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    SULIT

    BAHAGIAN PENGURUSAN

    SEKOLAH BERASRAMA PENUH / KLUSTER

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/1TINGKATAN EMPAT

    MATHEMATICS

    Kertas 1

    Oktober

    1 jam Satu jam lima belas minit

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    1. Kertas soalan ini adalah dalam Bahasa Inggeris.

    2. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

    Kertas soalan ini mengandungi 20 halaman bercetak.

    MOZ@C

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    MATHEMATICAL FORMULAE

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

    the ones commonly used.

    RELATIONS

    1 am x a

    n= a

    m+ n

    2 ama

    n= a

    m n

    3 ( am

    )n

    = amn

    4 A-1

    =bcad

    1

    ac

    bd

    5 Distance = 2 22 1 2 1( ) ( ) x x y y

    6 Midpoint, ( x, y ) =

    2,

    2

    2121 yyxx

    7 Average speed =

    8 Mean =

    9 Mean =

    10 Pythagoras Theorem

    c2

    = a2

    + b2

    11 P ( A ) =)(

    )(

    Sn

    An

    12 P ( A ) = 1 P(A)

    13 m =12

    12

    xx

    yy

    14 m =

    sum of data

    number of data

    sum of (class mark frequency)

    sum of frequencies

    y-intercept

    x-intercept

    distance travelled

    time taken

    MOZ@C

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    SHAPES AND SPACE

    1 Area of trapezium =2

    1 sum of parallel sides height

    2 Circumference of circle = d= 2r

    3 Area of circle = r2

    4 Curved surface area of cylinder = 2rh

    5 Surface area of sphere = 4r2

    6 Volume of right prism = cross sectional area length

    7 Volume of cylinder = r2

    h

    8 Volume of cone =3

    1r

    2h

    9 Volume of sphere =3

    4r3

    10 Volume of right pyramid =3

    1 base area height

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

    12360

    centreatsubtendedangle

    circleofncecircumfere

    lengtharc

    13360

    centreatsubtendedangle

    circleofarea

    sectorofarea

    14 Scale factor , k=PA

    PA'

    15 Area of image = k2

    area of object

    MOZ@C

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    INFORMATION FOR CANDIDATES

    1. This question paper consists of 40 questions.

    2. Answer all questions.

    3. Each question is followed by four alternative answers, A, B, C or D. For each

    question, choose one answer only. Blacken your answer on the objective answer

    sheet provided.

    4. If you wish to change your answer, erase the blackened mark that you have done.

    Then blacken the space for the new answer.

    5. The diagrams in the questions provided are not drawn to scale unless stated.

    6. A list of formulae is provided on page 2 to 3.

    7. You may use a non-programmable scientific calculator.

    MOZ@C

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    1. Round off 37 285 correct to three significant figures.

    A 37 000

    B 37 200

    C 37 290

    D 37 300

    2. Express 2937 105

    as a single number.

    A 2 937

    B 29 370

    C 293 700

    D 2 937 000

    3.144

    0160

    =

    A 28572

    10

    B 563

    10

    C 2857 410

    D 56 210

    4 136

    10 52 710 =

    A 12 710

    B 12 6

    10

    C 1057

    10

    D 105 6

    10

    5. A rectangular floor has a width of 2700 cm and a length of 3200 cm. The floor

    will be covered with tiles. Each tile is a square of side 24 cm. Calculate the number

    of tiles required to cover the floor fully.

    A 15 104

    B 36 104

    C 15 105

    D 36 105

    Answer all questions.

    MOZ@C

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    6. )3()2(5 yxyx

    A yx 92

    B yx 112

    C yx 8

    D yx 38

    7. xxx 31432 2

    A 9882 xx

    B 98162 xx

    C 9816

    2

    xxD 9128

    2 xx

    8. List all the subsets of set H= { p, q}.

    A {p}, {q}

    B {p}, {q}, { }

    C {p}, {q},{p, q}

    D {p}, {q}, {p, q},{ }

    9. Given the universal set, = TN , set N= {a, b, c} and set T= {b, c, d, e, f},

    find the value ofn().

    A 2

    B 4

    C 6

    D 8

    MOZ@C

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    10. Diagram 1 is a Venn diagram showing the universal set, = {Form Four students},

    set G = {Students who play badminton} and set H={Students who play tennis}.

    Given n() = 50, n(G) = 23, n(H) = 9 and n 6 HG , find the number of students

    who do not play the two games.

    A 44

    B 30

    C 24

    D 18

    11. Diagram 2 shows a straight line PQ on a Cartesian plane.

    The distance of OQ is 2 units.

    Find the gradient ofPQ.

    A2

    1

    B4

    3

    C 1

    D 2

    O

    y

    Q

    x

    (8, 6P

    G

    H

    DIAGRAM 1

    DIAGRAM 2

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    12. In Diagram 3, MNis a straight line on a Cartesian plane.

    Find the gradient ofMN.

    A 2

    B 4

    3

    C4

    3

    D 2

    13. Find the x-intercept of the straight line xy 23 = 12.

    A 6

    B61

    C 4

    D4

    1

    14. Diagram 4 shows the score obtained by a group of five pupils in a quiz where x is an

    integer. The mode score is 6.

    2 x x 4 9

    Then another three pupils with scores of 3, 3 and 8 joins the group.

    Find the median score of the group.

    A 35

    B 5

    C 5125

    D 6

    N

    M

    8

    6

    0

    y

    x

    DIAGRAM 3

    DIAGRAM 4

    MOZ@C

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    15. Diagram 5 is a bar chart showing the number of Mathematics textbooks sold in four

    months. The number of textbooks sold in March and May are not shown.

    DIAGRAM 5

    The total number of books sold in four months is 140. The ratio of books sold in

    March to books sold in May is 3 : 2. Find the number of books sold in May.

    A 14

    B 16

    C 24

    D 40

    16. Diagram 6 is a pie chart which shows the combined results of a time trial race taken

    by two groups of pupils. Table 1 shows the results obtained by the two groups but it

    is incomplete.

    Calculate the number of pupils in the Yellow Group.

    A 140

    B 146

    C 160

    D 194

    Month

    Numberoftextbook

    10

    20

    30

    40

    50

    60

    Feb Mar Apr May

    TABLE 1

    156

    Qualify

    Do not

    qualify

    DIAGRAM 6

    GroupNumber of pupils

    Qualify Do not qualify

    Yellow

    Blue 60 80

    Total 130

    MOZ@C

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    17 A number is chosen at random from set P = {x: x is an integer , 2 x 12}.

