spm trial 2010 addmath q&a (melaka)

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  • 8/8/2019 SPM Trial 2010 AddMath Q&A (Melaka)

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    SULIT

    [ Lihat sebelah

    3472/1 SULIT

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

    DENGAN KERJASAMA

    JABATAN PELAJARAN MELAKA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2010

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    Kertas soalan ini mengandungi 18 halaman bercetak

    Nama : ....

    Tingkatan: ..3472/1

    Matematik Tambahan

    Kertas 1

    Sept 2010

    2 jam

    1. This question paper consists of25 questionsKertas soalan ini mengandungi 25 soalan.

    2. Answer all questions.Jawabsemua soalan.

    3. Give only one answer for each questionBagi setiap soalan berikan SATU jawapan sahaja.

    4. Write the answers clearly in the space provided in the question paper. Jawapan hendaklah ditulis pada ruang yang disediakan dalam kertas soalan.

    5. Show your working. It may help you to get marks.Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh

    membantu anda untuk mendapatkan markah.

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

    you have done. Then write down the new answer.Sekiranya anda hendak menukar jawapan, batalkan kerja mengira yang telah

    dibuat. Kemudian tulis jawapan yang baru.

    7 The diagram in the questions provided are not drawn to scale unless

    stated.Rajah yang mengiringi soalan ini tidak dilukiskan mengikut skala kecuali dinyatakan.

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

    shown in brackets.Markah yang diperuntukkan bagi setiap soalan atau ceraian soalan ditunjukkan

    dalam kurungan.

    9.A list of formulae is provided on page 2 to 3Satu senarai rumus disediakan di halaman 2 hingga 3

    10. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak bolehdiprogram.

    11.This question paper must be handed in at the end of the examination. Kertas soalan ini hendaklah diserahkan pada akhir peperiksaan .

    Kod

    Pemeriksa

    SoalanMarkah

    Penuh

    Markah

    Diperoleh

    1 2

    2 2

    3 4

    4 3

    5 3

    6 3

    7 3

    8 4

    9 310 4

    11 4

    12 4

    13 3

    14 3

    15 4

    16 3

    17 4

    18 3

    19 3

    20 3

    21 322 3

    23 3

    24 3

    25 3

    Jumlah80

    MATEMATIK TAMBAHAN

    Kertas 1

    Dua Jam

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    SULIT

    3472/2 SULIT

    2

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

    used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang biasa

    digunakan.

    ALGEBRA

    12 4

    2

    b b acx

    a r

    2 am u an = a m + n

    3 am y an = a m - n

    4 (am) n = a

    nm

    5 logamn = log am + logan

    6 logan

    m= log am - logan

    7 log amn = n log am

    8 logab =ab

    c

    c

    loglog

    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(, (rz 1)

    13r

    aS

    f 1, r

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    SULIT 2STATISTICS

    1 Arc length, s = rT

    ( Panjang lengkok) s = j T

    2 Area of sector ,L = 21

    2rT

    ( Luas sektor L = T22

    1j )

    3 sin2A + cos

    2A = 1

    4 sec2A = 1 + tan

    2A

    5 cosec2A = 1 + cot2A

    6 sin 2A = 2 sinA cosA

    7 cos 2A = cos2A sin

    2A

    = 2 cos2A - 1

    = 1 - 2 sin2A

    8 tan 2A =A

    A2tan1

    tan2

    TRIGONOMETRY

    9 sin (ArB) = sinA cosB r cosA sinB

    10 cos (ArB) = cosA cosB # sinA sinB

    11 tan (ArB) =BtanAtan

    BtanAtan

    #1

    r

    12C

    c

    B

    b

    A

    a

    sinsinsin

    13 a2

    = b2

    + c2

    - 2bc cosA

    14 Area of triangle = Cabsin

    2

    1

    ( Luas Segitiga )

    1 x =N

    x

    2 x =

    f

    fx

    3 V =N

    xx 2)(=

    2_2

    xN

    x

    4 V =

    f

    xxf 2)(=

    22

    xf

    fx

    5 m = Cf

    FN

    Lm

    2

    1

    6 1

    0

    100Q

    IQ

    u

    71

    11

    w

    IwI

    8)!(

    !

    rn

    nP

    r

    n

    9!)!(

    !

    rrn

    nC

    r

    n

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

    11 P (X= r) = rnrr

    n qpC , p + q = 1

    12 Mean = np

    13 npqV

    14 z =V

    Px

    3

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    SULIT 4

    Answer all questions.

    Jawab semua soalan

    1 Diagram 1 shows the relation between two sets of number .Rajah 1 menunjukkan satu hubungan diantara dua set nombor.

    Diagram 1Rajah 1

    Based on the above information, the relation between P and Q is defined by the set

    of ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.Berdasarkan maklumat diatas hubungan antara P dan Q ditarifkan sebagai set pasangantertib { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.

    State,

    Nyatakan,(a) the image of 2.

    imej bagi 2

    (b) the object of 0.imej bagi 0

    [2 marks][ 2 markah ]

    Answer/Jawapan: (a) ..

    (b) ...

    2 Given the function g :x x2

    +1 , find the values of g-1

    (10)Di beri g :x x

    2+1 . Cari nilai nilai bagi g

    -1(10)

    [ 2 marks ][ 2 markah ]

    Answer/Jawapan: ......2

    2

    For

    examiners

    use only

    P ={ -3, -2, -1, 0, 1, 2 }

    Q ={ -1, 0, 1, 2, 3 }

    2

    1

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    5

    3472/1 [ Lihat sebelah

    SULIT

    3 The functionfis defined by f:x okx2 +p and the function g is defined by g:xo1 + 2x.Given the composite function fg :xox2 + x + 6, find the values of kandp.Fungsifditakrifkan sebagaif: x okx

    2+ p dan fungsi g ditarifkan sebagai g: x o1+ 2x

    Diberi fungsi gubahanfg : x ox2

    + x + 6, cari nilai k dan nilaip[4 marks]

    [ 4 markah]

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

    4 Given thatp

    1is one of the roots of the quadratic equation px

    2 + 7x 2p = 0, find the values ofp.

    Diberi bahawap

    1ialah salah satu punca bagi persamaan kuadratikpx

    2 + 7x 2p = 0, cari nilai-nilai

    bagip

    [ 3 marks ][ 3 markah ]

    Answer /Jawapan: ....

    For

    examiners

    use only

    4

    3

    4

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    SULIT 6

    ( 4, q )

    5 Diagram 5 shows the graph of a quadratic functionf(x) = 3(x +p)2 + 2, wherep

    is a constant. The curve y =f(x) has the minimum point (4, q), where q is a constant.Rajah 5 menunjukkan graf fungsi kuadratikf(x) = 3(x +p)

    2 + 2 , dimana p ialah pemalar

    Lengkung y =f(x) mempunyai titik minimum (4, q), dimana q ialah satu pemalar.

    State,Nyatakan,

    (a) the value ofp, nilai p

    (b) the value ofq, nilai q

    (c) the equation of the axis of symmetry.persamaan paksi semetri

    [ 3 marks ][ 3 markah]

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

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

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

    For

    examiners

    use only

    5

    Diagram 5Rajah 5

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    7

    3472/1 [ Lihat sebelah

    SULIT

    6 Find the range of values ofx for which 27)6( dxx .

    Cari julat nilai- nilai x dimana 27)6( dxx

    [3 marks][ 3 markah]

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

    7 Solve the equation 02781 321 xx .

    Selesaikan persamaan 02781 321 xx [ 3 marks ]

    [ 3 markah]

    Answer /Jawapan: x = ...

