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    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

    [ Lihat sebelah

    3472/1 SULIT

    Nama : ....

    Tingkatan: ..3472/1

    Matematik Tambahan

    Kertas 1

    Sept 2010

    2 jam

    1. This question paper consists of25 questions Kertas soalan ini mengandungi 25 soalan.

    2. Answerall questions. Jawabsemua soalan.

    3.Give only one answer for each question Bagi 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 bolehmembantu 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 areshown 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 boleh

    diprogram.

    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 37 3

    8 4

    9 3

    10 4

    11 4

    12 4

    13 3

    14 3

    15 4

    16 3

    17 418 3

    19 3

    20 3

    21 3

    22 3

    23 3

    24 3

    25 3

    Jumlah80

    MATEMATIK TAMBAHAN

    Kertas 1

    Dua Jam

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    STATISTICS

    1 Arc length,s = r

    ( Panjang lengkok)s = j

    2 Area of sector ,L =21

    2r

    ( Luas sektor L = 22

    1j )

    3 sin 2A + cos 2A = 1

    4 sec2A = 1 + tan2A

    5 cosec2A = 1 + cot2A

    6 sin 2A = 2 sinA cosA

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

    = 1 - 2 sin2A

    8 tan 2A =A

    A2tan1

    tan2

    TRIGONOMETRY

    9 sin (A

    B) = sinA cosB

    cosA sinB

    10 cos (AB) = cosA cosBsinA sinB

    11 tan (AB) =BtanAtan

    BtanAtan

    1

    12C

    c

    B

    b

    A

    a

    sinsinsin==

    13 a2

    = b2

    + c2

    - 2bc cosA

    14 Area of triangle = Cab sin2

    1

    ( Luas Segitiga )

    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

    61

    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) =rnr

    rn qpC , p + q = 1

    12 Mean = np

    13 npq=

    14 z =

    x

    3

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    3

    Answer all questions.

    Jawab semua soalan1 Diagram 1 shows the relation between two sets of number .

    Rajah 1 menunjukkan satu hubungan diantara dua set nombor.

    Diagram 1 Rajah 1

    Based on the above information, the relation betweenP and Q is defined by the setof ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.Berdasarkan maklumat diatas hubungan antaraPdan 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 ofg-1(10)Di beri g :x x2 +1 . Cari nilai nilai bagig-1(10)

    [ 2 marks ][ 2 markah ]

    Answer/Jawapan: ......

    [ Lihat sebelah

    3472/1 SULIT

    24

    2

    or examinersuse only

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

    2

    4

    1

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    3 The functionfis defined by f:x kx2 +p and the function gis defined by g:x1 + 2x.Given the composite function fg:xx2 + x + 6, find the values of kandp.Fungsifditakrifkan sebagaif: x kx2 + p dan fungsigditarifkan sebagai g: x 1+ 2x

    Diberi fungsi gubahanfg : x x2 + 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 px2 + 7x2p = 0, find the values ofp.

    Diberi bahawap

    1ialah salah satu punca bagi persamaan kuadratikpx2 + 7x2p = 0, cari nilai-nilai

    bagip

    [ 3 marks ]

    [ 3 markah ]

    Answer /Jawapan: ....

    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.

    For examiners

    use only

    For examiners

    use only

    4

    3

    3

    4

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    ( 4, q )

    5

    Rajah 5 menunjukkan graf fungsi kuadratikf(x) = 3(x +p)2 + 2 , dimana p ialah pemalarLengkung 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)..................................

    6 Find the range of values ofx for which 27)6( xx .Cari julat nilai- nilai x dimana 27)6( xx

    [ Lihat sebelah

    3472/1 SULIT

    For examiners

    use only3

    5

    Diagram 5Rajah 5

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    [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 : = .................................

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

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

    [3 marks][ 3

    markah]

    4

    8

    3

    2

    6

    3

    7

    For

    xaminers useonly

    3

    4

    J

    a

    w

    a

    p

    a

    n

    a

    n

    3

    .

    .

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    7

    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,

    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).

    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 .

    [ Lihat sebelah

    3472/1 SULIT

    4

    4

    10

    For examiners

    use only

    9

    4

    4

    11

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    x dany dihubungkan oleh persamaanm

    x nyx

    + = , dimana m dan n ialah pemalar.