    Find the probability that the number chosen is a prime factor of 15.

    A10

    1

    B5

    1

    C10

    3

    D5

    2

    18. Table 2 shows the types of food bought by 60 students at the canteen.

    If a student is chosen at random from the group, the probability of the student

    buying fried noodles is1

    4. Calculate the value ofq.

    A 11

    B 13

    C 15

    D 26

    19. A container holds 28 red marbles and a number of blue marbles. A marble is picked

    at random from the container. The probability of picking a red marble is8

    7.

    How many blue marbles are there in the container?

    A 4

    B 8

    C 21

    D 24

    Type of food Number of students

    Fried noodles m

    Nasi lemak 24

    Bread q

    Roti canai 10

    TABLE 2

    MOZ@C

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    20. A student puts 20 cards with serial number 21 to 40 in a box. A card is drawn at

    random. Find the probability of drawing a card with a serial number which is a

    multiple of 5.

    A 4

    1

    B5

    1

    C10

    1

    D20

    1

    21. In Diagram 7, EFG is a tangent to the circle FJHat F.

    Find the value of x.

    A 64

    B 58

    C 52

    D 26

    DIAGRAM 7

    J

    64

    x

    GF

    H

    E

    MOZ@C

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    22. In Diagram 8, KLMis a tangent to the circle centre O, at L. KJPO and NPL are

    straight lines.

    Find the value of y.

    A 28

    B 34

    C 56

    D 62

    23. In Diagram 9, FGH is a tangent to the circle centre O, at G.

    Find the value of z.

    A 77

    B 55

    C 45

    D 35

    F G H

    PQ

    O

    13

    68 z

    M

    N

    O

    28

    yJ

    L

    K

    P

    DIAGRAM 8

    DIAGRAM 9

    O

    MOZ@C

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    SULIT

    24. In Diagram 10, PQRS is a rectangle and PM= NR = 3 cm.

    Find the value of tan .

    A12

    5

    B12

    5

    C13

    5

    D135

    25. It is given that sin x =25

    24and 90 x 180.

    Find cos x.

    A25

    7

    B25

    7

    C7

    24

    D7

    24

    P

    S

    M

    N R

    Q

    13 cm

    M

    15 cm

    DIAGRAM 10

    MOZ@C

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    26. Diagram 11 shows the graph ofy = sin x .

    Find the value of m.

    A 190

    B 210

    C 240

    D 300

    27 In Diagram 12, PQ and RS are two vertical poles on a horizontal plane.

    Calculate the angle of depression of vertex R from vertex P.A 26 34

    B 41 59

    C 48 01

    D 63 26

    1

    1

    (m, 50 )

    DIAGRAM 11

    P

    Q

    R

    S

    20 m

    45 m

    50 m

    DIAGRAM 12

    O

    y

    x

    MOZ@C

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    29. Diagram 14 shows a cuboid with a horizontal base PQRS.

    Name the angle between the line NMand the plane PQM.

    A NQP

    B NQM

    C NMP

    D NMQ

    28 Diagram 13 shows a steel frame LKPMNplaced on a horizontal plane.

    KL and PMNare vertical while KMis horizontal.

    The angle of elevation of point Mfrom point L is 68.

    Calculate the height, in m, of PN.

    A 9

    B 11

    C 1342

    D 258

    P S

    Q

    M

    K

    R

    N

    L

    DIAGRAM 14

    P

    N

    M

    L

    K

    8 m

    10 m

    DIAGRAM 13

    MOZ@C

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    30. Diagram 15 shows a pyramid with rectangular base TUVW.

    Vertex S is vertically above W. Name the angle between the plane STUand the

    base TUVW.

    A USW

    B TSW

    C SUW

    D STW

    31 Diagram 16 shows a regular pentagon PQRST. PRUand VWUare straight lines.

    PRUis parallel to TS.

    DIAGRAM 16

    Calculate the value of x + y .

    A 69

    B 87

    C 94

    D 112

    S

    TW

    VU

    DIAGRAM 15

    P

    Q

    R

    ST V

    U

    xy

    2257

    W

    MOZ@C

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    32 In Diagram 17, JKLM is a parallelogram. VWis parallel to JK.

    DIAGRAM 17

    Calculate the value ofp + q .

    A 175

    B 140

    C 135

    D 100

    33 Diagram 18 shows five pentagons drawn on square grids.

    DIAGRAM 18

    Which of the pentagons A, B, C or D, is an image of pentagon Kunder a rotation?

    K

    A

    B

    C

    D

    J K

    LM

    VW

    70150

    q

    p

    80

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    SULIT

    34 Diagram 19 shows two quadrilaterals, L and M, drawn on square grids.

    DIAGRAM 19

    Mis the image ofL under an enlargement.

    Which of the point, A, B, C, or D, is the centre of the enlargement?

    35. Choose a suitable linear equation in one unknown for the following statement.

    A 3(x + 7 ) = 34

    B 3 + x + 7 = 34

    C 3 + 7x = 34

    D 3x + 7 = 34

    36. Given thatqr

    rp

    4 , express q in terms ofp and r.

    A

    2

    4

    1

    r

    p

    rq

    B 24

    1prrq

    C

    r

    p

    rq

    2

    1

    D prrq 21

    A

    B

    C D

    M

    L

    When a number is multiplied by 3 and increased by 7, the result is 34.

    MOZ@C

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    SULIT

    37.

    2

    2

    5

    32

    1

    25

    57

    =

    A7

    1

    B7

    5

    C 7

    D 35

    38. Simplify3

    82

    3

    2 )(

    n

    nm .

    A nm3

    B53

    nm

    C nm 43

    D

    54

    3

    nm

    39 Solve the inequalities 8 3x x + 16 and 5 2x > x 10.

    A

    B

    C

    D

    2

    2

    2

    2

    5

    6

    5

    6

    MOZ@C

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    40. Given that x is an integer, find all the values of x that satisfy both of the

    inequalities2

    4x

    5 and x32 > 3 .

