( A B ) = sin A cos B cos A sin B

    2. Area of sector, A = 22

    1r

    9. cos ( A B ) = cos A cos B sin A sin B

    3. sin A + cos A = 1 10 tan ( A B ) =

    BA

    BA

    tantan1

    tantan

    4. sec A = 1 + tan A 11 tan 2A =

    A

    A

    2tan1

    tan2

    5. cosec A = 1 + cot A 12

    C

    c

    B

    b

    A

    a

    sinsinsin

    6. sin 2A = 2sin A cos A 13 a = b + c 2bc cos A

    7. cos 2A = cos A sin A = 2 cos A 1

    = 1 2 sin A

    14 Area of triangle = 1

    sin2

    ab C

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  • 4

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  • 5

    ANALYSIS OF THE SPM PAPERS SIJIL PELAJARAN MALAYSIA

    ADDITIONAL MATHEMATICS (2006 2011)

    PAPER 1

    Question 2006 2007 2008 2009 2010 2011

    1 Functions Functions Functions Functions Functions Functions 2 Functions Functions Functions Functions Functions Functions

    3 Quadratic .Equations

    Functions Functions Functions Functions Functions

    4 Quadratic Functions

    Quadratic .Equations

    Quadratic .Equations

    Quadratic .Equations

    Quadratic Functions

    Quadratic .Equations

    5 Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    6 Indices & logarithms

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    Quadratic Functions

    7 Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    8 Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    Indices & logarithms

    9 Progressions Progressions Progressions Progressions Indices & logarithms

    Progressions

    10 Progressions Progressions Progressions Progressions Progressions Progressions 11 Linear Law Progressions Progressions Progressions Progressions Progressions

    12 Coordinate Geometry

    Linear Law Linear Law Circular Measures Linear Law Linear Law

    13 Vectors Coordinate Geometry

    Coordinate Geometry

    Vectors Coordinate Geometry

    Coordinate Geometry

    14 Vectors Coordinate Geometry

    Coordinate Geometry

    Vectors Coordinate Geometry

    Trigonometric Functions

    15 Trigonometric

    Functions Vectors Vectors Coordinate Geometry Vectors

    Trigonometric Functions

    16 Circular

    Measures Vectors Vectors Trigonometric Functions Vectors Vectors

    17 Differentiation Trigonometric

    Functions Trigonometric

    Functions Trigonometric

    Functions Circular

    Measures Vectors

    18 Differentiation Circular

    Measures Circular

    Measures Differentiation

    Trigonometric

    Functions

    Circular Measures

    19 Differentiation Differentiation Differentiation Differentiation Integration Integration

    20 Integration Differentiation Differentiation Differentiation Differentiatio

    n Differentiation

    21 Integration Integration Integration Integration Differentiatio

    n Integration

    22 Permutation

    & Combination Statistics Statistics Permutation & Combination Statistics Statistics

    23 Probability Permutation

    & Combination Permutation

    & Combination Probability

    Distributions

    Permutation &

    Combination

    Permutation &

    Combination 24 Statistics Probability Probability Statistics Probability Probability

    25 Probability

    Distributions Probability

    Distributions Probability

    Distributions Probability

    Distributions Probability

    Distributions Probability

    Distributions

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  • 6

    PAPER 2

    Question

    2006

    2007 2008 2009 2010 2011

    SECTION A

    1 Simultaneous

    Equations Simultaneous

    Equations Simultaneous

    Equations Simultaneous

    Equations Simultaneous

    Equations Simultaneous

    Equations

    2 Functions Coordinate Geometry Quadratic Functions

    Quadratic Equations & Functions

    Trigonometric Functions

    Indices & logarithms

    3 Progressions Trigonometric Functions Progressions Differentiation & Integration Progressions Progressions

    4 Trigonometric

    Functions Differentiation & Integration

    Trigonometric Functions

    Trigonometric Functions Integration

    Statistics

    5 Vectors Statistics Statistics Vectors Coordinate Geometry Coordinate Geometry

    6 Statistics Progressions Vectors Progressions

    Statistics

    Trigonometric Functions

    SECTION B

    7 Linear Law Linear Law Integration Integration

    Integration

    Linear Law

    8 Integration Vectors Linear Law Linear Law

    Linear Law

    Integration

    9 Coordinate Geometry

    Circular Measures

    Circular Measures

    Coordinate Geometry Vectors

    Circular Measures

    10 Circular

    Measures Integration Coordinate Geometry

    Circular Measures

    Probability Distributions Vectors

    11 Probability

    Distributions Probability

    Distributions Probability

    Distributions Probability

    Distributions Circular

    Measures Probability

    Distributions

    SECTION C

    12 Motion Along a Straight Line

    Motion Along a Straight Line

    Motion Along a Straight Line

    Solution of Triangles

    Motion Along a Straight Line

    Motion Along a Straight Line

    13 Solution of Triangles Index Number Index Number Index Number

    Solution of Triangles Index Number

    14 Linear

    Programming Linear

    Programming Solution of Triangles

    Linear Programming

    Linear Programming

    Solution of Triangles

    15 Index Number Solution of Triangles Linear

    Programming Motion Along

    a Straight Line Index Number Linear

    Programming

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  • 1

    Answer all questions.

    1 Diagram 1 shows a function : ,a

    f x x bb x

    Rajah 1 menunjukkan suatu fungsi : ,a

    f x x bb x

    f