    8 Given log7 2 = h and log7 5 = k. Express log7 2.8 in terms of h and k.Diberi log7 2 = h dan log7 5 = k. Ungkapkan log7 2.8 dalam sebutan h dan k.

    [ 4 marks ]

    [ 4 markah ]

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

    For

    examiner

    use only

    8

    6

    3

    7

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    SULIT 8

    9 Solve 1)1(log)4(log 33 xx

    Selesaikan 1)1(log)4(log 33 xx

    [3 marks][ 3 markah]

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

    10 The first three terms of an arithmetic progression are 6, t 2, 14,....Tiga sebutan pertama satu janjang arithmatik ialah 6, t 2, 14,....

    find,

    cari,(a) the value of t,nilai t

    (b) the sum of the first ten term .hasil tambah sepuluh sebutan pertama

    [ 4 marks ][ 4 markah ]

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

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

    11 The sum of the first n terms of the geometric progression, 64, 32, 16, .. is 126.Hasil tambah n sebutan pertama suatu janjang geometri, 64, 32, 16, .. ialah 126

    Find,Cari,

    (a) the value ofn,

    nilai n(b) the sum to infinity of the geometric progression.

    hasiltambah ketakterhingaan janjang geometri ini,

    [ 4 marks ][ 4 markah]

    Answer/Jawapan: (a) n = .

    (b).

    4

    10

    For

    examiners

    use only

    3

    9

    4

    11

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    9

    3472/1 [ Lihat sebelah

    SULIT

    12 x andy are related by the equationm

    x nyx

    , where m and n are constants.

    A straight line is obtained by plottingxy againstx2, as shown in Diagram 12 .

    x dany dihubungkan oleh persamaanm

    x nyx

    , dimana m dan n ialah pemalar.

    Satu garislurus diperolehi dengan memplotkan xy melawan x2, sebagaimana ditunjukkan

    dalam Rajah 12

    Calculate the value ofm and ofn.Kira nilai m dan nilai n

    [4 marks][ 4 markah]

    Answer/Jawapan: m=

    n =.....

    4

    12

    For

    examiner

    use only

    xy

    x (12, 2 )

    x ( 6, 0) x

    2

    Diagram 12Rajah 12

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    SULIT 10

    13 Given that the point P 3,2 divides the line segment that joining ),4( tA and )8,(rB inthe ratio AP : PB = 1 : 4. Find the value ofrand of t.

    Diberi bahawa titik P 3,2 membahagi segmen garis yang menghubungkan),4( tA dan )8,(rB dalam nisbah AP : PB = 1 : 4. Cari nilai r dan nilai t.

    [3 marks][3 markah]

    Answer/Jawapan: ..

    14 Given that 2 2a i j

    , 2 3b i j

    and 2c a b

    .

    Diberi bahawa 2 2a i j

    , 2 3b i j

    dan 2c a b

    .

    Find,Cari,

    (a) c

    (b) unit vector in the direction ofc

    .

    vektor unit dalam arah c

    [3 marks][3 markah]

    Answer: (a)

    (b) ...

    For

    examiners

    use only

    13

    14

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    11

    3472/1 [ Lihat sebelah

    SULIT

    15 Diagram 15 shows a triangle POQRajah 15 menunjukkan segitiga POQ

    Diagram 15Rajah 15.

    Given that OPo

    = p and OQo

    = q .PointX is lies on OP where OX:XP = 2 : 1 and point Y

    is lies on OQ where OY: YQ = 3 : 1 . Straight line QXand line PYintersect at point C.

    Diberi OPo = p dan OQo = q . TitikX terletak pada OP di mana OX:XP = 2 : 1 dan titikYadalah

    titik pada OQ di mana OY: YQ = 3 : 1 . Garis lurus QXdan garis lurus PY bersilang pada titikC.

    Express in terms of p and q

    Ungkapkan dalam sebutan p dan q

    (a) PYo

    (b) QXo

    [ 4 marks]

    [4 markah]

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

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

    O PX

    C

    Y

    Q

    4

    15

    For

    examiner

    use only

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    SULIT 12

    16 Given that T is an acute angle andq

    pTsin , find in terms of p and /orq

    Diberi bahawa T ialah sudut tirus danq

    pTsin , cari dalam sebutanp dan/atau q

    a) cos T kosT

    b) tan ( 180 - T)

    [3 marks][ 3 markah ]

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

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

    17 Solve 3cos 2T + 4 cos T +1 = 0 for

    00

    3600dd

    T Selesaikan 3cos 2T + 4 cos T +1 = 0 untuk 00 3600 ddT

    [4 marks][4 markah]

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

    4

    17

    For

    examiners

    use only

    3

    16

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    13

    3472/1 [ Lihat sebelah

    SULIT

    A

    C

    R

    S

    OB 1.6 S

    8 cm

    18 Diagram 18 shows a circleABC with centre O, of radius 8 cm. SR is an arc ofa circle with centerO. The reflex angleAOCis 1.6S radian.

    Rajah 18 menunjukkan satu bulatanABC dengan pusat O dan berjejari 8 cm, SR ialah

    lengkuk sebuah bulatan berpusat di O . Sudut reflekAOC ialah 1.6S radian.

    Given thatA and C are midpoints ofOS and OR respectively, find the area of shadedregion, in terms ofS .Diberi bahawa A dan C ialah titik tengah kepada OS dan OR , cari luas kawasan berlorek

    dalam sebutan S

    [ 3 marks][ 3 markah ]

    Answer / Jawapan : . cm2

    19 The radius of circle decreases at the rate of 10.5cms . Find the rate of change of the

    area of a circle when the radius is 4 cm. .[ Given the area of a circle is A = r2

    ]Jejari sebuah bulatan berkurang dengan kadar 0.5 cms-1.Cari kadar perubahan luas

    bulatan apabila jejarinya ialah 4 cm, [ Diberi luas bulatan A = r2]

    [ 3 marks]

    [ 3 markah]

    Answer/Jawapan:

    For

    examiner

    use only

    19

    3

    18

    Diagram 18

    Rajah 18

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    SULIT 14

    3472/1 SULIT

    20 Given that5

    1

    ( ) 5g x dx , find the value of m if5

    1

    [ 2 ( )] 3mx g x dx m

    Diberi bahawa

    5

    1

    ( ) 5g x dx , cari nilai m jika5

    1

    [ 2 ( )] 3mx g x dx m

    [ 3 marks ][ 3 markah ]

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

    21 A set of numbers 1 2 3 4, , , ,..., nx x x x x has a median of 5 and a standard deviation of 2.

    Find the median and the variance for the set of numbers

    1 2 36 1,6 1,6 1,.......,6 1nx x x x .

    Satu set nombor1 2 3 4, , , ,..., nx x x x x mempunyai median 5 dan sisihan piawai 2.

    Cari median dan variance bagi set nombor 1 2 36 1,6 1,6 1,.......,6 1nx x x x

    .

    [ 3 marks ][ 3 markah]

    Answer/Jawapan : median = ..

    variance =...