    A 1,0,1

    B 2,1,0,1

    C 1,0,1,2

    D 2,1,0,1,2

    END OF QUESTION PAPER

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    QUESTION ANSWER QUESTION ANSWER

    1 D 21 C

    2 C 22 B

    3 C 23 D

    4 D 24 A

    5 A 25 B

    6 A 26 B

    7 C 27 A

    8 D 28 D

    9 C 29 D

    10 C 30 D

    11 A 31 B

    12 C 32 B

    13 A 33 D

    14 B 34 C

    15 B 35 D

    16 C 36 A

    17 B 37 B

    18 A 38 A

    19 A 39 A

    20 B 40 C

    MOZ@C

    SMS MUZAFFAR SYAH , MELAKA

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    1449/2 Form Four

    [T

    1

    NAMA : ___________________________________

    TINGKATAN : _____________________________

    BAHAGIAN PENGURUSAN

    SEKOLAH BERASRAMA PENUH / KLUSTERBAHAGIAN SEKOLAH

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPAT

    MATHEMATICS

    Kertas 2

    Oktober

    2 jam Dua jam tiga puluh minit

    MATEMATIK

    Kertas 2

    Dua jam tiga puluh minit

    Pemeriksa

    Bahagian SoalanMarkah

    Penuh

    Markah

    Diperoleh

    A

    1 3

    2 8

    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.

    3 4

    4 4

    5 4

    6 4

    7 4

    8 6

    9 6

    10 4

    11 5

    B

    12 12

    13 12

    14 12

    15 12

    16 12

    Jumlah

    Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah

    SULIT

    MOZ@C

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    1449/2 Form Four2

    MATHEMATICAL FORMULAE

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

    ones commonly used.

    RELATIONS

    1 am an = am + n 12 Pythagoras Theorem

    c2

    = a2

    + b2

    2 am an = am n 13

    12

    12

    xx

    yym

    3 (am

    )n

    = am n

    14

    intercept

    intercept

    x

    ym

    4

    ac

    bd

    bcadA

    11

    5

    )(

    )()(

    Sn

    AnAP

    6 )(1)'( APAP

    7 Distance =2

    12

    2

    12 )()( yyxx

    8Midpoint,

    2,

    2),( 2121

    yyxxyx

    9

    takentime

    travelleddistancespeedAverage

    10

    dataofnumber

    dataofsumMean

    11

    sfrequencieofsum

    frequency)marks(classofsumMean

    MOZ@C

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    1449/2 Form Four

    [T

    3

    SHAPES AND SPACE

    1heightsidesparallelofsum

    2

    1trapeziumofArea

    2 Circumference of circle = d= 2 r

    3 Area of circle = r2

    4 Curved surface area of cylinder = 2 r h

    5 Surface area of sphere = 4 r2

    6 Volume of right prism = cross sectional area length

    7 Volume of cylinder = r2

    h

    8Volume of cone hr

    2

    3

    1

    9Volume of sphere

    3

    3

    4r

    10Volume of right pyramid heightareabase

    3

    1

    11 Sum of interior angles of polygon = (n 2)180

    12o360

    centreatsubtendedangle

    circleofncecircumfere

    lengtharc

    13o360

    centreatsubtendedangle

    circleofarea

    sectorofarea

    14

    PA

    PA'k,factorScale

    15 Area of image = k2 area of object

    MOZ@C

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    1449/2 Form Four4

    For

    Examiners

    Use

    Section A

    [52 marks]

    Answerall questions in this section.

    1 The Venn diagram in the answer space shows sets K, L and Msuch that the

    universal set, = K L M.

    On the diagrams in the answer space, shade

    (a) L M ,

    (b) ( K M) L.

    [3 marks]

    Answer:

    (a)

    (b)

    L

    KM

    L

    KM

    MOZ@C

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    1449/2 Form Four

    [T

    5

    2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.

    Right angled triangle MFG is the uniform cross-section of the prism.

    S is the midpoint of ND.

    DIAGRAM 1

    Identify and calculate the angle between the line FS and the base GMND.

    [4 marks]

    Answer:

    F

    Exam

    U

    E

    G

    D

    M

    S

    F

    N

    5 cm

    16 cm6 cm

    MOZ@C

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    1449/2 Form Four6

    For

    Examiners

    e 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .

    The isosceles triangle KLHis the uniform cross-section of the prism.

    N is the midpoint ofKL.

    DIAGRAM 2

    Identify and calculate the angle between the plane KLG and the plane KLH.

    [4 marks]

    Answer:

    J

    K L

    H

    G

    N

    M

    6 cm

    5 cm

    12 cm

    MOZ@C

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    1449/2 Form Four

    [T

    7

    3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.

    The height of the cone is 6 cm.

    By using7

    22 , calculate the volume, in cm3 , of the combined solid.

    [4 marks]

    Answer:

    F

    Exam

    U

    7 cm

    12 cm

    DIAGRAM 3

    MOZ@C

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    1449/2 Form Four8

    For

    Examiners

    Use

    4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.

    [4 marks]

    Answer:

    5 Using factorisation, solve the quadratic equation pp

    5

    23 2.

    [4 marks]

    Answer:

    MOZ@C

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    1449/2 Form Four

    [T

    9

    6 Calculate the value ofm and ofn that satisfy the following simultaneous

    linear equations:

    1223

    166

    nm

    nm

    [4 marks]

    Answer:

    Fo

    Exami

    Us

    7 Calculate the value ofh and ofkthat satisfy the following simultaneous

    linear equations:

    273

    644

    3

    hk

    hk

    [4 marks]

    Answer:

    MOZ@C

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    1449/2 Form Four10

    For

    Examiners

    Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.

    It is given that POQ = 60.

    By using =7

    22, calculate

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

    (b) the area, in cm2, of the shaded region.

    [ 6 marks ]

    Answer:

    (a)

    (b)

    T

    Q 14 cm

    7 cm

    R

    S

    O

    PDIAGRAM 4

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    1449/2 Form Four

    [T

    11

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

    m > 6 if and only if m 6 > 0

    (b) State the converse of the following statement and hence determine whether the

    converse is true or false.

    Ifx is a factor of 5, then x is a factor of 10.

    (c) Make a general conclusion by induction for the sequence of numbers

    1 , 6 , 15 , 28, . . . which follows the following pattern.

    1 = 2 ( 1 )2 1

    6 = 2 ( 2 )2 2

    15 = 2 ( 3 )2 3

    28 = 2 ( 4 )2 4

    =

    [6 marks]

    Answer:

    (a) Implication 1:

    Implication 2:

    (b)

    ...

