SPM Trial 2009 AddMath Q&A (Kedah)

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    3472/1 [Lihat sebelahSULIT

    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 22 43 34 35 36 47 48 39 3

    10 311 312 413 314 315 216 317 4

    18 419 320 221 422 323 324 325 4

    TOTAL 80

    M AT E M AT I K TA M B A H A N

    Kertas 1Dua jam

    J A N G A N B U K A K E RTA S S O A L A N IN ISEHINGGA DIBERITAHU

    1 This question paper consists of 25 questions.

    2. Answer all questions.

    3. Give onlyone answer for each question.

    4. Write your answers clearly in the spaces provided inthe question paper.

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

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

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

    8. The marks allocated for each question and sub-part of a question are shown in brackets.

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

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

    .11 You m ay use a non-programm able scientific

    calculator.

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

    Name : ..

    Form : ..

    3472/1 Additional Mathematics

    Paper 1Sept 20092 Hours

    ADDITIONAL MATHEMATICSPaper 1

    Two hours

    3 to 4.

    2kk

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    BLANK PAGE HALAMAN KOSONG

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

    ALGEBRA

    12 4

    2

    b b ac x

    a

    - -=

    2 a m a n = a m + n

    3 a m a n = a m - n

    4 (a m) n = a nm

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

    6 log anm

    = log a m log a n

    7 log a mn

    = n log a m

    8 log ab =a

    b

    c

    c

    log

    log

    9 T n = a + (n 1)d

    10 S n = ])1(2[2

    d nan -+

    11 T n = arn-1

    12 S n =r r a

    r r a nn

    --=

    --

    1)1(

    1)1(

    , (r 1)

    13r

    aS

    -=

    1, r

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    STATISTIC

    1 Arc length, s = r q

    2 Area of sector , A = 212

    r q

    3 sin 2 A + cos 2 A = 1

    4 sec 2 A = 1 + tan 2 A

    5 cosec 2 A = 1 + cot 2 A

    6 sin 2 A = 2 sin A cos A

    7 cos 2 A = cos 2 A sin 2 A= 2 cos 2 A 1= 1 2 sin 2 A

    8 tan 2 A = A

    A2tan1

    tan2-

    TRIGONOMETRY

    9 sin ( A B) = sin A cos B cos A sin B

    10 cos ( A B) = cos A cos B m sin A sin B

    11 tan ( A B) = B A B A

    tantan1tantan

    m

    12C

    c B

    b A

    asinsinsin

    ==

    13 a 2 = b2 + c2 2bc cos A

    14 Area of triangle = C ab sin21

    1 x = N

    x

    2 x =

    f

    fx

    3 s = N

    x x - 2)(= 2

    2

    x N

    x -

    4 s = -

    f

    x x f 2)(= 2

    2

    x f

    x f -

    5 m = C f

    F N L

    m

    -+ 2

    1

    6 10

    100Q

    I Q

    =

    71

    11

    w I w

    I

    =

    8)!(

    !r n

    nPr n

    -=

    9!)!(

    !r r n

    nC r

    n

    -=

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

    11 P ( X = r ) = r nr r n q pC - , p + q = 1

    12 Mean = np

    13 npq=s

    14 z =s

    m - x

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    Answer all questions. Jawab semua 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 of x.Cari nilai x. [ 2 marks]

    [2 markah]

    Answer/Jawapan : (a) ..

    (b) ...

    2. Given5

    3:1

    x x f

    -- , find the value of

    Diberi5

    3:1

    x x f

    -- , cari nilai bagi

    (a) )3(- f ,

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

    [4 markah]

    Answer/ Jawapan : (a) ..

    (b) ... 4

    2

    2

    1

    For examiners

    use only

    Set A Set B

    49

    9

    x 9

    7

    3

    Diagram 1Rajah 1

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    3. Given that function a x xg + 2: and 9:2 - bx xg . Diberi fungsi a x xg + 2: dan 9:2 - bx xg .

    Find the value of a and of bCari nilai bagi a dan b .

    [3 marks][3 markah]

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

    4. Given that the straight line 14 += x y is a tangent to the curve k x y += 2 .Find the value of k .

    Diberi garis lurus 14 += x y ialah tangen kepada lengkung k x y += 2 .Cari nilai k .

    [ 3 marks][3 markah]

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

    For examiners

    use only

    3

    4

    3

    3

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    5.

    4)2(3 2 --= x y

    Diagram above shows the graph of the function 4)2(3 2 --= x y . 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 --= x y . 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 a and b are the roots of the quadratic equation 0792 =+- x x .Find the value of

    Diberi a dan b adalah punca bagi persamaan kuadratik 0792 =+- x x . Cari nilaibagi

    (a) b a +(b) ab

    (c) 22 b a + [ 4 marks ][4 markah]

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

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

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

    3

    5

    4

    6

    For examiners

    use only

    x

    y

    P

    Q

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    7. Solve the equation:Selesaikan persamaan :

    x x x 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 of x and of y if y > 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

    For examiners

    use only

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    9. Given that 2loglog 93 =+ y x . Express y in terms of x.[ 3 marks ]

    Diberi 2loglog 93 =+ y x . 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

    For examiners

    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 is31- , 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 =+ r a 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 =+ r a dan hasil tambah hingga sebutan ketakterhinggaan ialah 32,cari nilai a dan r .

    [4 markah]

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

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

    12

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    use only

    3

    11

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    13. Given that A, B )4,4(- , C )7,2( are collinear and 3AB=BC, find the coordinates of A.[ 3 marks ]

    Diberi A, B )4,4(- ,C )7,2( adalah segaris dan 3AB=BC, c arikan koordinat titik A.[3 markah]

    Answer/Jawapan : ...

    14. Diagram below shows the graph of y10log against x . Rajah di bawah me