    For

    examiners

    use only

    20

    21

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    SULIT 15

    [Lihat sebelah

    3472/1 SULIT

    22 A box contains 6 black balls andp white balls. If a ball is taken out randomly from the

    box, the probability of getting a white ball is7

    4. Find the value ofp.

    Sebuah kotak mengandungi 6 biji bola hitam danp biji bola putih . Jika sebiji bola diambil

    secara rawak dari kotak itu kebarangkalian mendapat sebiji bola putih ialah7

    4. Cari nilai p.

    [ 3 marks ][3 markah]

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

    23 An expedition team consisting of 10 members to be chosen from a group of 4 teachersand 12 students.Satu kumpulan ekspedisi mengandungi 10 ahli yang akan dipilih daripada kumpulan 4orang guru dan 12 orang pelajar.

    (a) Calculate the number of teams that can be formed.Kira bilangan kumpulan yang boleh dibentuk .

    (b) If the team must consist of at least 2 teachers, calculate the numbers of teams thatcould be formed.Jika kumpulan ekspedisi itu mesti mengandungi sekurang-kurangnya 2 orang guru kira

    bilangan kumpulan yang boleh dibentuk.

    [3 marks][ 3 markah]

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

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

    For

    examiners

    use only

    3

    23

    22

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    SULIT 17

    [Lihat sebelah

    3472/1 SULIT

    25 Diagram 25 shows a standard normal distribution graph.Rajah 25 menunjukkan graf taburan normal piawai

    The probability represented by the area of the shaded region is 0.803.Kebarangkalian yang diwakili oleh kawasan berlorek ialah 0.803

    (a) Find the value of P( Z > k)Cari nilai P( Z > k)

    (b) X is a continuous random variable which is normally distributed with a mean of

    P and a standard deviation of 2. If the value ofXis 85 when the Z-score is k,

    find the value of P.

    Xialah pembolehubah rawak selanjar yang bertabur secara normal piawai dengan min

    P dan sisihan piawai 2. Jika nilaiXialah 85 bila skor- Z ialah k, cari nilai P .

    [3 marks][ 3 markah]

    Answer: (a)

    (b) .

    END OF THE QUESTION PAPER

    KERTAS SOALAN TAMAT

    3

    25

    For

    examiners

    use only

    -k k z

    f(z))

    0.803

    Diagram 25

    Rajah 25

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    SULIT 18

    3472/1 SULIT

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    SULIT 3472/2

    [ Lihat sebelah

    3472/2 SULIT

    3472/2

    Matematik

    Tambahan

    Kertas 2

    Sept

    2010

    2 jam

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

    DENGAN KERJASAMA

    JABATAN PELAJARAN MELAKA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2010

    MATEMATIK TAMBAHAN

    Kertas 2

    Dua jam tiga puluh minit

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    1. This question paper consists of three sections : Section A, Section BandSection CKertas soalan ini mengandungi tiga bahagian : Bahagian A, Bahagian B dan Bahagian C.

    2. Answer all questions in Section A, four questions from Section B and two

    questions from Section C.Jawab semua soalan dalam Bahagian A, empat soalan daripada Bahagian B, dan dua soalan

    daripada Bahagian C.

    3. Give only one answer/solution to each question.

    Bagi setiap soalan, berikan satu jawapan / penyelesaian sahaja.4. Show your working. It may help you to get marks.

    Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk

    mendapatkan markah.

    5. The diagrams in the questions provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan,

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

    bracketsMarkah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan.

    7. A list of formulae is provided on pages 2 and 3.Satu senarai rumus disediakan di halaman 2 dan 3.

    8. A booklet of four-figure mathematical tables is provided.Buku sifir matematik empat angka boleh digunakan.

    9. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

    Kertas soalan ini mengandungi 17 halaman bercetak

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    SULIT

    3472/2 SULIT

    2

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

    the ones commonly used.Rumus-rumus berikut boleh digunakan untuk membantu anda menjawab soalan. . Simbol-simbol yang diberi adalah yang

    biasa digunakan.

    ALGEBRA

    1

    2

    42

    b b acxa

    r

    2 am u an = a m + n

    3 am y 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(, (rz 1)

    13

    r

    aS

    f1

    , r

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    SULIT

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    3

    STATISTICS ( STATISTIK)

    1 Arc length , s = rT

    (Panjang lengkok, s = jT)

    2 Area of sector ,A =21

    2rT

    (Luas sektor , L =21

    2j T )

    3 sin2A + cos

    2A = 1

    4 sek2A = 1 + tan2A

    5 cosec2A = 1 + cot2A

    6 sin2A = 2 sinAcosA

    7 cos 2A = cos2A sin2A= 2 cos2A-1= 1- 2 sin

    2A

    8 tan2A =A

    A2

    tan1

    tan2

    TRIGONOMETRY

    9 sin (ArB) = sinAcosB r cosAsinB

    (sin (ArB) = sinAkosB r kosAsinB)

    10 cos (ArB) = cosAcosB # sinAsinB(kos (ArB) = kos AkosB # sinAsinB )

    11 tan (ArB) =BA

    BA

    tantan1

    tantan

    #

    r

    12C

    c

    B

    b

    A

    a

    sinsinsin

    13 a2

    = b2

    +c2

    - 2bc cosA

    ( a2 = b2 +c2 - 2bckosA )

    14 Area of triangle ( Luas segitiga) = Cabsin2

    1

    1 x =N

    x

    2 x = f

    fx

    3 V =N

    xx 2)(=

    2_2

    xN

    x

    4 V =

    f

    xxf2

    )(=

    22

    xf

    fx

    5 m = Cf

    FN

    Lm

    2

    1

    6 1

    0

    100Q

    IQ

    u

    71

    11

    w

    IwI

    8 )!(

    !

    rn

    n

    Prn

    9!)!(

    !

    rrn

    nC

    r

    n

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

    11 P(X=r) = rnrr

    n qpC , p + q = 1

    12 Mean, = np

    13 npqV

    14 z =V

    Px

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    Section A

    [40 marks]

    [ 40 markah]Answerall questions in this section .

    Jawabsemua soalan dalam bahagian ini.

    1 Solve the following simultaneous equations:

    Selesaikan persamaan serentak berikut

    284 2 nmmnm[5 marks]

    [5 markah]

    2 Solution by scale drawing will not be acceptedPenyelesaian secara lukisan berskala tidak diterima.

    Diagram 2 shows the rhombusABCD with vertexA( -1, 5). The vertexB lies on thex-axis.Rajah 2 menunjukkan sebuah rombusABCD dengan bucuA( -1, 5). BucuB terletak pada paksi x

    0

    y

    x

    E

    D

    C

    B

    A(-1,5)

    Diagram 2Rajah 2

    The equation of the straight lineBD is x + 2y = 4. The diagonalsACandBD intersect at pointE.Persamaan bagi garislurusBD ialah x + 2y = 4. Garis pepenjuruACdanBD bersilang pada titikE.

    FindCari

    (a) the equation of the straight lineAC [3 marks]persamaan bagi garislurusAC [3 markah]

    (b) the coordinates of the pointE [2 marks]koordinat bagi titikE [2 markah]

    (c) the coordinates of the point C [2 marks]koordinat bagi titikC [2 markah]

    4

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    5

    3 (a) Sketch the graph of y = 3sin 2x + 1 for S2

    30 ddx [4 marks]

    Lakarkan graf y = 3sin 2x + 1 bagi S2

    30 ddx [4 markah]

    (b) Hence, using the same axes, sketch a suitable straight line to find the numberof solutions for the equation xx 22sin3 S for S

    2

    30 ddx . State the number of solutions

    [3 marks]Seterusnya, gunakan paksi yang sama, lakarkan garislurus yang sesuai untuk mencari bilangan

    penyelesaian persamaan xx 22sin3 S bagi S2

    30 ddx .