    (c) ...

    Fo

    Exami

    Us

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    1449/2 Form Four12

    For

    Examiners

    Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.

    Find

    (a) the equation of the straight line PQ,

    (b) y intercept of the straight line PQ.

    [4 marks]

    Answer:

    (a)

    (b)

    x

    R ( 4 ,12)

    DIAGRAM 5

    y

    P ( 3 , 6 )

    O

    Q

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    1449/2 Form Four

    [T

    13

    11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.

    PQ is parallel to RS.

    The equation of the straight line KL is 62 xy .

    Find

    (a) the gradient of the straight line PQ,

    (b) the equation of the straight line RS.

    [5 marks]

    Answer:

    (a)

    (b)

    Fo

    Exami

    Us

    xO

    K

    R

    S

    L

    DIAGRAM 6

    y

    P

    Q (3, 3)

    3

    MOZ@C

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    1449/2 Form Four14

    For

    Examiners

    Use

    Section B

    [48 marks]

    Answer any four questions from this section.

    12(a) The Venn diagram in the answer space shows the universal set , sets P, Q

    and R. On the diagram in the answer space, shade the region for

    (i) P Q ,

    (ii) ( P Q ) R.

    [3 marks]

    Answer:

    (i)

    (ii)

    P

    Q

    R

    P

    Q

    R

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    1449/2 Form Four

    [T

    15

    12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .

    Find

    (i) the equation of the straight line RN,

    (ii) the x intercept of the straight line RN.

    [5 marks]

    Answer:

    (i)

    (ii)

    Fo

    Exam

    Us

    y

    x

    R

    N( 4,9 )

    Q (3, 4)

    O

    DIAGRAM 7

    MOZ@C

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    1449/2 Form Four16

    For

    Examiners

    Use

    12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.

    Trapezium PQGF is the uniform cross-section of the prism.

    U, V, and Ware midpoints ofPS, FEand QR respectively.

    DIAGRAM 8

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

    [4 marks]

    Answer:

    E

    P

    G

    H

    Q

    R

    F

    V

    U

    S

    W8 cm

    12 cm

    5 cm

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    1449/2 Form Four

    [T

    17

    13(a) (i) State whether the following sentences is a statement or

    non-statement.

    (a) 2x + 5y 6

    (b) 4 is a prime number.

    (ii) Combine the two statements below to form a false statement.

    Statement 1 : 3 13 = 39

    Statement 2 : 39 is a prime number.

    (iii) Write down Premise 1 to complete the following argument:

    Premise 1 :

    Premise 2 : 3 is a factor of 15

    Conclusion : 3 is a factor of 30

    (iv) Fill in the blanks with < or > to form

    (a) a true statement,

    6 3

    (b) a false statement.

    8 24

    [6 marks]

    Answer:

    (i)(a) _________________________________

    (b) _________________________________

    (ii) ______________________________________________________

    (iii) Premise 1 :______________________________________________

    (iv) (a) 6 3

    (b) 8 24

    F

    Exam

    U

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    1449/2 Form Four18

    For

    Examiners

    Use

    13(b) In Diagram 9, ORSTis a quadrant and KL is an arc of another circle both

    with centre O. ORKand OSL are straight lines.

    DIAGRAM 9

    OR = RK= 7 cm.

    Using7

    22 , calculate

    (i) the perimeter, in cm, of the whole diagram,

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

    . [6 marks]

    Answer:

    (i)

    (ii)

    60

    R

    S

    T

    L

    K

    O

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    1449/2 Form Four

    [T

    19

    14(a) Using factorisation, solve the quadratic equation mm

    6

    52.

    [4 marks]

    Answer:

    14(b) Calculate the value ofdand ofe that satisfy the following simultaneous linear

    equations:

    144

    102

    13

    ed

    ed

    [4 marks]

    Answer:

    F

    Exam

    U

    MOZ@C

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    1449/2 Form Four20

    For

    Examiners

    Use

    14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.

    The volume of the remaining solid is 292 cm3

    .

    Calculate the width, in cm, of the remaining solid.

    (Use =7

    22)

    [4 marks]

    Answer:

    2 cm

    2 cm

    8 cm

    7 cm

    DIAGRAM 10

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    1449/2 Form Four

    [T

    21

    15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run

    event.

    14 36 12 16 27 31 27 28 30 28

    16 18 23 18 24 32 23 14 18 31

    22 30 23 20 25 30 31 22 20 37

    12 26 36 23 28 30 34 38 33 36

    11 23 27 27 34 38 25 12 17 29

    DIAGRAM 11

    (a) Based on the data in Diagram 11 and by using a class interval of 5, complete

    Table 1 in the answer space.

    [4marks]

    (b) Based on Table 1 in (a),

    calculate the estimated mean of the age of the runners.

    [3marks]

    (c) For this part of the question, use the graph paper provided on page 23.

    By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1

    runner on the vertical axis, draw a frequency polygon for the data.

    [5marks]

    F

    Exam

    U

    MOZ@C

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    1449/2 Form Four22

    For

    Examiners

    Use

    Answer:

    (a)

    Age (years) Midpoint Frequency

    11 15

    TABLE 1

    (b) i)

    ii)

    (c) Refer graph on page 23.

    MOZ@C

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    1449/2 Form Four

    [T

    23MOZ@C

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    1449/2 Form Four24

    For

    Examiners

    Use

    16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.

    67 76 91 79 81 82 87 71

    79 82 88 83 72 84 71 89

    80 86 70 86 62 83 83 80

    75 84 84 77 84 86 85 76

    80 75 95 77 73 86 77 68

    DIAGRAM 12

    (a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in

    the answer space.

    [6 marks]

    (b) For this part of the question, use the graph paper provided on page 26.

    By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the

    y-axis, draw an ogive based on the data.

    [5 marks]

    (c) From your ogive in (b), find the third quartile.

    [1 mark]

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    1449/2 Form Four

    [T

    25

    Answer:

    a)

    Marks Frequency Cumulative Frequency Upper Boundary

    61 65

    TABLE 2

    b) Refer graph on page 26

    c)

    Fo

    Exam

    Us

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    1449/2 Form Four26MOZ@C

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    1449/2 Form Four

    [T

    27

    INFORMATION FOR CANDIDATES

    1. This question paper consists of two sections: Section A and Section B.

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

    3. Write your answers in the spaces provided in the question paper.

    4. Show your working. It may help you to get marks.

    5. If you wish to change your answer, cross out the answer that you have done. Then

    write down the new answer.

