2008 F5 Mid Year SBP Math K2

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Transcript of 2008 F5 Mid Year SBP Math K2

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    SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2008

    MATEMATIK

    Kertas 2

    Dua jam tiga puluh minit

    Pemeriksa

    Bahagian Soalan MarkahPenuh Markah

    Diperoleh

    A

    1 3

    2 4

    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

    3 4

    4 4

    5 5

    6 6

    7 6

    8 5

    9 6

    10 5

    11 4

    B

    12 12

    13 12

    14 12

    15 12

    16 12

    Jumlah

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

    SULIT 1449/2 Matematik Kertas 2 Mei 2008

    2 12 jam

    1449/2

    1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah SULIT

    NAMA :

    TINGKATAN :

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    SULIT 1449/2

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    For xaminer’s

    Use

    Section A [52 marks ]

    Answer all questions in this section.

    1 The Venn diagram in the answer space shows sets P , Q and R such that the universal set, RQ P .

    On the diagram in the answer space, shade

    (a) the set Q P .

    (b) the set ( P Q ) R . [3 marks ]

    Answer : (a) (b)

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

    112 wv

    73 3 2

    wv

    [4 marks ]

    Answer :

    P Q

    R

    P Q

    R

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    SULIT 1449/2

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    5

    For Examiner’s

    Only 3 Using factorisation, solve the following quadratic equation:

    2 2

    13 x

    x x

    [4 marks ] Answer :

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    SULIT 1449/2

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    For xaminer’s

    Use 4 Diagram 1 shows a right prism with a horizontal rectangular base PQRS . VUQR is a trapezium.

    Identify and calculate the angle between the plane QWR and the base PQRS.

    [4 marks ]

    Answer :

    T

    U

    W

    V

    P

    Q

    R

    S

    8 cm

    6 cm

    12 cm

    5 cm

    DIAGRAM 1

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    For Examiner’s

    Only 5 In Diagram 2, straight line TU is parallel to straight line VW and O is the origin .

    The equation of straight line VW is 02552 y x . Find: (a) the equation of the straight line TU. (b) the x-intercept of the straight line TU.

    [5 marks ]

    Answer:

    (a)

    (b)

    DIAGRAM 2

    y

    x

    W

    U ( 1,5)

    V

    T O

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    For xaminer’s

    Use 6 Diagram 3 shows two sectors of circle ORQ and OPS with centre O.

    By using = 7

    22 , calculate

    (a) the perimeter, in cm, of the whole diagram.

    (b) the area, in cm 2, of the shaded region.

    [ 6 marks ]

    Answer :

    (a)

    (b)

    O P

    Q

    R

    S

    150° 7 cm

    12 cm

    DIAGRAM 3

    7 cm

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    For Examiner’s

    Only 7 (a) State whether the following statements are true or false.

    (i) 2.0 2 1

    and3 aaaa

    (ii) Number 5 is an odd number or number 2 is a prime number.

    (b) State the antecedent and consequent of the implication:

    (c) Complete the following argument.

    Premise 1 : If y > 3, then 5 y > 15.

    Premise 2 : _________________________________________

    Conclusion : 5 y > 15.

    [6 marks ] Answer :

    (a) (i)

    (ii)

    (b) Antecedent : ______________________________

    Consequent : ______________________________

    (c) Premise 2 : ________________________________________________

    If y is less than zero, then y is a negative number.

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    For xaminer’s

    Use 8 (a) Complete the following statement using the quantifier “all” or “ some”, to make it a false statement.

    (b) Write down two implications based on the following statement:

    (c) Make a general conclusion by induction for the sequence of numbers 2, 14, 34, …

    which follows the following pattern.

    2 = 4(1) 2 2

    14 = 4(2) 2 2

    34 = 4(3) 2 2

    62 = 4(4) – 2

    … = ………..

    [ 5 marks ] Answer :

    (a) ____________ polygons have six sides.

    (b) Implication 1:

    ____________________________________________________________

    Implication 2 :

    _____________________________________________________________

    (c) _____________________________________________________________

    ______________________________________________________________

    ____________ polygons have six sides.

    x > y if and only if – x < y

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    For Examiner’s

    Only9 (a) The inverse matrix of

    45

    23 is p

    35

    4 q

    Find the value of p and of q. (b) Hence, using matrices, calculate the value of x and of y that satisfy the following

    simultaneous linear equations :

    3 x – 2 y = 8 5 x – 4 y = 13

    [6 marks ]

    Answer :

    (a)

    (b)

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    For xaminer’s

    Use 10 Diagram 4 shows the speed-time graph of a particle for a period of 50 seconds.

    (a) Calculate the rate of change of speed, in ms -2, in the first 10 seconds. (b) Calculate the value of u, if the total distance traveled in the last 40 seconds is 750 m.

    [5 marks ] Answer :

    (a)

    (b)

    Speed (ms -1)

    Time (s) 0

    5

    10 30

    20

    50

    DIAGRAM 4

    u

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    For Examiner’s

    Only 11 Diagram 5 shows a solid formed by joining a prism to a right pyramid. Trapezium

    ABGF is the uniform cross-section of the prism. FG = GH = 7 cm. The height of the pyramid is 6 cm.

    Calculate the volume, in cm 3, of the solid.

    [ Use = 722 ]

    [4 marks ]

    Answer:

    DIAGRAM 5

    8 cm

    11 cm A B

    C D

    E

    F G

    H

    V

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    For xaminer’s

    Use Section B

    [48 marks ]

    Answer four questions from this section.

    12 (a) Complete Table 1 in the answer space for the equation y = – 2 x2 + 4 x + 16.

    x – 4 – 3 – 2 – 1 0 1 2 3 4 y –32 h 0 10 16 18 k 10 0

    Calculate the values of h and of k .

    [2 marks ]

    (b) For this part of the question, use the graph paper on pag 15 . You may us flexible curve ruler.

    By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis , draw the graph of y = – 2 x2 + 4 x + 16 for – 4 ≤ x ≤ 4.

    [4 marks ] (c) From your graph, find

    (i) the value of y when x = 2.2

    (ii) the value of x when y = 5 [3 marks ]

    (d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2 x2 + x – 11 = 0 for – 4 ≤ x ≤ 4. State these values of x.

    [3 marks ]

    Answer:

    (a) h = …………………………

    k =…………………………

    (b) Refer graph on page 15

    (c) (i) y = ………………

    (ii ) x = ……………….

    (d) x = …………………………

    TABLE 1

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    For xaminer’s

    Use 13 (a) Transformation T is a translation

    3

    2 and transformation P is an anticlockwise

    rotation of 90 o about the centre (5, 0).

    State the coordinates of the image of point (9, 4) under each of the following

    transformations:

    (i) P,

    (ii) TP ,

    (iii) T 2

    [4 marks ]

    (b) Diag