    Nyatakan bilangan penyelesaian. markah]

    4 The gradient function of a curve is kx2

    x, where k is a constant. The equation of the normal tothe curve at point (1, - 2) is 5y +x = 7.Fungsi kecerunan bagi suatu lengkung ialah kx2 x, di mana k ialah pemalar. Persamaan garis normal

    kepada lengkung di titik (1, - 2) ialah 5y +x = 7.

    Find

    Cari

    (a) the value ofk, [4 marks]nilai k, [4 markah]

    (b) the equation of the curve, [3marks] persamaan lengkung itu, markah]

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    6

    5 Table 5 shows the frequency distribution of the ages of a group of villagers in a village.Jadual 5 menunjukkan taburan kekerapan umur bagi sekumpulan penghuni di sebuah kampung.

    Table 5Jadual 5

    (a) (i) Without drawing an ogive, calculate the third quartile [3 marks]

    Tanpa melukis ogif, hitungkan kuartil ketiga [3 markah]

    (ii) Calculate the standard deviation of the distribution [3 marks]Hitungkan sisihan piawai bagi taburan itu. [3 markah]

    (b) If two villagers with the ages of 20 and 40 years old respectively were shifted out from the

    village, find the new variance. [2 marks]Sekiranya dua orang penghuni kampung itu yang berumur 20 dan 40 tahun masing-masing telah

    berpindah keluar dari kampung itu, cari varians yang baru.

    [2 markah]

    Age/Umur

    (year/tahun)

    Number of villagers/

    bilangan penghuni kampung1 - 10 25

    11 - 20 32

    21 - 30 28

    31 - 40 9

    41 - 50 6

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    7

    6 Diagram 6 shows the waves formed when a stone is thrown into the water. Each wave has theshape of a circle and is rcm away from the one before it.Rajah 6 menunjukkan gelombang yang terbentuk apabila seketul batu telah dibaling ke dalam air. Setiap

    gelombang berbentuk bulatan dengan jaraknya rcm jauh daripada bulatan sebelumya.

    Diagram 2Rajah 2

    r cmr cmr cm

    (a) show that the circumferences of the waves form an arithmetic progression and find the common

    difference. [3 marks]Tunjukkan bahawa lilitan bulatan gelombang itu membentuk satu janjang aritmatik dan carikan beza

    sepunya. [3 markah]

    (b) If the radius of the smallest wave is 4 cm, find the radius of the tenth wave . Hence, find its

    circumference in terms of S . [3marks]Sekiranya jejari bagi gelombang terkecil ialah 4 cm, hitungkan jejari bagi gelombang yang kesepuluh.

    Seterusnya, cari lilitan bulatan gelombang kesepuluh dalam sebutan S . [3 markah]

    Diagram 6

    Rajah 6

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    8

    Section B

    [40 marks]

    [ 40 markah]

    Answerfour questions from this section.Jawab empat soalan dalam bahagian ini

    7 Table 7 shows the values of two variables,x andy, obtained from an experiment. The

    variables are related by the equation pyx k 5 , where kandp are constants.Jadual 7 menunjukkan nilai-nilai bagi dua pembolehubah,x dany, yang diperoleh dari suatu

    eksperimen. Pembolehubah-pembolehubah itu dihubungkan oleh persamaan pyx k 5 ,di mana kdanp adalah pemalar.

    x 1.4 1.9 2.5 3.2 4.1 5.5

    y 3.3 5.3 7.9 12 15.8 26.3

    Table 7

    Jadual 7

    (a) Based on Table 7, construct a table for the values of log10y and log10x

    [2 marks]Berdasarkan Jadual 7, bina satu jadual bagi nilai-nilai log10y and log10x

    [ 2 markah]

    (b) Plot log10y against log10x by using a scale of 2 cm to 0.1 unit on the log10x- axis and 2 cm to

    0.2 unit on the log10y- axis. Hence, draw the line of best fit.[3 marks]

    Dengan menggunakan skala 2 cm kepada 0.1 unit pada paksi- log10

    x and 2 cm kepada 0.2 unit pada

    paksi-log10y, plot log10y lawan log10x dan seterusnya lukiskan garis penyuaian terbaik.

    [3 markah]

    (c) Use your graph in (a) to find the value ofGunakan graf anda di (a) untuk cari nilai

    (i) k

    (ii) p[5 marks]

    [5 markah]

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    9

    8 Diagram 8 shows ODC, OEA,BDEandACB are straight lines.Rajah 8 menunjukkan ODC, OEA, BDEdanACB ialah garis-garis lurus.

    E

    D

    C

    B

    AO

    Diagram 8Rajah 8

    It is given that xOA 6 , yOB 3 , OE: OA = 1 : 3, andDE= 3BD.

    Diberi bahawa xOA 6 , yOB 3 , OE : OA = 1 : 3, danDE= 3BD.

    (a) Express in terms ofx and y

    Ungkapkan dalam sebutan x dan y

    (i) AB

    (ii) OD

    [3 marks] [3 markah]

    (b) If ODmOC and BAnBC , where m and n are constants. Find the value ofm and n.

    [5 marks]

    Jika ODmOC and BAnBC , di mana m dan n ialah pemalar. Cari nilai bagi m dan n.[5 markah]

    (c) Given that 4x unit and the area of the triangle OBEis 20 unit2. Find the perpendicular

    distance fromB to OA

    [2 marks]

    Diberi bahawa 4x unit dan luas segitiga OBEialah 20 unit2. Kirakan jarak serenjang dariB ke OA.

    [2 markah]

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    10

    9 Diagram 9 shows OQRS is a sector of a circle with centre O. SOP is a straight line and OPQ is a

    right angle tringle.Rajah 9 menunjukkan OQRS ialah sebuah sektor bulatan yang berpusat di O. SOP ialah garislurus dan

    OPQ ialah sebuah segitiga bersudut tegak.

    Given that OP = 12 cm, q 30OPQ and the length of the arc QR is cm2

    S.

    Diberi OP = 12 cm, q 30OPQ dan panjang lengkok QR ialah cm2

    S.

    Find,Cari,

    (a) the length, in cm, of OQ [2 marks] panjang , dalam cm, bagi OQ [2markah]

    (b) QOR , in radians, [2 marks]

    QOR , dalam radian, [2 markah]

    (c) the area, in cm2, of the sectorROS, [3 marks]

    luas, dalam cm2, bagi sektorROS, [3 markah]

    (d) the perimeter, in cm, of the shaded region. [3 marks] perimeter, dalam cm, bagi rantau berlorek. [3markah]

    Diagram 9Rajah 9

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    11

    10 Diagram 10 shows the straight liney = -x + k touching the curvey = 3x x2

    at pointA.Rajah 10 menunjukkan garislurusy = - x + k menyentuh lengkungy = 3x x2pada titikA.