    6. The diagrams in the questions provided are not drawn to scale unless stated.

    7. The marks allocated for each question and sub-part of a question are shown inbrackets.

    8. A list of formulae is provided on page 2 to 3.

    9. A booklet of four-figure mathematical tables is provided.

    10. You may use a non-programmable scientific calculator.

    11. Hand in this question paper to the invigilator at the end of the examination.

    MOZ@C

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    Mathematics Form 4 Final year 2008

    Section A[ 52 marks ]

    No Marking Scheme Marks

    1

    a)

    b)

    P1

    P2 3

    2 a) FSQ

    Tan22 86

    5

    '3426/57.26

    b) FSQ

    Tan4

    12

    '3471/57.71

    P1

    K2

    N1

    P1

    K2

    N1

    4

    4

    312

    2

    7

    2

    7

    7

    22

    2

    1

    627

    27

    722

    31

    21

    5.269/2

    1269

    62

    7

    2

    7

    7

    22

    3

    1

    2

    112

    2

    7

    2

    7

    7

    22

    2

    1

    K1

    K1

    K1

    N1 4

    L

    K

    M

    L

    K

    M

    MOZ@C

    SMS MUZAFFAR SYAH , MELAKA

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    No Marking Scheme Marks

    4

    1,6

    1

    0116

    0156 2

    x

    xx

    xx K1

    K1

    N1,N1 4

    5

    3

    1,2

    0132

    0253 2

    p

    pp

    pp K1

    K1

    N1,N1 4

    6

    2,3

    6020

    48183

    mn

    n

    nm K1

    K1

    N1, N1 4

    7

    8,3

    5117

    24163

    kh

    h

    hk K1

    K1N1, N1 4

    8 a) 77

    222

    360

    6021

    7

    222

    360

    450

    0

    0

    0

    OR

    83.65/6

    565

    777

    222

    360

    601421

    7

    222

    360

    4521

    0

    0

    0

    0

    b) 22 77

    22

    360

    6021

    7

    22

    360

    45

    OR

    42.174@12

    5174

    772

    17

    7

    22

    360

    6021

    7

    22

    360

    45 220

    0

    K1

    K1

    N1

    K1

    K1

    N1 6

    MOZ@C

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    No Marking Scheme Marks

    9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6

    b) If x is a factor of 10, then x is a factor of 5False

    c) ,2 2 nn .......,4,3,2,1n

    P1

    P1

    P1P1

    P1

    P1 6

    10 a) 304

    012

    ORPQ mm

    153

    15336

    xy

    cORc

    b) 15y

    K1

    K1

    N1

    N1 4

    11 a)2

    1

    33

    03

    PQm

    62

    1

    6)0(2

    16

    2

    1

    xy

    cORc

    mm RSPQ

    K1, N1

    K1

    K1

    N1 5

    MOZ@C

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    Section B

    [48 marks]

    No Marking Scheme Marks

    12 a)i

    ii.

    b)i.

    3

    4m

    83

    4

    )9(3

    44

    xy

    c

    ii. 83

    40 x

    6x

    c) VWU

    Tan12

    5

    '3722/62.22

    P1

    P2

    K1

    K1

    N1

    K1

    N1

    P1

    K2

    N1 12

    P Q

    R

    P Q

    R

    MOZ@C

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    No Marking Scheme Marks

    13 a) i) a) Non-statement

    b) Statement

    ii) andiii) all factors of 15 are factors of 30

    iv) a )

    (b) i) 147

    222

    360

    600

    0

    OR 77

    222

    360

    300

    0

    147

    222

    360

    600

    0

    + 77

    222

    360

    300

    0

    +14+7+7

    3

    146 OR 46.34

    ii) 14147

    22

    360

    600

    0

    OR 777

    22

    360

    300

    14147

    22

    360

    600

    0

    + 777

    22

    360

    300

    = 89.832

    cm or 6

    589

    P1

    P1

    P1P1

    P1P1

    K1

    K1

    N1

    K1

    K1

    N1 12

    14

    5,1

    051

    056)( 2

    m

    mm

    mma

    2

    3

    62

    206)(

    e

    d

    d

    edb

    cm

    cmw

    wc

    6292298

    292727

    22

    2

    187

    87)(

    22

    K1N1

    N1,N1

    K1

    K1

    N1

    N1

    K1

    K1, K1

    N112

    MOZ@C

    SMS MUZAFFAR SYAH , MELAKA

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    No Marking Scheme Marks

    15 (a)

    Age(years) Midpoint Frequency

    11 - 15 13 6

    16 20 18 8

    21 25 23 10

    26 30 28 13

    31 35 33 7

    36 40 38 6

    All values in Column 1 correct

    All values in Column 2 correctAll values in Column 3 correct

    (b)

    5.25

    50

    1275

    50

    )6(38)7(33)13(28)10(23)8(18)6(13

    (c) Refer to the graph

    Axes drawn in the correct direction , uniform scale for 438 xand 130 y .

    Horizontal axis labeled using midpoint / upper boundary / classinterval

    6 points plotted correctly

    (8,0) and (43,0).Straight line passing 8 point.

    P1

    P1

    P2

    K2

    N1

    K1

    P1

    P1

    P1P1

    12

    MOZ@C

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    No Marking Scheme Marks

    16 Marks Frequency Cumulative

    frequency

    Upper

    boundary

    I

    55 60

    II

    0

    III

    0

    IV

    60.561 65 1 1 65.5

    66 70 3 4 70.5

    71 75 6 10 75.5

    76 80 10 20 80.5

    81 85 11 31 85.5

    86 90 7 38 90.5

    91 - 95 2 40 95.5

    All values in Column ( I ) correct

    All values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correct

    All values in Column ( IV ) correct

    (b) x-axis and y-axis are drawn with the right direction and in

    uniform scale from 60.5 5.95 x , 110 y

    All eight points* plotted correctly.

    Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed through

    All the right eight points plotted correctly and ogive is drawn

    smoothly passing through all the points.

