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  • SULIT

    [Lihat sebelah

    SULIT

    JABATAN PELAJARAN NEGERI SABAH

    SIJIL PELAJARAN MALAYSIA 2010 3472/1

    EXCEL 2

    ADDITIONAL MATHEMATICS

    PAPER 1

    OGOS 2010

    2 Jam Dua jam

    JANGAN BUKA KERTAS SOALAN INI

    SEHINGGA DIBERITAHU

    1. Tuliskan angka giliran dan nombor kad

    pengenalan anda pada ruang yang

    disediakan.

    2. Calon dikehendaki membaca arahan di

    halaman 2.

    Question Full

    Marks

    Marks

    Obtained

    1 2

    2 2

    3 3

    4 4

    5 3

    6 3

    7 3

    8 3

    9 2

    10 3

    11 3

    12 4

    13 3

    14 2

    15 3

    16 4

    17 4

    18 3

    19 3

    20 4

    21 4

    22 4

    23 4

    24 3

    25 4

    Total

    80

    __________________________________________________________________________

    This paper consists of 18 printed pages.

    NAMA : ________________________________

    KELAS : ________________________________

    http://chngtuition.blogspot.com

  • INFORMATION FOR CANDIDATES

    1. This question paper consists of 25 questions.

    2. Answer all questions.

    3. Give only one answer for each question.

    4. Write your answers clearly in the space provided in the question paper.

    5. Show your working. It may help you to get marks.

    6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer.

    7. The diagrams in the questions provided are not drawn to scale unless stated.

    8. The marks allocated for each question are shown in brackets.

    9. A list of formulae is provided on pages 3 to 5.

    10. A booklet of four-figure mathematical tables is provided.

    11. You may use a non-programmable scientific calculator.

    12. This question paper must be handed in at the end of the examination.

    http://chngtuition.blogspot.com

  • SULIT 3 3472/1

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

    ones commonly used.

    ALGEBRA

    1. 2 4

    2

    b b acx

    a

    2. m n m na a a

    3. m n m na a a

    4. ( )m n mna a

    5. log log loga a amn m n

    6. log log loga a am

    m nn

    7. log logna am n m

    8. log

    loglog

    ca

    c

    bb

    a

    9. ( 1)nT a n d

    10. [2 ( 1) ]2

    n

    nS a n d

    11. 1nnT ar

    12. ( 1) (1 )

    , 11 1

    n n

    n

    a r a rS r

    r r

    13. , 11

    aS r

    r

    CALCULUS

    1. , dy dv du

    y uv u vdx dx dx

    2. 2

    ,

    du dvv u

    u dy dx dxyv dx v

    3. dy dy du

    dx du dx

    4. Area under a curve

    =

    b

    a

    y dx or

    =

    b

    a

    x dy

    5. Volume generated

    = 2b

    a

    y dx or

    = 2b

    a

    x dy

    http://chngtuition.blogspot.com

  • STATISTICS

    1. x

    xN

    2. fx

    xf

    3.

    2 2

    2( )x x x

    xN N

    4.

    2 2

    2( )f x x fx

    xf f

    5.

    1

    2

    m

    N F

    m L cf

    6. 1 100o

    QI

    Q

    7. i i

    i

    W I

    I

    W

    8.

    !

    !

    n

    r

    nP

    n r

    9.

    !

    ! !

    n

    r

    nC

    n r r

    10. P A B P A P B P A B

    11. , 1n r n rrP X r C p q p q

    12. Mean, = np

    13. npq

    14. X

    Z

    GEOMETRY

    1. Distance

    = 2 2

    1 2 1 2x x y y

    2. Midpoint

    1 2 1 2, ,2 2

    x x y yx y

    3. A point dividing a segment of a

    line

    1 2 1 2, ,nx mx ny my

    x ym n m n

    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

    5. 2 2r x y

    6. 2 2

    xi yj

    rx y

    http://chngtuition.blogspot.com

  • SULIT 5 3472/1

    TRIGONOMETRY

    1. Arc length, s r

    2. Area of sector, 21

    2A r

    3. 2 2sin cos 1A A

    4. 2 2sec 1 tanA A

    5. 2 2cosec 1 cotA A

    6. sin 2 2sin cosA A A

    7. 2 2cos2 cos sinA A A

    2

    2

    2 os 1

    1 2sin

    c A

    A

    8. sin ( ) sin cos cos sinA B A B A B

    9. cos( ) os os sin sinA B c Ac B A B

    10. tan tan

    tan ( )1 tan tan

    A BA B

    A B

    11. 2

    2 tantan 2

    1 tan

    AA

    A

    12. sin sin sin

    a b c

    A B C

    13. 2 2 2 2 cosa b c bc A

    14. Area of triangle1

    sin2

    ab C

    http://chngtuition.blogspot.com

  • Answer all questions.