    Diagram 10Rajah 10

    Find,Cari,

    (a) the value ofk [2 marks]nilai k [2 markah]

    (b) the coordinates of pointA [2 marks]titik koordinatA [2 markah]

    (c) the area of the shaded region [3 marks]luas rantau berlorek [3 markah]

    (d) the volume generated,in terms ofS , when the region bounded by the curvey = 3x x2

    and thex-axis

    is revolved through 360 about thex-axis. [3 marks]isipadu janaan apabila rantau yang dibatasi oleh lengkungy = 3x x2 dan paksi -x dikisarkan melalui 360

    pada paksi -x. [3 markah]

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    12

    11 (a) In a survey carried out in a school, it is found that 3 out of 5 students have computer at home. If10 students from that school are chosen at random, calculate the probability thatDalam suatu soalselidik yang telah dijalankan di sebuah sekolah, didapati 3 daripada 5 orang pelajar

    mempunyai komputer di rumah. Sekiranya 10 orang pelajar dipilih secara rawak, hitung kebarangkalian

    (i) exactly 7 students have computer at home

    tepat 7 orang pelajar mempunyai komputer di rumah(ii) at least 2 students have computer at home

    sekurang-kurangnya 2 orang pelajar mempunyai komputer di rumah

    [ 5 marks] [5 markah]

    (b) The mass of a packet of cake produced by a factory is normally distributed with the mean of

    350g and a variance of 25g2.

    Jisim bagi sebungkus kek yang dihasilkan oleh sebuah kilang bertaburan normal, dengan minnya ialah

    350g dan varians 25g2.

    Find,

    Cari,(i) the probability that the mass of a packet of cake chosen at random will be less than 345g,

    kebarangkalian sebungkus kek yang dipilih secara rawak mempunyai jisim kurang daripada

    345g,

    (ii) the number of the packet of cakes whose masses exceed 342g if the factory produced

    1500 packets of cake daily.Bilangan bungkus kek yang berjisim lebih daripada 342g yang dapat dihasilkan oleh kilang itu

    jika ia menghasilkan 1500 bungkus kek sehari.

    [5 marks] [5 markah]

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    13

    Section C

    [20 marks]

    [ 20 markah]

    Answertwo questions from this section.

    Jawabdua soalan dalam bahagian ini

    12 A product is make up of four components,A,B, CandD .Table 12 shows the prices of the four

    components in the year 2004 and 2005 as well as their respective weightages.Suatu keluaran dihasilkan daripada gabungan empat komponen iaituA,B, CdanD. Jadual 12 menunjukkan

    harga setiap komponen pada tahun 2004 dan 2005 serta pemberat masing-masing.

    Componentkomponen

    Price/harga(RM) Price index for the year 2005based on the year 2004

    Index harga tahun 2005

    berasaskan tahun 2004

    WeightagepemberatYear/tahun

    2004

    Year/tahun

    2005

    A 90 x 150 2

    B 60 90 150 m

    C y 100 125 4

    D 30 42 z 8

    Table 12Jadual 12

    (a) Calculate the values ofx,y danz [3 marks]Hitungkan nilai bagix,y, danz [3 markah]

    (b) Given that the composite index of the product in the year 2005 based on the year 2004 was 141,

    find the value ofm. [3 marks]

    Diberi indeks gubahan bagi keluaran itu pada tahun 2005 berasaskan tahun 2004 ialah 141, Cari nilai m.[3 markah]

    (c) If the product is sold for RM350 a unit in the year 2004. Calculate the selling price of the

    product in the year 2005 in order to maintain the same profit. [2 marks]Sekiranya keluaran itu dijual dengan harga RM350 pada tahun 2004. Hitungkan harganya pada tahun 2005

    jika keuntungan yang sama dikekalkan. [markah]

    (d) If the prices of all components of the product was increased by 50% from the year 2004 to theyear 2006, find the composite index of the product in the year 2006 based on the year 2005.

    [2 marks]

    Sekiranya harga bagi semua komponen keluaran itu meningkat sebanyak 50% dari tahun 2004 ke tahun2006, cari indeks gubahan bagi keluaran itu pada tahun 2006 berasaskan tahun 2005.

    [2 markah]

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    14

    13 Diagram 13 shows a pyramid with a triangular base. The peakVis vertically above P.Rajah 13 menunjukkan sebuah piramid dengan tapak berbentuk segitiga. PuncakVterletak tegak di atas P.

    V

    6 cm

    8 cm

    11 cm

    Q

    R

    P

    Diagram 13Rajah 13

    Given that PR = 8 cm, PV= 6 cm, VQ = 11 cm and q 40PQR ,

    Diberi PR = 8 cm, PV= 6 cm, VQ = 11 cm dan q 40PQR ,

    Find,Cari,

    (a) the length, in cm, ofPQ; correct to 2 decimal places [2 marks] panjang PQ, dalam cm; betul kepada 2 tempat perpuluhan [2markah]

    (b) the length, in cm, ofQR [4 marks]panjang QR, dalam cm [4 markah]

    (c) the area, in cm2, of the inclined plane QVR [4 marks]

    luas , dalam cm2 bagi permukaan condong QVR [4 markah]

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    15

    14 Use graph paper to answer this question.Gunakan kertas graf untuk menjawab soalan ini.

    On a particular ferry trip to Langkawi, the passengers in the ferry comprisex adults andy

    children, with each adult paying a fare of RM40 and each children paying a fare of RM30. Thisparticular ferry trip is based on the following constraints.

    Pada suatu perjalanan feri pergi ke Langkawi, penumpang feri itu mengandungix orang dewasa danyorang kanak-kanak di mana setiap dewasa dan kanak-kanak perlu membayar tambang RM40 dan RM30

    masing-masing. Perjalanan feri itu perlu mematuhi syarat-syarat berikut.

    1 : The ferry can accommodate up to 40 passengers onlyFeri itu boleh muat sebanyak 40 orang penumpang sahaja.

    11 : The amount collected from the passengers fares must at least RM360, in

    order for the ferry company to make profit.Jumlah tambang yang dikutip daripada penumpang mesti sekurang-kurangnya

    RM360 supaya syarikat feri itu boleh memperoleh keuntungan daripada perjalanan

    itu.

    III : The number of adult passengers is not more than twice the number of childrenBilangan penumpang dewasa tidak lebih daripada dua kali ganda bilangan penumpangkanak-kanak.

    (a) Write three inequalities, other than 0tx and 0ty , which satisfy the above constraints.

    [3 marks]Tulis tiga ketaksamaan, selain daripada 0tx dan 0ty , yang mematuhi syarat- syarat di atas.

    [3 markah]

    (b) Using a scale of 2 cm to 5 passengers on both axes, construct and shade the region R, which

    satisfies all the above constraints. [3 marks]Dengan menggunakan skala 2 cm kepada 5 orang penumpang bagi kedua-dua paksi, bina dan lorekkan

    rantau R yang mematuhi semua syarat-syarat di atas. [3 markah]

    (c) By using your graph from (b), findDengan menggunakan graf anda dari (b), cari

    (i) the minimum number of passengers on this ferry trip if there are five adult passengers

    only.bilangan minima penumpang dalam perjalanan feri ini jika hanya ada lima orang penumpang

    dewasa sahaja.

    (ii) the maximum amount collected from the fares of the passengers.amaun maksima tambang penumpang

    [4 marks][4 markah]

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    16

    15 A particle moves along a straight line and passes through a fixed point O. Its velocity, V ms-1

    ,is given by v = t

    2- 9t+ 18, where t is the time in second after passing through O.

    [Assume motion to the right is positive]Suatu zarah bergerak sepanjang garislurus dan melalui titik tetap O. Diberi halaju zarah itu, Vms-1, ialah

    v = t2 - 9t+ 18, Di mana t ialah masa dalam saat selepas zarah itu melalui titikO.