    (c) 85 0.5

    P1

    P2P2

    P1

    K1

    K2

    K1

    N1

    N1

    12

    MOZ@C

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    8 13 18 23 28 330

    2

    4

    6

    8

    10

    12

    14

    Graph is not drawn to scale.

    38

    43

    Frequency

    Mid-po

    Graph for Question 15.

    MOZ@C

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    655605 705 755 805 855 905

    0

    5

    10

    15

    20

    25

    30

    35

    40

    Graph is not drawn to scale.

    Graph for Question 16.

    95.5

    Cumulative

    Frequency

    UpperBoundar

    MOZ@C

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    SULIT 1449/1

    1449/1

    Matematik

    Kertas1

    Peraturan

    Pemarkahan

    Oktober

    2008

    SEKTOR SEKOLAH BERASRAMA PENUH

    BAHAGIAN SEKOLAH

    KEMENTERIAN PELAJARAN MALAYSIA

    PERATURAN PEMARKAHANPEPERIKSAAN AKHIR TAHUN TAHUN 2008

    TINGKATAN 4

    MATEMATIK

    KERTAS 1 & 2

    1449/1/2

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    QUESTION ANSWER QUESTION ANSWER

    1 D 21 C

    2 C 22 B

    3 C 23 D

    4 D 24 A

    5 A 25 B

    6 A 26 B

    7 C 27 A

    8 D 28 D

    9 C 29 D

    10 C 30 D

    11 A 31 B

    12 C 32 B

    13 A 33 D

    14 B 34 C

    15 B 35 D

    16 C 36 A

    17 B 37 B

    18 A 38 A

    19 A 39 A

    20 B 40 C

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    1449/2 Form Four

    [T

    1

    NAMA : ___________________________________

    TINGKATAN : _____________________________

    BAHAGIAN PENGURUSAN

    SEKOLAH BERASRAMA PENUH / KLUSTERBAHAGIAN SEKOLAH

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPAT

    MATHEMATICS

    Kertas 2

    Oktober

    2 jam Dua jam tiga puluh minit

    MATEMATIK

    Kertas 2

    Dua jam tiga puluh minit

    Pemeriksa

    Bahagian SoalanMarkah

    Penuh

    Markah

    Diperoleh

    A

    1 3

    2 8

    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.

    3 4

    4 4

    5 4

    6 4

    7 4

    8 6

    9 6

    10 4

    11 5

    B

    12 12

    13 12

    14 12

    15 12

    16 12

    Jumlah

    Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah

    SULIT

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    1449/2 Form Four2

    MATHEMATICAL FORMULAE

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

    ones commonly used.

    RELATIONS

    1 am an = am + n 12 Pythagoras Theorem

    c2

    = a2

    + b2

    2 am an = am n 13

    12

    12

    xx

    yym

    3 (am

    )n

    = am n

    14

    intercept

    intercept

    x

    ym

    4

    ac

    bd

    bcadA

    11

    5

    )(

    )()(

    Sn

    AnAP

    6 )(1)'( APAP

    7 Distance =2

    12

    2

    12 )()( yyxx

    8Midpoint,

    2,

    2),( 2121

    yyxxyx

    9

    takentime

    travelleddistancespeedAverage

    10

    dataofnumber

    dataofsumMean

    11

    sfrequencieofsum

    frequency)marks(classofsumMean

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    1449/2 Form Four

    [T

    3

    SHAPES AND SPACE

    1heightsidesparallelofsum

    2

    1trapeziumofArea

    2 Circumference of circle = d= 2 r

    3 Area of circle = r2

    4 Curved surface area of cylinder = 2 r h

    5 Surface area of sphere = 4 r2

    6 Volume of right prism = cross sectional area length

    7 Volume of cylinder = r2

    h

    8Volume of cone hr

    2

    3

    1

    9Volume of sphere

    3

    3

    4r

    10Volume of right pyramid heightareabase

    3

    1

    11 Sum of interior angles of polygon = (n 2)180

    12o360

    centreatsubtendedangle

    circleofncecircumfere

    lengtharc

    13o360

    centreatsubtendedangle

    circleofarea

    sectorofarea

    14

    PA

    PA'k,factorScale

    15 Area of image = k2 area of object

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    1449/2 Form Four4

    For

    Examiners

    Use

    Section A

    [52 marks]

    Answerall questions in this section.

    1 The Venn diagram in the answer space shows sets K, L and Msuch that the

    universal set, = K L M.

    On the diagrams in the answer space, shade

    (a) L M ,

    (b) ( K M) L.

    [3 marks]

    Answer:

    (a)

    (b)

    L

    KM

    L

    KM

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    1449/2 Form Four

    [T

    5

    2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.

    Right angled triangle MFG is the uniform cross-section of the prism.

    S is the midpoint of ND.

    DIAGRAM 1

    Identify and calculate the angle between the line FS and the base GMND.

    [4 marks]

    Answer:

    F

    Exam

    U

    E

    G

    D

    M

    S

    F

    N

    5 cm

    16 cm6 cm

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    1449/2 Form Four6

    For

    Examiners

    e 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .

    The isosceles triangle KLHis the uniform cross-section of the prism.

    N is the midpoint ofKL.

    DIAGRAM 2

    Identify and calculate the angle between the plane KLG and the plane KLH.

    [4 marks]

    Answer:

    J

    K L

    H

    G

    N

    M

    6 cm

    5 cm

    12 cm

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    1449/2 Form Four

    [T

    7

    3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.

    The height of the cone is 6 cm.

    By using7

    22 , calculate the volume, in cm3 , of the combined solid.

    [4 marks]

    Answer:

    F

    Exam

    U

    7 cm

    12 cm

    DIAGRAM 3

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    1449/2 Form Four8

    For

    Examiners

    Use

    4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.

    [4 marks]

    Answer:

    5 Using factorisation, solve the quadratic equation pp

    5

    23 2.

    [4 marks]

    Answer:

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    1449/2 Form Four

    [T

    9

    6 Calculate the value ofm and ofn that satisfy the following simultaneous

    linear equations:

    1223

    166

    nm

    nm

    [4 marks]

    Answer:

    Fo

    Exami

    Us

    7 Calculate the value ofh and ofkthat satisfy the following simultaneous

    linear equations:

    273

    644

    3

    hk

    hk

    [4 marks]

    Answer:

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    1449/2 Form Four10

    For

    Examiners

    Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.

    It is given that POQ = 60.