    Jawab semua soalan.

    1 The relation between 4,6,15,17P and 2,3,5,7Q is defined by the ordered

    pairs of 4,2 , 6,2 , 6,3 , 15,3 , 15,5 .

    Hubungan di antara 4,6,15,17P dan 2,3,5,7Q ditakrif oleh pasangan

    bertertib 4,2 , 6,2 , 6,3 , 15,3 , 15,5 .

    State

    Nyatakan

    (a) the object of 5,

    objek bagi 5,

    (b) the range of the relation.

    julat bagi hubungan tersebut.

    [2 marks]

    [2 markah]

    Answer / Jawapan : (a).....

    (b).

    2 Given that 2:f x x and 2: 2,gf x x find the function g. [2 marks]

    Diberi bahawa 2:f x x dan 2: 2,gf x x carikan fungsi g. [2 markah]

    Answer / Jawapan : .....

    For

    Examiners

    Use

    2

    2

    1

    2

    http://chngtuition.blogspot.com

  • SULIT 7 3472/1

    3. Given that : 6 5f x x and : 2 3,g x x find the function 1fg .

    Diberi bahawa : 6 5f x x dan : 2 3,g x x cari fungsi 1fg .

    [3 marks]

    [3 markah]

    Answer / Jawapan : ...

    4 Given one of the roots of the quadratic equation 2 27 0x px is the square of

    the other root.

    Diberi salah satu daripada punca persamaan kuadratik 2 27 0x px ialah

    kuasa dua punca satu lagi.

    (a) Find the value of p.

    Cari nilai p.

    (b) State the roots of the quadratic equation.

    Nyatakan punca persamaan kuadratik itu.

    [4 marks]

    [4 markah]

    Answer / Jawapan : (a) .

    (b) .....

    For

    Examiners

    Use

    3

    3

    4

    4

    http://chngtuition.blogspot.com

  • 5 Find the range of values of x for which 25 2 3.x x [3 marks]

    Cari julat nilai x bagi 25 2 3.x x [3 markah]

    Answer / Jawapan : ........

    6 Solve the equation 2 32 3 12.x x [3 marks]

    Selesaikan persamaan 2 32 3 12.x x [3 markah]

    Answer / Jawapan : ...

    7 Solve the equation 4 4log ( 6) log 1x x . [3 marks]

    Selesaikan persamaan 4 4log ( 6) log 1x x [3 markah]

    Answer / Jawapan : ...

    5

    3

    For

    Examiners

    Use

    6

    3

    7

    3

    http://chngtuition.blogspot.com

  • SULIT 9 3472/1

    8 Diagram 8 shows the graph of quadratic function 2( ) ( 1)f x a x k , where

    a and k are constants. The graph has a minimum point (1, 8) .

    Rajah 8 menunjukkan graf fungsi kuadratik 2( ) ( 1)f x a x k , dengan keadaan

    a dan k adalah pemalar. Graf itu mempunyai titik minimum (1, 8).

    Diagram 8

    Rajah 8

    State

    Nyatakan

    (a) the value of k,

    nilai bagi k,

    (b) the value of a,

    nilai bagi a,

    (c) the equation of axis of symmetry.

    persamaan bagi paksi simetri.

    [3 marks]

    [3 markah]

    Answer / Jawapan : (a) k = ...

    (b) a =...

    (c)

    For

    Examiners

    Use

    8

    3

    f (x)

    (1, 8)

    x O 3

    http://chngtuition.blogspot.com

  • 9 Find the number of terms in the arithmetic progression, 18, 13, 8, , 57.

    Cari bilangan sebutan dalam janjang aritmetik, 18, 13, 8, , 57.

    [2 marks]

    [2 markah]

    Answer / Jawapan : ...

    10 The first three terms of a geometric progression are h + 3, h, h 2.

    Tiga sebutan pertama suatu janjang geometri ialah h + 3, h, h 2.

    Find

    Cari

    (a) the value of h,

    nilai h,

    (b) the common ratio of the progression.

    nisbah sepunya janjang itu.

    [3 marks]

    [3 markah]

    Answer / Jawapan : (a) h = .

    (b)

    9

    2

    For

    Examiners

    Use

    10

    3

    http://chngtuition.blogspot.com

  • SULIT