    [Anggap gerakkan ke kanan sebagai positif]

    Find,Cari,

    (a) the initial velocity, in ms-1

    , of the particle. [1 mark]halaju awal, dalam ms-1, bagi zarah itu [1markah]

    (b) the maximum velocity , in ms-1

    , of the particle. [3 marks]halaju maksima, dalam ms-1, bagi zarah itu [3markah]

    (c) the range of values of t when the particle moves to the left [2 marks]Julat nilai t apabila zarah itu bergerak ke arah kiri [2 markah]

    (d) the total distance, in m, travelled by the particle in the first 5 seconds [4 marks]Jumlah jarak, dalam m, yang dilalui oleh zarah itu dalam 5 saat pertama [4 markah]

    END OF QUESTION PAPER

    KERTAS SOALAN TAMAT

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    17

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    Additional

    Mathematics

    Paper 1

    Sept

    2010

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

    DENGAN KERJASAMA

    JABATAN PELAJARAN MELAKA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2010

    ADDITIONAL MATHEMATICS

    Paper 1

    MARKING SCHEME

    This marking scheme consists of 5 printed pages

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    PAPER1

    QUESTION

    NUMBERSWORKING MARKS

    FULL

    MARKS

    1

    (a) 3

    (b) 1

    1

    1

    2

    2

    3,3

    x2+1=10or 11 xg

    2

    B1 2

    3

    4

    23

    4

    1 pandk

    4

    23

    4

    1 pork

    614 pkork

    pxk 2)21(

    4

    B3

    B2

    B1

    4

    4

    2 , -2

    028

    pp

    02)

    1

    (7)

    1

    (

    2 pppp

    3

    B2

    B1

    3

    5

    a) -4

    b) 2

    c) x = 4

    1

    1

    1

    3

    6

    3 9x d d

    2

    ( 9)( 3) 0

    6 27 0

    x x

    x x

    d

    d

    3

    B2

    B13

    7

    2

    13x

    4 4 6 9x x

    033 )32(3)1(4 xx

    3

    B2

    B1

    3

    3 9or or -3 and 9

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    QUESTION

    NUMBERSWORKING MARKS

    FULL

    MARKS

    8

    7 7 7

    7 7

    7

    1

    log 2 log 7 log 5

    log 2 log 7

    28

    log 10

    h k

    4

    B3

    B2

    B1

    4

    9

    1

    4log

    31

    4

    3

    3x

    x

    x

    x

    x

    3

    B2

    B13

    10

    a)t=12

    t8=16t

    b)240

    10

    [(2(6) 9(4)]2

    2

    B1

    2

    B1

    4

    11

    a) n=6

    5.01

    )5.01(64

    126

    n

    b) 128fs

    5.01

    64

    fs

    2

    B1

    2

    B1

    4

    12

    m = -6 and n = 3

    m = -6 or n = 3

    n

    m

    n 6

    0 and n

    m

    n 12

    2

    n

    m

    n

    60 or

    n

    m

    n

    122

    4

    B3

    B2

    B1

    4

    13

    r=6and7

    4t

    3

    3

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    QUESTION

    NUMBERSWORKING MARKS

    FULL

    MARKS

    4

    7t orr=6

    5

    )4(42

    r or

    5

    843

    t

    B2

    B1

    14 (a) 10

    6 8i j

    b) )43(5

    1ji

    2

    B1

    1

    3

    15(a) PY

    o= p +

    3

    4q

    PY

    o= OQPO

    o

    o

    4

    3

    (b) QXo

    =q+2

    3p

    QXo

    = OPQOo

    o

    3

    2

    2

    B1

    2

    B1

    4

    16a)

    q

    pq 22

    b) 22 pq

    p

    22 pq

    p

    1

    2

    B1

    3

    17 70.53 ,180 , 289.47$ $ $

    B3: 70.53 ,180$ $

    B2:(3cosT 1)(cosT +1)=0

    B1:2cos2T 1

    4

    B3

    B2

    B1

    4

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    QUESTION

    NUMBERSWORKING MARKS

    FULL

    MARKS

    18

    2 2

    38.4

    1 116 0.4 8 0.4

    2 2

    S

    S Su u u u

    2 21 116 0.4 8 0.42 2

    orS Su u u u

    3

    B2

    B1

    3

    19

    4

    2 (4)( 0.5)

    2dA

    rdr

    S

    S

    S

    3

    B2

    B1

    3

    2023

    B2:

    2 25 1[ ] 10 3

    2 2m m

    B1:

    5 52

    1 1

    2 ( )2

    mxor mx dx g x dx

    3

    B2

    B1

    3

    21

    2

    2

    31 var 144

    6(5) 1 6 (4)

    6(5) 1 6 (4)

    median and iance

    and

    or

    3

    B2

    B1

    3

    22

    pp

    p

    p

    p

    6

    7

    4

    6

    8

    3

    B2

    B1

    3

    23 (a) 8008

    (b) 7062

    B1:4 12 4 12 4 12

    2 8 3 7 4 6C C C C C C Or

    4 12 4 12

    1 9 0 108008 C C C C

    3

    2

    B1

    3

    or12.57

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    QUESTION

    NUMBERSWORKING MARKS

    FULL

    MARKS

    24 (a) 20

    B1: )4.0)(6.0(N =5

    24

    (b) 12

    2

    B1

    1 3

    25 (a) 0.0985

    (b) 82.42

    B1:85

    1.292

    orP

    1

    2

    B1

    3

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    SULIT

    3472/2

    Additional

    Mathematics

    Paper 2Sept

    2010

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

    DENGAN KERJASAMA

    JABATAN PELAJARAN MELAKA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2010

    ADDITIONAL MATHEMATICS

    Paper 2

    MARKING SCHEME

    This marking scheme consists of 13 printed pages

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    Question Mark Scheme of Paper 2 Trial SPM 2010 Melaka Sub

    Marks

    Total

    Marks

    1.n= -6 4m or n = m2 +m-2 or

    4

    6 nm

    m2+m+6+4m=2 or 4m+m2+m-2+8=2 or 2)4

    6(2)4

    6( nnn

    (m+4)(m+1)=0 or (n-10)(n+2)=0 or use formula/completing the square

    m= -4, -1 or n=10, -2

    n=10, -2 or m= -4, -1

    P1

    K1

    K1

    N1

    N1

    5

    2.(a)

    (b)

    (c)

    m2 = 2

    y -5= 2(x+1) or equivalent

    y = 2x +7

    Solve simultaneous equations: 22

    172 xx

    E( -2, 3)

    )3,2()2

    5,2

    )1((

    yx

    C( -3, 1)

    K1

    K1

    N1

    K1

    N1

    K1

    N1

    7

    3.(a)

    (b)

    Shape of sin x

    Graph of sin x shifted up 1 unit

    Miximum = 4, minimum = -2

    1 cycles in S

    2

    30 ddx

    12

    xyS

    or equivalent

    Sketch the straight line involves x and y

    Number of solutions = 4

    P1

    P1

    P1

    P1

    N1

    K1

    N1

    7

    4.(a) Gradient of tangent = 5

    kx2-x = 5

    substitute x = 1 to kx2-x = 5

    K1

    K1

    K1

    xSx

    4x

    1

    -2

    02

    S

    2

    3S

    3

    y

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    (b)

    k = 6

    cxx

    y 23

    6 23

    c2

    )1(

    3

    )1(62

    23

    2

    7

    22

    23

    xxy or equivalent

    N1

    K1

    K1

    N1 7

    5.(a)(i)