    By using =7

    22, calculate

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

    (b) the area, in cm2, of the shaded region.

    [ 6 marks ]

    Answer:

    (a)

    (b)

    T

    Q 14 cm

    7 cm

    R

    S

    O

    PDIAGRAM 4

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    1449/2 Form Four

    [T

    11

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

    m > 6 if and only if m 6 > 0

    (b) State the converse of the following statement and hence determine whether the

    converse is true or false.

    Ifx is a factor of 5, then x is a factor of 10.

    (c) Make a general conclusion by induction for the sequence of numbers

    1 , 6 , 15 , 28, . . . which follows the following pattern.

    1 = 2 ( 1 )2 1

    6 = 2 ( 2 )2 2

    15 = 2 ( 3 )2 3

    28 = 2 ( 4 )2 4

    =

    [6 marks]

    Answer:

    (a) Implication 1:

    Implication 2:

    (b)

    ...

    (c) ...

    Fo

    Exami

    Us

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    1449/2 Form Four12

    For

    Examiners

    Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.

    Find

    (a) the equation of the straight line PQ,

    (b) y intercept of the straight line PQ.

    [4 marks]

    Answer:

    (a)

    (b)

    x

    R ( 4 ,12)

    DIAGRAM 5

    y

    P ( 3 , 6 )

    O

    Q

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    1449/2 Form Four

    [T

    13

    11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.

    PQ is parallel to RS.

    The equation of the straight line KL is 62 xy .

    Find

    (a) the gradient of the straight line PQ,

    (b) the equation of the straight line RS.

    [5 marks]

    Answer:

    (a)

    (b)

    Fo

    Exami

    Us

    xO

    K

    R

    S

    L

    DIAGRAM 6

    y

    P

    Q (3, 3)

    3

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    1449/2 Form Four14

    For

    Examiners

    Use

    Section B

    [48 marks]

    Answer any four questions from this section.

    12(a) The Venn diagram in the answer space shows the universal set , sets P, Q

    and R. On the diagram in the answer space, shade the region for

    (i) P Q ,

    (ii) ( P Q ) R.

    [3 marks]

    Answer:

    (i)

    (ii)

    P

    Q

    R

    P

    Q

    R

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    1449/2 Form Four

    [T

    15

    12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .

    Find

    (i) the equation of the straight line RN,

    (ii) the x intercept of the straight line RN.

    [5 marks]

    Answer:

    (i)

    (ii)

    Fo

    Exam

    Us

    y

    x

    R

    N( 4,9 )

    Q (3, 4)

    O

    DIAGRAM 7

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    1449/2 Form Four16

    For

    Examiners

    Use

    12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.

    Trapezium PQGF is the uniform cross-section of the prism.

    U, V, and Ware midpoints ofPS, FEand QR respectively.

    DIAGRAM 8

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

    [4 marks]

    Answer:

    E

    P

    G

    H

    Q

    R

    F

    V

    U

    S

    W8 cm

    12 cm

    5 cm

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    1449/2 Form Four

    [T

    17

    13(a) (i) State whether the following sentences is a statement or

    non-statement.

    (a) 2x + 5y 6

    (b) 4 is a prime number.

    (ii) Combine the two statements below to form a false statement.

    Statement 1 : 3 13 = 39

    Statement 2 : 39 is a prime number.

    (iii) Write down Premise 1 to complete the following argument:

    Premise 1 :

    Premise 2 : 3 is a factor of 15

    Conclusion : 3 is a factor of 30

    (iv) Fill in the blanks with < or > to form

    (a) a true statement,

    6 3

    (b) a false statement.

    8 24

    [6 marks]

    Answer:

    (i)(a) _________________________________

    (b) _________________________________

    (ii) ______________________________________________________

    (iii) Premise 1 :______________________________________________

    (iv) (a) 6 3

    (b) 8 24

    F

    Exam

    U

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    1449/2 Form Four18

    For

    Examiners

    Use

    13(b) In Diagram 9, ORSTis a quadrant and KL is an arc of another circle both

    with centre O. ORKand OSL are straight lines.

    DIAGRAM 9

    OR = RK= 7 cm.

    Using7

    22 , calculate

    (i) the perimeter, in cm, of the whole diagram,

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

    . [6 marks]

    Answer:

    (i)

    (ii)

    60

    R

    S

    T

    L

    K

    O

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    1449/2 Form Four

    [T

    19

    14(a) Using factorisation, solve the quadratic equation mm

    6

    52.

    [4 marks]

    Answer:

    14(b) Calculate the value ofdand ofe that satisfy the following simultaneous linear

    equations:

    144

    102

    13

    ed

    ed

    [4 marks]

    Answer:

    F

    Exam

    U

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    1449/2 Form Four20

    For

    Examiners

    Use

    14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.

    The volume of the remaining solid is 292 cm3

    .

    Calculate the width, in cm, of the remaining solid.

    (Use =7

    22)

    [4 marks]

    Answer:

    2 cm

    2 cm

    8 cm

    7 cm

    DIAGRAM 10

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    1449/2 Form Four22

    For

    Examiners

    Use

    Answer:

    (a)

    Age (years) Midpoint Frequency

    11 15

    TABLE 1

    (b) i)

    ii)

    (c) Refer graph on page 23.

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    1449/2 Form Four

    [T

    23

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    1449/2 Form Four24

    For

    Examiners

    Use

    16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.

    67 76 91 79 81 82 87 71

    79 82 88 83 72 84 71 89

    80 86 70 86 62 83 83 80

    75 84 84 77 84 86 85 76

    80 75 95 77 73 86 77 68

    DIAGRAM 12

    (a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in

    the answer space.

    [6 marks]

    (b) For this part of the question, use the graph paper provided on page 26.

    By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the

    y-axis, draw an ogive based on the data.

    [5 marks]

    (c) From your ogive in (b), find the third quartile.

    [1 mark]

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    1449/2 Form Four

    [T

    25

    Answer:

    a)

    Marks Frequency Cumulative Frequency Upper Boundary

    61 65

    TABLE 2

    b) Refer graph on page 26

    c)

    Fo

    Exam

    Us

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    1449/2 Form Four26

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    1449/2 Form Four

    [T

    27

    INFORMATION FOR CANDIDATES

    1. This question paper consists of two sections: Section A and Section B.

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

    3. Write your answers in the spaces provided in the question paper.

    4. Show your working. It may help you to get marks.

    5. If you wish to change your answer, cross out the answer that you have done. Then

    write down the new answer.

