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  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN PERCUBAAN

    SIJIL PELAJARAN MALAYSIA 2011

    MATHEMATICS 1449

    MARKING SCHEME

    Paper 1

    1 A 11 A 21 B 31 A

    2 B 12 D 22 B 32 D

    3 C 13 D 23 D 33 D

    4 C 14 D 24 D 34 D

    5 D 15 B 25 C 35 B

    6 B 16 A 26 C 36 C

    7 A 17 A 27 B 37 B

    8 B 18 D 28 C 38 C

    9 B 19 A 29 C 39 A

    10 A 20 D 30 C 40 D

    A - 9 , B - 10, C - 9, D - 12

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    2

    Paper 2

    1 (a)

    Straight dotted line 1x correctly drawn.

    Region correctly shaded.

    Note:

    1. Accept solid line 1x for K1. 2. Award P1 to the shaded region bounded by two correct lines. (Must

    include part of region R)

    K1

    P2

    3

    0

    4

    6 x

    2 4y x

    2 12y x

    y

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    3

    2 (a)

    (b)

    FEB or BEF

    8

    3tan or equivalent

    20.56 or 2033

    P1

    K1

    N1

    3

    3

    3n2 7n 6 = 0 or equivalent

    ( 3n + 2 )( n 3 ) = 0 or equivalent

    OR

    )3(2

    )6)(3(4)7()7( 2

    x or equivalent (K1)

    n = 3

    2

    n = 3

    Note:

    1. Accept without = 0 .

    2. Accept three terms on the same side, in any order.

    3. Accept )3)(3

    2( nn with n =

    3

    2 or n = 3 for Kk2.

    K1

    K1

    N1

    N1

    4

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    4

    4

    1863 qp or 62qp or equivalent

    Note

    Attempt to equate the coefficient of one of the unknowns, award K1.

    84p or 328q or equivalent

    OR

    pq2

    13 or qp 26 or

    2

    143pq or

    3

    142qp

    or equivalent. (K1)

    Note

    Attempt to make one of the unknowns as the subject, with 2 terms on the

    other side, award K1

    84p or 328q or equivalent . (K1)

    OR

    14

    3

    2

    13

    12

    )3(1)2(2

    1

    1

    q

    p (K2)

    Note

    Attempt to write the matrix equation, award K1.

    2p

    4q

    Note:

    4

    2

    q

    p as final answer, award N1.

    K1

    K1

    N1

    N1

    4

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    5

    5

    35.27

    22

    3

    4

    2

    1

    )7)(6)(710(2

    1

    35.27

    22

    3

    4

    2

    1 + )7)(6)(710(

    2

    1

    389.72 389.74

    Note:

    1. Accept for K mark.

    2. Accept correct values from incomplete substitution for K mark.

    3. Correct answer from incomplete working, award KK2.

    4. Accept answer within range.

    K1

    K1

    K1

    N1

    4

    6 (a)

    (b)

    (c)

    1073 and 10km = 104m

    OR

    50 = 5 or 1073 (P1)

    OR

    50 = 5 or 10km = 10

    4m (P1)

    If 42x , then 2x . // Jika 42x , maka 2x .

    False // Palsu

    3 is a factor of 12 // 3 adalah faktor bagi 12

    P1

    P1

    P1

    K2

    5

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    6

    7 (a)

    (b)

    (c)

    5k

    )3(5

    04PRm or 2

    PRmx

    y*

    )3(

    0 or cmPR )3(*0

    Note: Accept * PRm using ( -3 , 0) and ( *k , 4) only

    62xy or equivalent

    6

    Note:

    Do not accept )6,0(

    P1

    P1

    K1

    N1

    N1

    5

    8 (a)

    (b)(i)

    (ii)

    { (S,E) , (S,F) , (S,4) , (S,5) , (P,E) , (P,F) , (P,4) , (P,5) , (6,E) , (6,F) , (6,4) ,

    (6,5) }

    12

    4 or

    1

    3

    12

    3 or

    1

    4

    P1

    N2

    N2

    5

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    7

    9 (a)

    (b)

    77

    222

    360

    180 or 28

    7

    222

    360

    60

    77

    222

    360

    180+ 28

    7

    222

    360

    60+ 28 +28 + 14

    3

    364 or

    3

    1121 or 121.31 121.33

    2287

    22

    360

    60 or 27

    7

    22

    360

    180

    2287

    22

    360

    60 277

    22

    360

    180

    3

    1001 or

    3

    2333 or 333.53 333.67

    Note:

