[Edu. ] Pahang JUJ 2012 SPM Add Maths [E1129FED]

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  • JUJ 2012 MATEMATIK TAMBAHAN

    1

    MODUL

    MATEMATIK TAMBAHAN

    PROJEK

    JAWAB UNTUK JAYA

    (JUJ)2012

    Wahana Kecemerlangan SPM Negeri Pahang Darul Makmur

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  • JUJ 2012 MATEMATIK TAMBAHAN

    2

    KANDUNGAN

    PENDAHULUAN 2

    ANALISIS KERTAS SOALAN SPM (2003-2011) 3

    MODUL

    -STATISTICS 6

    -TRIGONOMETRIC FUNCTIONS 15

    JAWAPAN 23

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  • JUJ 2012 MATEMATIK TAMBAHAN

    3

    PENDAHULUAN

    Modul Matematik Tambahan dalam Projek Jawab Untuk Jaya(JUJ) 2012 Negeri Pahang

    disediakan khusus untuk menambahkan informasi serta latihan kepada pelajar-pelajar

    disamping Praktis Bestari. Pada tahun 2012 tajuk yang dipilih adalah Statistics dan

    Trigonometric Functions. Saban tahun panel JUJ Matematik Tambahan telah menyediakan

    sekurang-kurangnya dua topik untuk dijadikan Modul dalam JUJ. Topik Statistics dan

    Trigonometric Functions merupakan tajuk yang penting untuk dikuasai terutamanya dalam

    Kertas 2 kerana kedua-dua topik ini merupakan tajuk yang popular dan kekerapan keluar

    adalah sangat tinggi. Penguasaan pelajar dalam tajuk ini amat dituntut kerana peruntukan

    markahnya adalah tinggi. Turut disertakan sekali dalam modul ini adalah analisis kertas

    soalan Matematik Tambahan SPM bermula tahun 2003 sehingga 2011. Analisis ini boleh

    membantu pelajar mahupun guru mengkaji pecahan dan bilangan soalan bagi tahun-tahun

    terdahulu. Melalui analisis ini juga pelajar dan guru boleh merancang ulangkaji dan latih tubi

    dengan lebih tersusun dan berfokus. Diharapkan dengan adanya modul ini, kemahiran para

    pelajar terutamanya dalam topik Statistics dan Trigonometric Functions dapat

    dipertingkatkan serta meningkatkan lagi keyakinan bagi menghadapi SPM 2012.

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  • JUJ 2012 MATEMATIK TAMBAHAN

    4

    ANALISIS KERTAS SOALAN SPM (2003-2011)

    PAPER 1 YEAR

    Form Chapter 03 04 05 06 07 08 09 10 11

    4

    1 Functions 2 3 3 2 3 3 3 3 3

    2 Quadratic Equations 1 1 2 1 1 1 1 1 1

    3 Quadratic Functions 1 2 1 1 2 2 2 2 2

    4 Simultaneous Equations

    5 Indices and Logarithms 2 2 3 3 2 2 2 2 2

    6 Coordinate Geometry 2 2 1 1 2 2 1 2 1

    7 Statistics 1 1 1 1 1 1 1

    8 Circular Measure 1 1 1 1 1 1 1 1 1

    9 Differentiation 2 2 2 3 2 2 3/2 2 1

    10 Solution of Triangle

    11 Index Number

    5

    1 Progressions 2 4 3 2 3 3 3 3 3

    2 Linear Law 1 1 1 1 1 1 1 1

    3 Integration 2 1 1 2 1 1 5/2 1 2

    4 Vectors 3 2 2 2 2 2 2 2 2

    5 Trigonometric Functions 2 1 1 1 1 1 2 1 2

    6 Permutations / Combinations 2 1 1 1 1 1 1 1 1

    7 Probability 1 1 1 1 1 1 1 1

    8 Probability Distributions 2 1 1 1 1 1 1 1 1

    9 Motion Along A Straight Line

    10 Linear Programming

    Total 25 25 25 25 25 25 25 25 25

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  • JUJ 2012 MATEMATIK TAMBAHAN

    5

    PAPER 2 SECTION / YEAR

    Form Chapter Section A Section B

    03 04 05 06 07 08 09 10 11 09 04 05 06 07 08 09 10 11

    4

    1 Functions 1 1

    2 Quadratic Equations

    1/2

    3 Quadratic Functions

    1 1 1/2

    4 Simultaneous Equations

    1 1 1 1 1 1 1 1

    5 Indices and Logarithms

    1

    6 Coordinate Geometry

    1 1 1 1 1 1 1 1

    7 Statistics 1 1 1 1 1 1 1 1

    8 Circular Measure

    1 1 1 1 1 1 1 1 1

    9 Differentiation 1 1/2 1/2 2/3 1 1/2 1/2 1/3 1/3 1/3 1

    10 Solution of Triangle

    11 Index Number

    5

    1 Progressions 1 1 1 1 1 1 1 1

    2 Linear Law 1 1 1 1 1 1 1 1 1

    3 Integration 1/2 1/2 1/3 1 1/2 1/2 2/3 1 2/3 2/3 1 1

    4 Vectors 1 1 1 1 1 1 1 1 1

    5 Trigonometric Functions

    1 1 1 1 1 1 1 1 1

    6 Permutations / Combinations

    7 Probability

    8 Probability Distributions

    1 1 1 1 1 1 1 1 1

    9 Motion Along A Straight Line

    10 Linear Programming

    Total 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5

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  • JUJ 2012 MATEMATIK TAMBAHAN