    6. The diagrams in the questions provided are not drawn to scale unless stated.

    7. The marks allocated for each question and sub-part of a question are shown inbrackets.

    8. A list of formulae is provided on page 2 to 3.

    9. A booklet of four-figure mathematical tables is provided.

    10. You may use a non-programmable scientific calculator.

    11. Hand in this question paper to the invigilator at the end of the examination.

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    Mathematics Form 4 Final year 2008

    Section A[ 52 marks ]

    No Marking Scheme Marks

    1

    a)

    b)

    P1

    P2 3

    2 a) FSQ

    Tan22 86

    5

    '3426/57.26

    b) FSQ

    Tan4

    12

    '3471/57.71

    P1

    K2

    N1

    P1

    K2

    N1

    4

    4

    312

    2

    7

    2

    7

    7

    22

    2

    1

    627

    27

    722

    31

    21

    5.269/2

    1269

    62

    7

    2

    7

    7

    22

    3

    1

    2

    112

    2

    7

    2

    7

    7

    22

    2

    1

    K1

    K1

    K1

    N1 4

    L

    K

    M

    L

    K

    M

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    No Marking Scheme Marks

    4

    1,6

    1

    0116

    0156 2

    x

    xx

    xx K1

    K1

    N1,N1 4

    5

    3

    1,2

    0132

    0253 2

    p

    pp

    pp K1

    K1

    N1,N1 4

    6

    2,3

    6020

    48183

    mn

    n

    nm K1

    K1

    N1, N1 4

    7

    8,3

    5117

    24163

    kh

    h

    hk K1

    K1N1, N1 4

    8 a) 77

    222

    360

    6021

    7

    222

    360

    450

    0

    0

    0

    OR

    83.65/6

    565

    777

    222

    360

    601421

    7

    222

    360

    4521

    0

    0

    0

    0

    b) 22 77

    22

    360

    6021

    7

    22

    360

    45

    OR

    42.174@12

    5174

    772

    17

    7

    22

    360

    6021

    7

    22

    360

    45 220

    0

    K1

    K1

    N1

    K1

    K1

    N1 6

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    No Marking Scheme Marks

    9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6

    b) If x is a factor of 10, then x is a factor of 5False

    c) ,2 2 nn .......,4,3,2,1n

    P1

    P1

    P1P1

    P1

    P1 6

    10 a) 304

    012

    ORPQ mm

    153

    15336

    xy

    cORc

    b) 15y

    K1

    K1

    N1

    N1 4

    11 a)2

    1

    33

    03

    PQm

    62

    1

    6)0(2

    16

    2

    1

    xy

    cORc

    mm RSPQ

    K1, N1

    K1

    K1

    N1 5

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    Section B

    [48 marks]

    No Marking Scheme Marks

    12 a)i

    ii.

    b)i.

    3

    4m

    83

    4

    )9(3

    44

    xy

    c

    ii. 83

    40 x

    6x

    c) VWU

    Tan12

    5

    '3722/62.22

    P1

    P2

    K1

    K1

    N1

    K1

    N1

    P1

    K2

    N1 12

    P Q

    R

    P Q

    R

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    No Marking Scheme Marks

    13 a) i) a) Non-statement

    b) Statement

    ii) andiii) all factors of 15 are factors of 30

    iv) a )

    (b) i) 147

    222

    360

    600

    0

    OR 77

    222

    360

    300

    0

    147

    222

    360

    600

    0

    + 77

    222

    360

    300

    0

    +14+7+7

    3

    146 OR 46.34

    ii) 14147

    22

    360

    600

    0

    OR 777

    22

    360

    300

    14147

    22

    360

    600

    0

    + 777

    22

    360

    300

    = 89.832

    cm or 6

    589

    P1

    P1

    P1P1

    P1P1

    K1

    K1

    N1

    K1

    K1

    N1 12

    14

    5,1

    051

    056)( 2

    m

    mm

    mma

    2

    3

    62

    206)(

    e

    d

    d

    edb

    cm

    cmw

    wc

    6292298

    292727

    22

    2

    187

    87)(

    22

    K1N1

    N1,N1

    K1

    K1

    N1

    N1

    K1

    K1, K1

    N112

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    No Marking Scheme Marks

    15 (a)

    Age(years) Midpoint Frequency

    11 - 15 13 6

    16 20 18 8

    21 25 23 10

    26 30 28 13

    31 35 33 7

    36 40 38 6

    All values in Column 1 correct

    All values in Column 2 correctAll values in Column 3 correct

    (b)

    5.25

    50

    1275

    50

    )6(38)7(33)13(28)10(23)8(18)6(13

    (c) Refer to the graph

    Axes drawn in the correct direction , uniform scale for 438 xand 130 y .

    Horizontal axis labeled using midpoint / upper boundary / classinterval

    6 points plotted correctly

    (8,0) and (43,0).Straight line passing 8 point.

    P1

    P1

    P2

    K2

    N1

    K1

    P1

    P1

    P1P1

    12

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    No Marking Scheme Marks

    16 Marks Frequency Cumulative

    frequency

    Upper

    boundary

    I

    55 60

    II

    0

    III

    0

    IV

    60.561 65 1 1 65.5

    66 70 3 4 70.5

    71 75 6 10 75.5

    76 80 10 20 80.5

    81 85 11 31 85.5

    86 90 7 38 90.5

    91 - 95 2 40 95.5

    All values in Column ( I ) correct

    All values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correct

    All values in Column ( IV ) correct

    (b) x-axis and y-axis are drawn with the right direction and in

    uniform scale from 60.5 5.95 x , 110 y

    All eight points* plotted correctly.

    Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed through

    All the right eight points plotted correctly and ogive is drawn

    smoothly passing through all the points.

    (c) 85 0.5

    P1

    P2P2

    P1

    K1

    K2

    K1

    N1

    N1

    12

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    8 13 18 23 28 330

    2

    4

    6

    8

    10

    12

    14

    Graph is not drawn to scale.

    38

    43

    Frequency

    Mid-po

    Graph for Question 15.

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    15

    20

    25

    30

    35

    40

    Graph is not drawn to scale.

    Graph for Question 16.

    Cumulative

    Frequency