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    3472/2 2008 Hak Cipta SBP [Lihat sebelah

    SULIT

    SEKOLAH BERASRAMA PENUHBAHAGIAN PENGURUSAN

    SEKOLAH BERASRAMA PENUH / KLUSTER

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2008

    Kertas soalan ini mengandungi 15 halaman bercetak

    For examiners use only

    Question Total MarksMarks

    Obtained

    1 3

    2 3

    3 34 3

    5 3

    6 3

    7 3

    8 3

    9 3

    10 4

    11 4

    12 4

    13 4

    14 3

    15 2

    16 3

    17 4

    18 3

    19 3

    20 3

    21 3

    22 3

    23 3

    24 4

    25 3

    TOTAL 80

    M A T E M A T I K T A M B A H A N

    Kertas 1

    Dua jam

    J A N G A N B U K A K E R T A S SO A L A N IN I

    S E H IN G G A D IB E R IT A H U

    1 This quest ion paper consists of 25 quest ions.

    2 . Answer a ll quest ions.

    3. Give only one answer for each qu est ion.

    4. Write your answers clearly in the spaces provided in

    the quest ion paper.

    5. Show yo ur working. I t may help you to get marks.

    6. If you wish to change your answ er, cross out the work

    that you have done. Then wri te down the newanswer .

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

    8. The marks al located for each quest ion and sub-part

    of a quest ion are shown in brackets.

    9. A l ist of formulae is provided on pages 2 to 3.

    10. A bo oklet of four- f igure m athematical tables isprovided.

    .11 You may use a n on-programm able scient if ic

    calculator.

    12 This quest ion paper must be handed in at the end of

    the examinat ion .

    Name : ..

    Form : ..

    3472/1

    Matematik Tambahan

    Kertas 1

    Ogos 2008

    2 Jam

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    SULIT

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

    ALGEBRA

    1

    24

    2

    b b acx

    a

    =

    2 am an = a m + n

    3 am an = a m - n

    4 (am)

    n= a

    nm

    5 loga mn = log am + loga n

    6 logan

    m= log am - loga n

    7 log a mn = n log a m

    8 logab =a

    b

    c

    c

    log

    log

    9 Tn = a + (n-1)d

    10 Sn = ])1(2[2

    dnan

    +

    11 Tn = arn-1

    12 Sn =r

    ra

    r

    ra nn

    =

    1

    )1(

    1

    )1(, (r 1)

    13r

    aS

    =

    1, r

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    3

    STATISTIC

    1 Arc length, s = r

    2 Area of sector ,L = 212

    r

    3 sin2A + cos

    2A = 1

    4 sec2A = 1 + tan

    2A

    5 cosec2A = 1 + cot

    2A

    6 sin 2A = 2 sinA cosA

    7 cos 2A = cos2A sin

    2A

    = 2 cos2A - 1

    = 1 - 2 sin2A

    8 tan 2A =A

    A2

    tan1

    tan2

    TRIGONOMETRY

    9 sin (A B) = sinA cosB cosA sinB

    10 cos (A B) = cosA cosB sinA sinB

    11 tan (A B) =BA

    BA

    tantan1

    tantan

    m

    12C

    c

    B

    b

    A

    a

    sinsinsin==

    13 a2

    = b2

    + c2

    - 2bc cosA

    14 Area of triangle = Cabsin2

    1

    1 x =N

    x

    2 x = f

    fx

    3 =N

    xx 2)(=

    2_2

    xN

    x

    4 =

    f

    xxf 2)(=

    22

    xf

    fx

    5 m = Cf

    FN

    Lm

    + 2

    1

    6 1

    0

    100Q

    IQ

    =

    71

    11

    w

    IwI

    =

    8 )!(

    !

    rn

    n

    Prn

    =

    9!)!(

    !

    rrn

    nC

    r

    n

    =

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

    11 P (X= r) =rnr

    r

    n qpC , p + q = 1

    12 Mean = np

    13 npq=

    14 z =

    x

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    2

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    Answer all questions.

    1. A functionfmaps the elements from set { 3, 4, 9,16, 25}P m=

    to set Q = { 0, 3, 8, 15, 24 } as shown below in ordered pairs :

    { ( 3m , 0), (4, 3), (9, 8), (16, 15), (25, 24) }(a) Write down the function notation forf.

    (b) State the value ofm.

    (c) State the codomain.

    [ 3 marks ]

    Answer: ( a )..

    ( b )......

    ( c )..................................

    2. Given that function : 3, 0f x ax a < and 2 : 16f x x b , find the value ofa and ofb.

    [ 3 marks ]

    Answer: a =.

    b =..............................3

    2

    3

    1

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    4

    3. Given that function : 3 , 0k

    f x xx

    , and 1 4: ,f x x hx h

    +

    , find the value ofh

    and of k.

    [ 3 markah ]

    Answer: h =.........

    k=.....................................

    4. Given m and -3 are the roots of a quadratic equation 22 4 1x x k = , find the valueofm and ofk.

    [ 3 marks ]

    Answer: m =.........

    k =.....................

