2009 PSPM Kedah AddMath 12 w Ans

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    3472/1 [Lihat sebelah

    SULIT

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUASEKOLAH MENENGAH

    NEGERI KEDAH DARUL AMAN

    PEPERIKSAAN PERCUBAAN SPM 2009

    Kertas soalan ini mengandungi 17 halaman bercetak

    For Examiners use only

    Question Total MarksMarks

    Obtained

    1 2

    2 4

    3 3

    4 3

    5 3

    6 4

    7 4

    8 3

    9 3

    10 3

    11 3

    12 4

    13 3

    14 3

    15 2

    16 3

    17 4

    18 419 3

    20 2

    21 4

    22 3

    23 3

    24 3

    25 4

    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 S O A L A N IN I

    S E H I N G G A D I B E R I T A H U

    1 This question paper consists of 25 questions.

    2. Answerall questions.

    3. Give on ly on e answer for each quest ion.

    4. Write your answers clearly in the spaces provided in

    the question paper.

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

    6. If you wish to change you r answer, cross out the work

    tha t 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 a l loca ted for each quest ion and sub- art

    of a question are shown in brackets.

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

    10 . A boo klet of four-figure ma thematical tables is

    provided .

    .

    11 You m ay use a non-programm able scien t if iccalculator.

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

    the examinat ion .

    Name : ..

    Form : ..

    3472/1

    Additional Mathematics

    Paper 1

    Sept 2009

    2 Hours

    ADDITIONAL MATHEMATICSPaper 1

    Two hours

    3 to 4.

    2kk

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    SULIT

    2

    BLANK PAGE

    HALAMAN KOSONG

    2kk

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

    commonly used.

    ALGEBRA

    12 4

    2

    b b acx

    a

    - -=

    2 am an = a m + n

    3 am an = a m - n

    4 (am)

    n= a

    nm

    5 log a mn = log a m + log a n

    6 log an

    m= log a m log a n

    7 log a mn

    = n log a m

    8 logab =

    a

    b

    c

    c

    log

    log

    9 Tn = a + (n1)d

    10 Sn = ])1(2[2

    dnan

    -+

    11 Tn = arn-1

    12 Sn =r

    ra

    r

    rann

    -

    -=

    -

    -

    1

    )1(

    1

    )1(, (r 1)

    13

    r

    aS

    -

    =1

    , r

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    4

    STATISTIC

    1 Arc length,s = rq

    2 Area of sector ,A = 21

    2rq

    3 sin 2A + cos2A = 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 m sinA sinB

    11 tan (A B) =BA

    BA

    tantan1

    tantan

    m

    12C

    c

    B

    b

    A

    a

    sinsinsin==

    13 a2 = b2 + c

    2 2bc cosA

    14 Area of triangle = Cabsin2

    1

    1 =N

    x

    2 =

    f

    fx

    3 s =N

    xx - 2)(= 2

    2

    xN

    x-

    4 s =

    -f

    xxf 2)(= 2

    2

    xf

    xf-

    5 m = Cf

    FN

    Lm

    -

    + 2

    1

    6 1

    0

    100Q

    IQ

    =

    71

    11

    w

    IwI

    =

    8)!(

    !

    rn

    nPrn

    -=

    9!)!(

    !

    rrn

    nCr

    n

    -=

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

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

    12 Mean = np

    13 npq=s

    14 z =s

    m-x

    2kk

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    Answer all questions.

    Jawabsemua soalan.

    1. Diagram 1 shows the relation between set A and set B.

    Rajah 1 menunjukkan hubungan antara set A dan set B.

    a) State the image of 9.Nyatakan imej bagi 9.

    b) Find the value ofx.

    Cari nilai x. [ 2 marks]

    [2 markah]

    Answer/Jawapan : (a) ..

    (b) ...

    2. Given5

    3:

    1 xxf-

    - , find the value of

    Diberi5

    3:

    1 xxf

    -- , cari nilai bagi

    (a) )3(-f ,

    (b)p if 7)( -=pf .[ 4 marks ]

    [4 markah]

    Answer/ Jawapan : (a) ..