    Satu garislurus diperolehi dengan memplotkan xy melawan x2, sebagaimana ditunjukkandalam Rajah 12

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

    [4 marks][ 4 markah]

    Answer/Jawapan: m=

    n =.....

    13 Given that the pointP( )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 titikP( )3,2 membahagi segmen garis yang menghubungkan

    4

    12

    r examiners

    use only

    3

    3

    3

    3

    xy

    (12, 2 )

    ( 6, 0) x2

    Diagram 12Rajah 12

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    9

    ),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) ...

    15 Diagram 15 shows a trianglePOQ Rajah 15 menunjukkan segitigaPOQ

    [ Lihat sebelah

    3472/1 SULIT

    3

    13

    3

    14

    For examiners

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    Diagram 15Rajah 15.

    Given that OP

    = p and OQ =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 linePYintersect at point

    C.

    DiberiOP

    = p dan OQ =q . TitikX terletak pada OP di mana OX:XP= 2 : 1 dan titikY

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

    Express in terms of p and q

    Ungkapkan dalam sebutan p dan q

    (a)PY

    (b) QX

    [ 4 marks]

    [4 markah]

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

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

    16 Given that is an acute angle andq

    p=sin , find in terms ofp and /orq

    Diberi bahawa ialah sudut tirus danq

    p=sin , cari dalam sebutanp dan/atau q

    O PX

    C

    Y

    Q

    4

    15

    or examiners

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    11

    a) cos

    kos

    b) tan ( 180 - )[3 marks]

    [ 3 markah ]

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

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

    17 Solve 3cos 2 + 4 cos +1 = 0 for 00 3600

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

    [4 marks][4 markah]

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

    18 Diagram 18 shows a circleABC with centre O, of radius 8 cm. SR is an arc of

    a circle with centerO. The reflex angleAOCis 1.6 radian.

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

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

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    use only

    4

    4

    17

    3

    4

    16

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    A

    C

    R

    S

    OB 1.6 rad

    8 cm

    Given thatA and C are midpoints ofOSand OR respectively, find the area of shaded

    region, in terms of .Diberi bahawa A dan C ialah titik tengah kepada OSdan OR , cari luas kawasan berlorek

    dalam sebutan

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

    [ 3 marks][ 3 markah]

    Answer/Jawapan:

    20 Given that

    5

    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 ]

    r examiners use only

    3

    19

    3

    18

    Diagram 18Rajah 18

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    13

    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 1

    nx x x x+ + + + .

    Satu set nombor 1 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 =...

    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.

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    3

    20

    3

    21

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    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 teachers

    and 12 students. Satu kumpulan ekspedisi mengandungi 10 ahli yang akan dipilih daripada kumpulan 4

    orang 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 that

    could 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) ..................................

    24 In a survey, the probability that a family having one unit of computer is 0.6.

    Nfamilies were selected at random. The standard deviation of the numbers of

    3

    3

    23

    3

    3

    22

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    15

    family having one unit of computer is5

    24

    Dalam satu tinjauan , kebarangkalian sebuah keluarga mempunyai satu unit komputerialah 0.6. N keluarga dipilih secara rawak . Sisihan piawai keluarga yang mempunyai

    komputer ialah5

    24

    Find,

    Cari,

    (a) the value of N nilai N

    (b) the mean of the numbers of family having one unit of computer.min keluarga yang mempunyai satu unit komputer

    [3 marks][ 3 markah]

    Answer/Jawapan: (a) ..

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

    25 Diagram 25 shows a standard normal distribution graph.

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    24

    For examiners

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

    Xialah pembolehubah rawak selanjar yang bertabur secara normal piawai dengan min dan sisihan piawai 2. Jika nilaiXialah 85 bila skor- Z ialah k, cari nilai .

    [3 marks]

    [ 3 markah]

    Answer: (a)

    (b) .

    END OF THE QUESTION PAPER

    KERTAS SOALAN TAMAT

    3

    25

    -k k z

    f(z))

    0.803

    Diagram 25

    Rajah 25

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    17

    [ Lihat sebelah

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