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    5. Given that quadratic equationx(3x p) = 2x 3 has no roots, find the range of values

    ofp.

    [ 3 marks ]

    Answer: .................................

    ___________________________________________________________________________

    6. Diagram 1 shows the graph of a curve qpxxf ++= 2)(2)( , wherepand q are constants.

    Diagram 1

    Given the straight line 3=x is the axis of symmetry of the curve and parallel to they-axis. Find

    (a) the value ofp,

    (b) the value ofq,

    (c) the turning point of the curve )(xf .

    [3 marks]

    Answer: (a) .........................

    (b) ........................

    (c)..................................

    3

    5

    3

    6

    For

    examiners

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    x

    qpxxf ++= 2)(2)(

    8

    O

    3=x

    f(x)

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    6

    7. Find the range of the values of x for which )52(2)12(3 + xxx .[3 marks]

    Answer: ..................................

    8. Solve the equation 23

    2

    1

    8 +

    = xx

    .

    [3 marks]

    Answer: . ..................................

    9. Solve the equation xx 2log1)25(log 55 = .[3 marks]

    Answer: ....................................

    7

    3

    9

    3

    8

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    10. Given that 2log2log 927 = qp , expressp in terms ofq.[4 marks]

    Answer: .........

    11. An arithmetic progression has 9 terms. The sum of the first four terms is 24 and the

    sum of all the odd number terms is 55. Find

    a) the first term and the common difference,

    b) the seventh term.

    [4 marks]

    Answer: ( a )............

    ( b).....................................

    10

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    8

    12. For a geometric progression, the sum of the first two terms is 30 and the third

    term exceeds the first term by 15. Find the common ratio and the first term

    of the geometric progression.

    [4 marks]

    Answer: .............___________________________________________________________________________

    13. Diagram 2 shows the graph ofxy against2x .

    The variablesx andy are related by the equationx

    kxy +=2 , where kis a

    constant. Find the value ofh and ofk.[4 marks]

    Answer: h = .

    k = ......4

    13

    4

    12

    For

    examiners

    use only

    (0 , h)

    2x

    (7 , 2)

    O

    xy

    Diagram 2

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    14. In Diagram 3 below, the equation of straight lineLM is 6

    x1

    4=

    y. The points

    L and M lie on thex-axis andy-axis respectively.

    Find the equation of a straight line which is perpendicular toLMand passes

    through the pointM.

    [3 marks]

    Answer : .

    15. In Diagram 4, OA a

    = and OB b

    = . On the same square grid , draw the line that

    represents the vector 3OC a b = + .[ 2 marks ]

    2

    15

    3

    14

    For

    examiners

    use only

    x

    y

    0

    M

    L

    Diagram 3

    O

    A

    B

    Diagram 4

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    10

    16. Given (2, 5), (3, 4)A B and ( , )C p q . Find the values ofp and q such that

    ~ ~

    2 9 5AB BC i j

    = .

    [3 marks]

    Answer: ......

    ___________________________________________________________________________

    17. Solve the equation 3sin2cos4 =+ xx for 3600 x .

    [4 marks]

    Answer: ............4

    17

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    18. Diagram 5 shows a sectorBOCof a circle with centre O.

    Given the perimeter of the sectorBOCis 24.5 cm, calculate

    (a) the radius of the sector

    (b) the area of the sector.

    [3 marks]

    Answer: a)...

    b) .

    ___________________________________________________________________________

    19. Given3

    )35(

    2)(

    xxf

    = , find the value of (2)f .

    [3 marks]

    Answer:

    3

    19

    3

    18

    For

    examiners

    use only

    B

    O

    C

    0.45 rad

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    20. Find the equation of normal to the curve xxy 53 += at the point when 1=x .

    [ 3 marks ]

    Answer: ............

    ___________________________________________________________________________

    21. Given that

    =

    2

    5

    6)( dxxf , calculate dxx

    xf

    5

    2 4

    )( .

    [3 marks]

    Answer: ..

    22. It is given that the sum of 5 numbers is . The mean of the sum of the square is 200and the variance is 3 2 . Express in terms of .

    [3 marks]

    Answer: ..

    3

    20

    3

    21

    3

    22

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    23. A pack of present containing three pens are chosen from 4 blue pens and 5 black pens.

    Find the probability of getting at least one black pen in the pack of present.

    [3 marks]

    Answer: ............

    ___________________________________________________________________________

    24.

    Diagram 6

    Diagram 6 shows six cards of different letters.

    (a) Find the number of possible arrangements beginning with P.

    (b) Find the number of these arrangements in which the vowels are separated.

    [ 4 marks ]

    Answer: ( a )

    ( b )

    For

    examiners

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    4

    24

    3

    23

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    25. Xis a random variable which is normally distributed with mean and standard

    deviation of 6. Find

    (a) the value of , if thez-value is 1.5 whenx = 42,

    (b) P(X < 47 ).

    [3 marks ]

    Answer: ( a)............

    ( b )...................................

    END OF QUESTION PAPER

    3

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