    6

    PAPER 2 SECTION / YEAR

    Form Chapter Section C

    09 04 05 06 07 08 09 10 11

    4

    1 Functions

    2 Quadratic Equations

    3 Quadratic Functions

    4 Simultaneous Equations

    5 Indices and Logarithms

    6 Coordinate Geometry

    7 Statistics

    8 Circular Measure

    9 Differentiation

    10 Solution of Triangle 1 1 1 1 1 1 1 1 1

    11 Index Number 1 1 1 1 1 1 1 1 1

    5

    1 Progressions

    2 Linear Law

    3 Integration

    4 Vectors

    5 Trigonometric Functions

    6 Permutations / Combinations

    7 Probability

    8 Probability Distributions

    9 Motion Along A Straight Line 1 1 1 1 1 1 1 1 1

    10 Linear Programming 1 1 1 1 1 1 1 1 1

    Total 4 4 4 4 4 4 4 4 4

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  • JUJ 2012 MATEMATIK TAMBAHAN

    7

    STATISTICS

    FACTS AND FORMULAE

    Measures of Central Tendency

    Ungrouped Data Grouped Data

    Mean

    x = N

    x ,

    x = Sum of all the values N = Number of data

    x =

    f

    fx ,

    x = midpoint of class f = class frequency

    Mode

    Data that occurs most frequently

    Histogram

    Median

    The middle value in a set of data which is arranged in ascending or descending

    order

    Ogive

    Median , m = L + Cf

    FN

    m

    2

    1

    ,

    L = Lower boundary of median class N = Total frequency C = Size of median class

    mf = Frequency of median class

    F = Cumulative frequency before class median

    y

    x

    mode

    The bar representing the modal class

    N

    Cum

    ula

    tive

    fre

    qu

    en

    cy

    median

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  • JUJ 2012 MATEMATIK TAMBAHAN

    8

    Measures of Dispersion

    Ungrouped Data Grouped Data

    Range Largest Value/Data Smallest Value/Data

    Largest Class Mark/Mid Point Smallest Class Mark/Mid Point

    Interquartile range

    Third Quartile First Quartile

    3 1Q Q

    3 1Q Q

    3

    3 33

    34

    Q

    N F

    Q L Cf

    1

    1 11

    14

    Q

    N F

    Q L Cf

    L = Lower Boundary N = Total Frequency F = Cumulative Frequency

    before 1st or 3rd quartile class f = Frequency of the 1st or 3rd quartile class C= Size of the class interval

    Variance

    2

    2x x

    N

    2

    22 x xN

    2

    2f x x

    f

    2

    22 fx xf

    Standard Deviation

    2

    x x

    N

    2

    2( )x

    xN

    2

    f x x

    f

    22( )

    fxx

    f

    f = frequency x = class midpoint

    x = mean = x

    N

    f = frequency x = class midpoint

    x = mean =

    f

    fx

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  • JUJ 2012 MATEMATIK TAMBAHAN

    9

    Effects on Measures of Central Tendency

    Mode Median Mean Initial measure of central tendency

    a b c

    Each value increased by k

    a + k b + k c + k

    Each value decreased by k

    a - k b - k c k

    Each value multiplied by k

    ka kb kc

    Each value divide by k

    a

    k

    b

    k

    c

    k

    Exist an extreme value

    No effect No effect

    Too small or too big to be a suitable

    measure of central tendency

    Effects on Measures of Dispersion

    Range Interquartile range

    Variance Standard Deviation

    Initial measure of dispersion

    R r 2

    Each value increased by k

    R r 2

    Each value decreased by k

    R r 2

    Each value multiplied by k

    kR kr 2 2k k

    Each value divide by k

    R

    k

    r

    k

    2

    2k

    k

    Exist an extreme value

    Too big to be a suitable measure of dispersion

    No effect Too big to be a suitable measure of dispersion

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  • JUJ 2012 MATEMATIK TAMBAHAN

    10

    STATISTICS

    1 The mean of a set of data 2k 3 , 8 , k + 1 is 7. Find

    (a) The value of k (b) The new mean if each of the data multiflied by 3.

    [3 marks]

    2 The set of positive integers y , 2 , 11 , 5 , 7 , x , 9 has a mean 8 and median 9. Find the values of x and of y if y > x.

    [3 marks]

    3 A set of 10 scores x1 , x2 , x3 , , x