    (ii)

    (b)

    L = 20.5 F = 57 fQ3 = 28

    1028

    57)100(4

    3

    5.203

    Q

    = 26.93

    100

    )5.45(6)5.35(9)5.25(28)5.15(32)5.5(25 x

    =19.4

    222222

    4.19100

    )5.45(6)5.35(9)5.25(28)5.15(32)5.5(25

    V

    = 11.30

    222

    2

    98

    20401940

    98

    204050415

    V

    = 126.02

    P1

    K1

    N1

    K1

    K1

    N1

    K1

    N1

    8

    6. (a)

    (b)

    d = 2r or 2r, 4r, 6r

    d = 4r - 2r = 6r - 4r

    2r = 2r

    T10 = 4 + 9(4) or T10 = 2r + 9 (2r )= 40 = 20 (r)

    Circumference = 2(40) = 20 (4)

    = 80 = 80

    P1

    K1

    N1

    K1

    N1

    N1

    6

    7.(a)

    (b)

    (c)

    (i)

    (ii)

    log10x 0.15 0.28 0.40 0.51 0.61 0.74

    log10y 0.52 0.72 0.90 1.08 1.20 1.42

    Refer to the appendix

    One point correctly plotted with uniform scales

    6 points correctly plotted with uniform scales

    Line of best fit

    xkpy 101010 log5loglog

    -5k=1.52

    35.025.0 lk

    log10p = 0.29

    N1

    N1

    K1

    N1

    N1

    P1

    K1

    N1

    K1

    N1

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    0.29.1 lp 10

    8(a)(i)

    (ii)

    (b)

    (c)

    OBAOAB or equivalent

    yx 36

    xyOD 2

    1

    4

    9

    )2

    1

    4

    9( xymOC

    )36( yxnBC

    )36()2

    1

    4

    9(3 yxnxymy

    5

    6m

    10

    1n

    x 8 x h = 20

    h = 5

    K1

    N1

    N1

    P1

    P1

    K1

    N1

    N1

    K1

    N1

    10

    9(a)

    (b)

    (c)

    (d)

    1230sin

    OQq or equivalent

    OQ = 6

    TS

    62

    QOR rad12

    ST // 0.2618 rad

    radradROS 833.1/127/1051560180 Sqqqq

    Area of sector ROS = ROSuu 262

    1

    =32.99 or 10.5

    Perimeter of shaded region = )5.52sin6(2)12

    7(6 qS

    =20.52

    K1

    N1

    K1

    N1

    P1

    K1

    N1

    K1K1

    N1

    10

    10(a)

    (b)

    (c)

    Use b2 4ac = 0

    (-4)2 4(1)k =0

    k = 4

    Solve equation : (x 2)(x 2) = 0

    A(2, 2)3

    2

    32

    32

    3

    xx

    3

    2

    2

    )2(3

    3

    3

    2

    )3(3 3232

    K1

    N1

    K1

    N1

    K1

    K1

    N1

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    (d)

    =6

    7

    3

    0

    543

    54

    6

    3

    9

    xxxS

    = 05

    34)3(6

    3)3(9

    543

    S

    = 8.1

    K1

    K1

    N1

    10

    11(a)(i)

    (ii)

    (b)(i)

    (ii)

    377

    10 )4.0()6.0(C

    = 0.215

    1 P(x=0) P(x=1) or P(x=2)+P(x=3)+P(x+4)+ .+P(x=10)

    = 91110100

    010 )4.0()6.0()4.0()6.0(1 CC

    = 0.9983

    )5

    350345(

    zP

    = 0.1587 // 0.15866

    P(x >342) = 1 P(z > 1.6) or other valid method

    Number of cakes = 0.9452 x 1500

    = 1417 // 1418

    K1

    N1

    P1

    K1

    N1

    K1

    N1

    K1

    K1

    N1

    10

    12(a)

    (b)

    (c)

    (d)

    Use 100

    0

    1 u

    P

    PI

    x = 135, y = 80, z = 140

    141842

    )8(140)4(125150)2(150

    m

    m

    m = 6

    141100350

    2005 uP

    P2005 = 493.50

    100141

    11502005/2006 uuI

    = 106.38

    K1

    N2,1,0

    K1K1

    N1

    K1

    N1

    K1

    N110

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    Substitute t = 3 or t = 5 into ttt

    s 182

    9

    3

    23

    S3 = 22.5

    S5 =6

    119

    Total distance traveled= )

    6

    1195.22()05.22(

    6

    525

    OR5

    3

    233

    0

    23

    182

    9

    318

    2

    9

    3

    ttt

    tt

    )3(18

    2

    )3(9

    3

    3)5(18

    2

    )5(9

    3

    50)3(18

    2

    )3(9

    3

    3232323

    =6

    525

    K1

    K1

    N1

    K1K1

    K1

    N1

    10

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    7(a)

    14(b)

    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8 lg y

    (0.15,0.52)

    (0.28,0.72)

    (0.40,0.90)

    (0.51,1.08)

    (0.61,1.20)

    (0.74,1.42)

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    Rx+y=40

    x2y

    4x+3y=36

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    1

    PEPERIKSAAN PERCUBAAN SPM TAHUN 2010

    KERTAS SELARAS NEGERI MELAKA

    JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN

    (PAPER 1 & PAPER 2)

    TOPICSTotal

    Question

    s PAPER 1PAPER 2

    Section A Section B Section C

    No

    Marks

    No

    Marks

    No

    Marks

    No

    Marks

    1) A1 Functions (F4) 3

    1 2

    2 4

    3 3

    2) A2 Quadratic Equations (F4) 1 4 3 2 7

    3) A3 Quadratic Functions (F4) 25 2

    6 3

    4) A4 Simultaneous Equations (F4) 1 - - 1 5

    5) A5 Indices and Logarithms (F4) 27 3

    8 3

    6) A6 Progressions (F5) 3

    9 3 6 6

    10 2

    11 4

    7) A7 Linear Law (F5) 1 - - 8 10

    8) T1 Circular Measure (F4) 1 12 4 10 10

    9) G2 Vectors (F5) 213 4 5 8

    14 4

    10) G1 Coordinate Geometry (F4) 1 15 3 9 10

    11) T2 Trigonometric Functions (F5) 216 3 4 617 3

    12) C2 Integration (F5) 218 3 7 10

    19 4

    13) C1 Differentiation (F4) 1 20 3 3 7

    14) S2 Permutations/Combinations (F5) 1 21 4

    15) S3 Probability (F5) 1 22 3

    16) Statistics ( F4) 1 23 3

    17) S4 Probability Distributions (F5) 324 3 11 10

    25 4

    18) AST1 Solution of Triangles (F4) 1 - - 12 1019) ASS1 Index Number (F4) 1 - - 13 10

    20) AST2 Motion Along a Straight Line

    (F5)1 - - 15 10

    21) ASS2 Linear Programming (F5) 1 - - 14 10

    TOTAL 25 80 6 40 5 50 4 40

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    2

    TEST SPECIFICATION TABLE

    KERTAS SELARAS NEGERI MELAKA

    JADUAL SPESIFIKASI UJIAN MATEMATIK TAMBAHAN

    (PAPER 1 & PAPER 2)

    Paper 1

    Question Topics Construct Level ofDifficulty Marks

    1 Functions

    Knowledge

    Interpret from ordered pairs.

