Transcript
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    SULIT

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

    PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2010

    MATEMATIK TAMBAHANKertas 1Dua Jam

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    Kertas soalan ini mengandungi 18 halaman bercetak

    [ Lihat sebelah3472/1 SULIT

    Nama : ....

    Tingkatan: ..

    3472/1Matematik TambahanKertas 1Sept 20102 jam

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

    2. Answer all questions . Jawab semua 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 telahdibuat. 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 ditunjukkandalam kurungan.

    9. A list of formulae is provided on page 2 to 3Satu senarai rumus disediakan di halaman 23 hingga 3

    10. You may use a non-programmable scientific calculator .Buku sifir matematik empat angka boleh digunakan.

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

    KodPemeriksa

    Soalan MarkahPenuhMarkah

    Diperoleh1 22 23 44 35 36 3

    7 38 49 3

    10 411 412 413 314 315 416 317 4

    18 319 320 321 322 323 324 325 3

    Jumlah 80

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    SULIT

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

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

    ALGEBRA

    1 2 4

    2b b ac

    xa

    =

    2 am a n = a m + n

    3 am a n = a m - n

    4 (a m) n = a nm

    5 log a mn = log am + log a n

    6 log a nm = log am - log a n

    7 log a mn = n log a m

    8 log a b =ab

    c

    c

    loglog

    9 T n = a + (n -1)d

    10 S n = ])1(2[2

    d nan +

    11 T n = ar n-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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    STATISTICS

    1 Arc length, s = r

    ( Panjang lengkok ) s = j

    2 Area of sector , L = 212

    r

    ( Luas sektor L = 221

    j )

    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 B10 cos ( A B) = cos A cos B sin A sin B

    11 tan ( A B) = Btan Atan

    Btan Atan1

    12C

    c B

    b A

    asinsinsin

    ==

    13 a2

    = b2

    + c2

    - 2bc cos A

    14 Area of triangle = C ab sin21

    ( Luas Segitiga )

    1 x = N

    x

    2 x =

    f

    fx

    3 = N

    x x 2)( =2 _ 2

    x N

    x

    4 =

    f

    x x f 2)(=

    22

    x f

    fx

    5 m = C f

    F N L

    m

    + 2

    1

    6 10

    100Q

    I Q

    =

    71

    11

    w I w

    I

    =

    8 )!(

    !

    r n

    n P r

    n

    =

    9 !)!(!

    r r nn

    C 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=

    14 z =

    x

    3

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    3

    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 1 / Rajah 1Based 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 pasangan tertib{ (-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 x2 +1 . Cari nilai nilai bagi g -1(10)

    [ 2 marks ][ 2 markah ]

    Answer/ Jawapan : ......

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    24

    2

    or examinersuse only

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

    24

    1

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    3. The function f is defined by f : x kx2 + p and the function g is defined by g : x 1 + 2 x.Given the composite function fg : x x2 + x + 6, find the values of k and p.Fungsi f ditakrifkan sebagai f: x kx2 + p dan fungsi g ditarifkan sebagai g: x 1 + 2xDiberi fungsi gubahan fg : x x2 + x + 6 , Cari nilai k dan nilai p

    [4 marks ]

    [ 4 markah]

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

    4 Given that p1

    is one of the roots of the quadratic equation px2 + 7 x 2 p = 0, find the values of p.

    Diberi bahawa p1

    ialah salah satu punca bagi persamaan kuadratik px2 + 7 x 2 p = 0, Cari nilai-

    nilai p

    [ 3 marks ][ 3 markah ]

    Answer /Jawapan: ....

    5 Diagram 5 shows the graph of a quadratic function f ( x) = 3( x + p)2 + 2, where p is a constant. The curve y = f ( x) has the minimum point ( 4, q), where q is a constant.

    For examinersuse only

    or examinersuse only

    4

    3

    3

    4

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    Cari julat nilai- nilai x dimana 27)6( x x[3 marks ]

    [ 3 markah ]

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

    7 Solve the equation 02781 321 = + x x . Selesaikan persamaan 02781 321 = + x x

    [ 3 marks ][ 3 markah ]

    Answer / Jawapan : x = ...

    8. Given log 7 2 = h and log 7 5 = k . Express log 7 2.8 in terms of h and k .Diberi log 7 2 = h dan log 7 5 = k . Ungkapkan log 7 2.8 in terms of h and k .

    [ 4 marks ][ 4 markah ]

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

    9 Solve 1)1(log)4(log 33 =+ x xSelesaikan 1)1(log)4(log 33 =+ x x

    [3 marks ][ 3

    markah ]

    4

    8

    32

    6

    3

    7

    or examinersuse only

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    x dan y dihubungkan oleh persamaanm

    x ny x

    + = , dimana m dan n ialah pemalar.