    (b) ...4

    2

    2

    1

    Forexaminers

    use only

    Set A Set B

    49

    9

    9

    7

    3

    Diagram 1

    Rajah 1

    2kk

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    3. Given that function axx +2: and 9:2 -bxxg .

    Diberi fungsi axg +2: dan 9:2 -bxxg .

    Find the value of a and ofb

    Cari nilai bagi a dan b .

    [3 marks]

    [3 markah]

    Answer/Jawapan : a =.........................b =.........................

    4. Given that the straight line 14 +=y is a tangent to the curve kxy += 2 .

    Find the value of k.

    Diberi garis lurus 14 += xy ialah tangen kepada lengkung kxy += 2 .

    Cari nilai k.

    [ 3 marks]

    [3 markah]

    Answer/Jawapan : k=......

    For

    examiners

    use only

    3

    4

    3

    3

    2kk

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    5.

    4)2(3 2 --= xy

    Diagram above shows the graph of the function 4)2(3 2 --= xy . Q is the minimum pointof the curve and the curve intersects the y-axis at point P. Find the equation of the straightline PQ.

    [ 3 marks ]

    Rajah di atas menunjukkan graf bagi fungsi 4)2(3 2 --= xy . Q ialah titik minimum bagi

    lengkung itu dan lengkung tersebut bersilang dengan paksi-y di titik P. Cari persamaan garislurus PQ.

    [3 markah]

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

    ___________________________________________________________________________

    6. Given that aand b are the roots of the quadratic equation 0792 =+- x .

    Find the value of

    Diberi a danb adalah punca bagi persamaan kuadratik 0792 =+- x . Cari nilai

    bagi

    (a) ba+(b) ab

    (c)22 ba + [ 4 marks ]

    [4 markah]

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

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

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

    3

    5

    4

    6

    Forexaminers

    use only

    x

    y

    P

    Q

    2kk

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    7. Solve the equation:

    Selesaikan persamaan:

    xxx 51 4)8(2 =- .

    [4 marks][4 markah]

    Answer/Jawapan :x =................................

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

    values ofx and ofy ify >x.

    [3 marks]

    Satu set integer positif 2, 5, 7, 9, 11, x, y mempunyai min 8 dan median 9. Cari

    nilai-nilai bagi x dan y jika y > x.

    [3 markah]

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

    4

    7

    3

    8

    Forexaminers

    use only

    2kk

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    9. Given that 2loglog 93 =+ yx . Expressy in terms ofx.

    [ 3 marks ]

    Diberi 2loglog 93 =+ yx . Ungkapkan y dalam sebutan x.

    [3 markah]

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

    10. The sixth and eleventh terms of an arithmetic progression are 12 and 37 respectively.Find the value of the sixteenth term of this arithmetic progression.

    [3 marks]

    Sebutan keenam dan kesebelas bagi suatu janjang aritmetik ialah 12 dan 37 masing-masing. Cari nilai bagi sebutan keenambelas bagi janjang aritmetik ini.

    [3 markah]

    Answer/Jawapan : ......

    3

    10

    Forexaminers

    use only

    3

    9

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    11. The first three terms of a geometric progression are 36, 36 p and q. If the

    common ratio is3

    1- , find the value of

    Tiga sebutan pertama suatu janjang geometri ialah 36, 36 p dan q. Jika nisbah

    sepunya ialah31- , cari nilai bagi

    (a) p ,

    (b) q.

    [ 3 marks ][3 markah]

    Answer/Jawapan: a) p = ...........

    b) q =...............................

    12. The first term of a geometric progression is a and the common ratio is r. Given that

    096 =+ ra and the sum to infinity is 32, find the value of a and of r.

    [ 4 marks ]

    Sebutan pertama bagi suatu janjang geometri ialah a dan nisbah sepunya r.Diberi 096 =+ ra dan hasil tambah hingga sebutan ketakterhinggaan ialah 32,cari nilai a dan r.

    [4 markah]

    Answer/Jawapan:a=...........

    r=...............................4

    12

    Forexaminers

    use only

    3

    11

    2kk

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