    Find object and determine the type of relation.Find the range of relation

    L 2

    2 FunctionsUnderstanding

    Inverse function and composite function.L 4

    3. Function

    Understanding

    Determine one of the functions in a given

    composite function given the other related

    function..

    L 3

    4QuadraticEquations

    Understanding

    Find the roots for the equation that cannot be

    factorized.

    I 3

    5QuadraticFunctions

    Understanding

    Find the range of values for quadratic

    inequalities.

    I 3

    6Quadratic

    Functions

    Application

    Find the axis of symmetry and minimum point

    from completing the square method.

    H 3

    7Indices and

    LogarithmsApplication

    Solving equation involving indices.L 3

    8Indices andLogarithms

    ApplicationSolve problems involving the change of base and

    laws of logarithms

    H 3

    9 ProgressionsApplication

    Find the value a and Sun to n terms for API 3

    11 Progressions

    Application

    Find the value of n, given the sum of the first nterms of G P

    I 4

    12 ProgressionApplication

    Geometric Progression: Sum to infinityI 2

    13 Linear LawApplication

    Given the line of best fit; convert to linear formand find the gradient andy-intercept .

    H 4

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    4

    ADDITIONAL MATHEMATICS

    PAPER 2

    TEST SPECIFICTION TABLE

    Question Topics Construct Level of Difficulty Marks

    1 SimultaneousEquations

    Application

    Solving two simultaneous equations :

    one linear equation and one non-linear

    equation.

    L 5

    2 Integration (a) Application

    Find the unknown from gradient

    function.

    (b) Application

    By integration, find the the equation

    of the curve.

    L

    I

    3

    3

    3 Progressions (a) Problem Solving / Application

    Find the a from Tn.

    Application

    (b) Find the Sn(c) Find n from given Tn

    L

    I

    I

    2

    2

    2

    4 Trigonometric

    Functions

    (a) Application

    Prove the identity.

    (b) Application

    Sketch the trigonometric graph and a

    straight line.Find the number of solutions from the

    graph.

    L

    H

    2

    6

    5 Coordinate

    Geometry

    Application

    (a) Find the coordinate of a point

    divides a segment internally at a

    ratio.

    (b) Find the equation of a

    perpendicular line.

    (c) Find the area of parallelogram

    L

    I

    I

    2

    3

    3

    6 Statistics (a) Application

    Find the mean and standard deviation

    from the Histogram.

    (b) Understanding

    The effect of change to the mean and

    standard deviation.

    I

    L

    4

    3

    7 Linear Law (a) Understanding

    Plot the graph and draw the line of best

    fit.

    (b) Application

    Change the equation to linear form.

    Use the gradient and y-intercept to find

    the unknowns.

    I

    H

    4

    6

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    5

    8 Vectors (a) Application

    Find the resultant vector using polygon

    law.

    (b) Application

    Express a vector as a combination ofother vectors.

    (c) Understanding

    Solve simultaneous equations to find theconstants.

    (d) UnderstandingNegative vector.

    L

    I

    I

    L

    2

    3

    4

    1

    9 Circular

    Measure

    (a) Application

    Find the angle of sector using

    trigonometry.

    (b) Application

    Find the perimeter of shaded region.

    (c) Application

    Find the area of triangle.

    (d) ApplicationFind the area of shaded region.

    L

    I

    L

    H

    2

    3

    2

    3

    10 Progressions (a) Understanding

    Show the areas form a geometric

    progression.

    (b) Problem Solving/Application

    (i) Find n from Tn.

    (ii) Find the sum of specific terms.

    (iii) Find Sum to Infinity

    L

    I

    I

    L

    2

    3

    3

    2

    11 Probability

    Distributions

    (a) Application

    Find the area of the shaded region.(b) Application

    Find the minimum point of the curve.

    (c) Application

    Find the volume generated.

    H

    I

    H

    3

    3

    4

    12 Solutions of

    Triangle

    (a) Application

    Use the Sine Rule or Cosine Rule to find

    the length.(b) Application

    Use the Sine Rule or Cosine Rule to find

    the angle.

    (c) Application

    Use the area formula to find the area oftriangle.

    (d) Application

    Use the Cosine Rule to find the length.

    L

    L

    L

    H

    2

    3

    2

    3

    13 Index Number Problem solving(a) (i) Find the price of the base year.

    (ii) Find the price index.

    (b) (i) Given the composite function,

    find the price index.

    (ii) Find the cost of item in the base

    L

    H

    I

    L

    2

    3

    3

    2

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    6

    year, given the composite index.

    14 Motion Along a

    Straight Line

    Problem solvinga). Determine displacement of a particlefrom a fixed point.b). Determine the total distance traveledby a particle over a time interval using

    graphical methodc). Determine velocity function of aparticle by differentiation.d) Determine instantaneous velocity of aparticlee ) Determine acceleration function of aparticle by differentiation

    L

    L

    H

    L

    H

    2

    2

    2

    2

    2

    15 Linear

    Programming

    Problem solving

    a) writing linear inequalities and

    equations describing asituation.

    b) shading the region of feasible

    solutions.

    c) determining and drawing the

    objective functionax + by = k where a, b and k

    are constants.

    d) determining graphically the

    optimum value of the

    objective function.

    L

    L

    H

    H

    3

    3

    2

    2

    Level of Difficulty : L LowI Intermediate

    H- High

    JOB DISTRIBUTION

    Paper 1

    No 1 - 7 Horsiah No 8 - 14 Saripah

    No 15 20 GanNo 21 24 Kee

    Paper 2

    Part A and B

    No 1 4 Horsiah

    No 5 7 Saripah

    No 8 9 KeeNo 10 - 11 Gan

    Paper 2

    Part C

    No 12 Horsiah

    No 13 Kee

    No 14 GanNo 15 Saripah

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    3(56,'$1*$1.(%$1*6$$13(1*(78$3(1*(78$

    6(.2/$+0(1(1*$+0$/$

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    7KHIROORZLQJIRUPXODHPD\EHKHOSIXOLQDQVZHULQJWKHTXHVWLRQV7KHV\PEROVJLYHQDUHWKHRQHVFRPPRQO\XVHG5XPXVUXPXVEHULNXWEROHKGLJXQDNDQXQWXNPHPEDQWXDQGDPHQMDZDEVRDODQ6LPEROVLPERO\DQJGLEHULDGDODK\DQJELDVDGLJXQDNDQ

    $/*(%5$

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    DPu DQDPQ

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    DPQDQP

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    ORJDE

    D

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    ORJ

    ORJ

    7QDQG

    6Q @>

    GQDQ

    7QDUQ

    6QU

    UD

    U

    UD QQ

    Uz

    U

    D6

    f

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    &$/&8/86KALKULUS

    1 \XYG[

    GXY

    G[

    GYX

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    Y

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    GYX

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    GXY

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    G\u

    $UHDXQGHUDFXUYH/XDVGLEDZDKOHQJNXQJ

    E

    D

    \ G[RU

    E

    D

    [ G\

    9ROXPHJHQHUDWHG,VLSDGX-DQDDQ

    E

    D

    \ S G[RU

    E

    D

    [ S G\

    1 'LVWDQFH -DUDN =

    \\[[

    2 0LGSRLQW ( 7LWLN7HQJDK

    [[\[ ,

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