    Satu garisurus diperolehi dengan memplotkan xy melawan x2, sebagaimana ditunjukandalam Rajah 12

    Calculate the value of m and of n.Kira nilai m dan nilai n

    [4 marks ][ 4 markah ]

    .

    Answer /Jawapan : m =

    n=..

    13 Given that the point P ( )3,2 divides the line segment that joining ),4( t A and)8,( r B

    inthe ratio AP : PB = 1 : 4. Find the value of r and of t .Diberi bahawa titik P ( )3,2 membahagi segmen garis yang menghubungkan

    4

    12

    r examinersuse only

    xy

    (12, 2 )

    ( 6, 0) x 2

    DIAGRAM 12/ Rajah 12

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    9

    ),4( t A dan )8,( r B 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 of c .Vektor unit dalam arah c

    [3 marks ][3 markah ]

    Answer : (a )

    (b) 15 Diagram 15 shows a triangle POQ

    Rajah 3 menunjukkan segitiga POQ

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    3

    13

    3

    14

    For examinersuse only

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    DIAGRAM 3RAJAH 3.

    Given that OP

    = p and OQ = q .Point X is lies on OP where OX : XP = 2 : 1 and point Y is lies on OQ where OY : YQ = 3 : 1 . Straight line OX and line PY intersect at pointC.Diberi OP

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

    titik Y adalah titik pada OQ di mana OY : YQ = 3 : 1 . Garis lurus QX dan garis lurus PY bersilang pada titik C .

    Express in terms of p and q

    (a) PY

    (b) QX [ 4 marks]

    [4 markah ]

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

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

    16 Given that

    is an acute angle and q p= sin

    , Find in terms of p and /or q

    O P X

    C

    Y Q

    4

    15

    or examinersuse only

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    11

    Diberi bahawa ialah sudut tirus dan q p= sin , Cari dalam sebutan p dan/atau q

    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 circle ABC with centre O, of radius 8 cm. SR is an arc of a circle with center O. The reflex angle AOC is 1.6 radian.

    Rajah 18 menunjukkan satu bulatan ABC dangan pusat O dan berjejari 8 cm, SR ialah

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    44

    17

    34

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    A

    C R

    S

    O B 1.6 rad

    8 cm

    lengkuk sebuah bulatan berpusat di O . Sudut reflek AOC ialah 1.6 radian.

    Given that A and C are midpoints of OS and OR respectively, find the area of shadedregion, in terms of .Diberi bahawa A dan C ialah titik tengah kepada OS dan OR , Cari luas kawasan

    berlorek dalam sebutan

    [ 3 marks ][ 3 markah ]

    Answer / Jawapan : . cm 2

    19 . The radius of circle decreases at the rate of 10.5cms . Find the rate of change of thearea of a circle when the radius is 4 cm. .[ Given the area of a circle is A = r 2 ]Jejari sebuah bulatan berkurang dengan kadar 0.5 cms -1.Cari kadar perubahan luas

    bulatan apabila jejarinya ialah 4 cm, [ Diberi luas bulatan A = r 2]

    [ 3 marks ][ 3 markah ]

    Answer /Jawapan :

    20 Given that5

    1

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

    1

    [ 2 ( )] 3mx g x dx m =

    Diberi bahawa5

    1

    ( ) 5 g x dx = , cari nilai m jika5

    1

    [ 2 ( )] 3mx g x dx m =

    examiners use only

    3

    19

    3

    18

    DIAGRAM 18/RAJAH 18

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    13

    [ 3 marks ][ 3 markah ]

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

    21 . A set of numbers 1 2 3 4, , , ,..., n x 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 1n x x x x+ + + + .

    Satu set nombor 1 2 3 4, , , ,..., n x 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 1n x x x x+ + + + .

    [ 3 marks ][ 3 markah]

    Answer ::/Jawapan : median = ..

    variance =...

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

    box, the probability of getting a white ball is 7

    4

    . Find the value of p.

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    3

    20

    3

    21

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    Sebuah kotak mengandungi 6 biji bola hitam dan p biji bola putih . Jika sebiji boladiambil secara random dari kotak itu kebarangkalian mendapat sebiji bola putih ialah

    74

    . 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 expedisi 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 expedisi itu mesti mengandungi sekurang-kurangnya 2 orang gurukira bilangan kumpulan yang boleh dibentuk.

    [3 marks ][ 3 markah ]

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

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

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

    N families were selected at random. The standard deviation of the numbers of family owning one unit of computer is

    524

    33

    22

    33

    21

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    15

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

    computer ialah5

    24

    Find,Cari,

    (a) the value of N nilai N

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

    [3 marks ][ 3 markah ]

    Answer /Jawapan :(a) ..

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

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

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    24

    For examiners

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    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 of X is 85 when the Z- score is k,find the value of .

    X ialah pembolehubah rawak selanjar yang bertabur secara normal piawaidengan mean dan sisihan piawai 2. Jika nilai X ialah 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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