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  • 8/10/2019 Sabah Add Math P1 & Ans 2

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    SULIT

    3472/1

    ADDITIONAL

    MATHEMATICS

    PAPER 1AUGUST 2008

    2 HOURS

    JABATAN PELAJARAN NEGERI SABAH

    SIJIL PELAJARAN MALAYSIA TAHUN 2008

    EXCEL 2

    ___________________________________________________________________________

    ADDITIONAL MATHEMATICSPAPER 1 (KERTAS 1)

    TWO HOURS (DUA JAM)

    ___________________________________________________________________________

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    1. Tuliskan angka giliran dan nombor kad

    pengenalan anda pada ruang yangdisediakan.

    2. Calon dikehendaki membaca arahan di

    halaman 2 .

    ___________________________________________________________________________This question paper consists of 14 printed pages.

    (Kertas soalan ini terdiri daripada 14 halaman bercetak.)3472/1 [Turn over (Lihat sebelah)

    NAMA : _____________________

    KELAS : _____________________

    NO K.P : _____________________

    A. GILIRAN : _________________-

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    2

    INFORMATION FOR CANDIDATES

    1. This question paper consists of 25 questions.

    2. Answer allquestions.

    3. Give only oneanswer 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.

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    3

    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 r S 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

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    STATISTICS

    1.

    x

    x N

    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 Fm L c

    f

    6. 1 100o

    QI

    Q

    7.i i

    i

    W II

    W

    8.

    !

    !r

    nnn rP

    9.

    !

    ! !r

    nnn r rC

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

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

    12. Mean, = np

    13. npq

    14. XZ

    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 3

    1( ) ( )

    2x y x y x y x y x y x y

    5. 2 2r x y

    6.2 2

    xi yj

    rx y

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    5

    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 2

    cosec 1 cotA A 6. sin 2 2sin cosA A A

    7. 2 2cos2 cos sinA A A

    2

    2

    2 os 1

    1 2 sin

    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

    2tantan 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

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    Answer allquestions.

    (a) State the type of relation between setPand set Q .(b) Using function notation, state the relation between setPand set Q.

    [2 marks]

    Answer : (a)

    (b) ..

    2. Given that : 7 4f x x . Find the value of pif (2) 5 3f p .

    [2 marks]

    Answer : p=

    ForExaminers

    Use

    1

    2

    2

    2

    1. In Diagram 1, set Pis the domain and set Qis the codomain of a relation.

    4

    9

    16

    4

    3

    2

    SetP Set Q

    Diagram 1

    2

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    3. Given that 13

    : 2, and ( ) .2

    g x ax g x b x Find the values of aand b.

    [3 marks]

    Answer : a=..

    b=..

    4. (a) Solve the following quadratic equation:24 4 3 0x x

    (b) Given the quadratic equation 2 9 0x px has two equal roots. Find the

    values of p. [4 marks]

    Answer : (a).

    (b).

    5. Find the range of the values ofxfor 2( 1) (2 3)( 1).x x x [3 marks]

    Answer :

    3

    3

    4

    4

    For

    ExaminersUse

    5

    3

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    6. The quadratic function 2( ) 3 6 5 can be expressed in thef x x x 2form 3( )x p q , wherepand qare constants. Find the values of pand q.

    [3 marks]

    Answer :p= ..

    q= ..

    7. Given that log 2a p and1

    log2

    aq , find the value of

    2

    logap q

    a.

    [3 marks]

    Answer : ..

    8. Solve the equation1

    2 1

    16 4

    y

    y y . [3 marks]

    Answer : ..

    ForExaminers

    Use

    7

    3

    8

    3

    6

    3

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    9. An arithmetic progression has 15 as the second term and 3 as the commondifference. List the first five terms of the progression. [2 marks]

    Answer : .

    10. The first three terms of an arithmetic progression are 4, 3,2 2p p p .

    Find(a) the value ofp,

    (b) the sum of the first 8 terms of the progression. [4 marks]

    Answer : (a).

    (b).

    11. The first term and the fourth term of a geometric progression are 16 and 2

    respectively. Calculate the sum to infinity of the geometric progression.

    [3 marks]

    Answer : ....

    9

    2

    ForExaminers

    Use

    10

    4

    11

    3

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    (b).. ...

    17. Solve the equation 3cos 2 8sin 5 for 0 360o o . [ 4 marks]

    Answer : ..

    18. The curve ( )y f x is such that2

    1dy pdx x

    , wherepis a constant.

    The gradient of the curve at 2x is1

    2. Find the value of p. [2 marks]

    Answer : ..

    19. Diagram 4 shows a circle with centre O and radius 4 cm.Given that the area of the

    minor sectorAOBis 9 cm2, calculate the length, in cm, of the major arcAB.

    [Use = 3.142] [4 marks]

    Diagram 4

    Answer : ..

    For

    ExaminersUse

    17

    4

    18

    2

    19

    4

    O

    A

    B

    4 cm

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    20. The curve 22 8 3y x x has a maximum point atx=p, wherepis a

    constant. Find the value ofp. [3 marks]

    Answer : .

    21. Given that3

    1

    ( ) 6g x dx , find

    (a) the value of1

    3

    ( ) ,g x dx

    (b) the value ofpif3

    1

    [ ( )] 18px g x dx . [4 marks]

    Answer : (a) ...

    (b) ...

    22. A set of data consists of five numbers. The sum of the numbers is 175 and the

    sum of the squares of the numbers is 6845. Find, for the five numbers(a) the mean,

    (b) the standard deviation. [3 marks]

    Answer : (a) ...

    (b) ...

    ForExaminers

    Use

    22

    3

    21

    4

    20

    3

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    23. A badminton team that consists of 8 students is