F5 SBP MATHS P2 [MID 2007] - Andrew · PDF fileAnswer all questions in this section. 12 (a)...

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Transcript of F5 SBP MATHS P2 [MID 2007] - Andrew · PDF fileAnswer all questions in this section. 12 (a)...

  • SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2007

    Pemeriksa

    Bahagian Soalan Markah Penuh

    Markah Diperoleh

    1 3

    MATEMATIK

    Kertas 2

    Dua jam tiga puluh minit

    2 3

    3 4

    4 4

    5 5

    6 4

    7 7

    8 4

    9 6

    10 6

    A

    11 6

    12 12

    13 12

    14 12

    B

    15 12

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    1. Kertas soalan ini mengandungi dua bahagian :

    Bahagian A dan Bahagian B. Jawab semua soalan daripada Bahagian A dan empat soalan dalam Bahagian B.

    2. Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas soalan. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah.

    3. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

    4. Satu senarai rumus disediakan di halaman 2 & 3

    5. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

    Jumlah

    Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak

    SULIT 1449/2 Matematik Kertas 2 Mei 2007

    2

    1 2 jam

    1449/2

    1449/2  2007 Hak Cipta Sektor SBP [Lihat sebelah SULIT

    NAMA :

    TINGKATAN :

  • SULIT 1449/2

    1449/2 SULIT

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    Untuk Kegunaan Pemeriksa

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

    RELATIONS 1 am x an = a m+ n 2 am ÷ an = a m – n 3 ( am )n = a mn

    4 A-1 = bcad −

    1  

      

    − − ac

    bd

    5 P ( A ) = )(

    )(

    Sn

    An

    6 P ( A′ ) = 1 − P(A)

    7 Distance = 2 21 2 1 2( ) ( )x x y y− + −

    8 Midpoint, ( x, y ) =  

      

     ++ 2

    , 2

    2121 yyxx

    9 Average speed = 10 Mean = 11 Mean = 12 Pythagoras Theorem c2 = a2 + b2

    13 m = 12

    12

    xx

    yy

    − −

    14 -intercept

    -intercept

    y m

    x =

    distance travelled time taken

    sum of data number of data

    sum of (class mark × frequency) sum of frequencies

  • SULIT 1449/2

    1449/2 [Lihat sebelah SULIT

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    Untuk Kegunaan Pemeriksa

    SHAPES AND SPACE

    1 Area of trapezium = 2

    1 × sum of parallel sides × height

    2 Circumference of circle = πd = 2πr 3 Area of circle = πr2 4 Curved surface area of cylinder = 2πrh 5 Surface area of sphere = 4πr2 6 Volume of right prism = cross sectional area × length 7 Volume of cylinder = πr2h

    8 Volume of cone = 3

    1 πr2h

    9 Volume of sphere = 3

    4 πr3

    10 Volume of right pyramid = 3

    1 × base area× height

    11 Sum of interior angles of a polygon = ( n – 2) × 180˚

    12 arc length angle subtended at centre

    circumference of circle 360 =

    o

    13 area of sector angle subtended at centre

    area of circle 360 =

    o

    14 Scale factor , k = PA

    PA'

    15 Area of image = k 2 × area of object

  • SULIT 1449/2

    1449/2 SULIT

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    Section A [52 marks]

    Answer all questions in this section.

    1 On the graph in the answer space, shade the region which satisfies the three inequalities 3 12,y x≤ + 2 4y x≥ − + and 2x < .

    [3 marks]

    Answer :

    3 12y x= +

    2 4y x= − + O

    x

    y

  • SULIT 1449/2

    1449/2 [Lihat sebelah SULIT

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    Untuk Kegunaan Pemeriksa

    2 If ξ = {x : 1 ≤ x ≤ 10 , x is an integer}

    E = {x : x is a multiple of 4}

    F = {x : x is a factor of 20}

    (a) List all the elements in set E, (b) Find ( )∪n E F .

    [3 marks]

    Answer :

    (a) (b)

  • SULIT 1449/2

    1449/2 SULIT

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    3 Diagram 1 shows a solid cube. A part of the cube in the shape of a half-cylinder is removed from its upper surface.

    Calculate the total surface area of the remaining solid. [Use π =3.142]

    [4 marks]

    Answer :

    10 cm

    DIAGRAM 1

  • SULIT 1449/2

    1449/2 [Lihat sebelah SULIT

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    4 Diagram 2 shows a right prism with a horizontal rectangular base PQRS. VUQR is a trapezium. M and N are the midpoints of PS and QR respectively.

    Calculate the angle between the line TR and the base PQRS.

    [4 marks]

    Answer :

    T

    U

    W

    V

    P

    Q

    R

    S M

    N

    • 8 cm

    6 cm

    12 cm

    5 cm

    DIAGRAM 2

  • SULIT 1449/2

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    5 (a) State whether the following statement is true or false.

    “ 3 33 9 or 8 2= = ” (b) Write down two implications based on the sentence below. “The inverse matrix of a 2 2× matrix exists if and only if the determinant is ≠ 0”

    (c) Given the number sequence 3, 8, 15, 24, …….. and 3 = 1 2 + 2(1)

    8 = 2 2 + 2(2)

    15 = 3 2 + 2(3)

    24 = 4 2 + 2(4)

    Make a general conclusion by using the induction method for the numerical sequence above.

    [5 marks]

    Answer :

    (a) (b) (c)

  • SULIT 1449/2

    1449/2 [Lihat sebelah SULIT

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    6 Calculate the value of v and of w that satisfy the following simultaneous linear equations:

    3 4 8

    2 8 4

    3

    + =

    − =

    v w

    v w

    [4 marks] Answer :

    .

  • SULIT