    1. Accept for K mark.

    2. Accept correct values from incomplete substitution for K mark.

    3. Correct answer from incomplete working, award KK2.

    K1

    K1

    N1

    K1

    K1

    N1

    3

    3

    10 (a)

    (b)

    (c)

    4

    08

    0400 or equivalent

    50

    3618

    d or 36

    18

    400400 d or equivalent

    d = 648

    P1

    K1

    N1

    K2

    N1

    6

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    8

    11(a)

    (b)

    3n

    2

    1m

    Note : Determinant )]4)(3()2(5[ or 2, award P1.

    13

    17

    24

    35

    k

    h

    13

    17

    54

    32

    )4)(3()2(5

    1

    k

    h or

    13

    17*

    matrix

    inverse

    2

    5h or

    2

    12 or 2.5

    2

    3k or

    2

    11 or 5.1

    Note:

    1. Do not accept 24

    35*

    matrix

    inverse or

    10

    01*

    matrix

    inverse

    2.

    2

    32

    5

    k

    h as final answer, award N1.

    3. Do not accept any solutions solved not using matrices.

    P1

    P2

    P1

    K1

    N1

    N1

    3

    4

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    9

    12 (a)

    (b)

    (c)

    8

    6.4

    Graph

    Axes drawn in correct directions with uniform scales for 44 x and

    3232 y .

    All 7 points and *2 points correctly plotted or the curve passes through all the

    points for 44 x .

    A smooth and continuous curve without any straight line and passes through

    all 9 correct points using the given scale for 44 x .

    Note:

    1. 7 or 8 points correctly plotted, award K1.

    2. Ignore curve out of range.

    (i) 1210 y

    (ii) 6.075.0 x

    Note

    1. Allow P marks if value of x and of y are shown on the graph.

    2. Value of x and of y obtained by calculation, award P0.

    P1

    P1

    P1

    K2

    N1

    P1

    P1

    2

    4

    2

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    10

    (d)

    Identify equation 2010xy

    Straight line 2010xy correctly drawn.

    (Check any two points (0, 20), (1, 30), (2, 40), and accurate to 2

    1square

    grid vertically)

    7.06.0 x

    5.26.2 x

    Note:

    1. Allow N marks if values of x are shown on the graph.

    2. Values of x obtained by calculation, award N0.

    K1

    K1

    N1

    N1

    4

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    11

    13 (a)

    (b) (i)

    (b) (ii)

    (i) (-2, 3)

    (ii) (2, 1)

    Note:

    Point (2, 1) marked or (-2, 3) seen or (-2, 3) marked, award P1

    (a) X : Rotation 90 clockwise / 270 anticlockwise at centre (0, 4) //

    Putaran 90 arah jam / 270 lawan arah jam pada pusat (0, 4)

    Note :

    1. Rotation 90 clockwise / 270 anticlockwise //

    Putaran 90 arah jam / 270 lawan arah jam //

    Rotation at centre (0, 4) //

    Putaran pada pusat (0, 4), award P2

    2. Rotation // Putaran, award P1.

    (b) Y : Enlargement with scale factor 3 at centre P(-3, 2) //

    Pembesaran dengan faktor skala 3 di pusat P(-3, 2)

    Note:

    1. Enlargement with scale factor 3 // Pembesaran dengan faktor skala 3//

    Enlargement at centre P(-3, 2) //

    Pembesaran pada pusat P(-3, 2), award P2.

    2. Enlargement // Pembesaran, award P1.

    xx 2* )3(96

    12x

    Note:

    96x or x2* )3( or equivalent, give K1

    P1

    P2

    P3

    P3

    K2

    N1

    3

    6

    3

  • 1449 SULIT Marking Scheme

    Peperiksaan Percubaan SPM

    1449/1 SULIT

    12

    14 (a)

    (b)

    Class Interval

    Selang Kelas

    Midpoint

    Titik Tengah

    Frequency

    Kekerapan

    I 30 34 32 0

    II 35 39 37 4

    III 40 44 42 6

    IV 45 49 47 5

    V 50 54 52 9

    VI 55 59 57 7

    VII 60 64 62 4

    VIII 65 69 67 0

    Class Interval : (II to VII)

    Midpoint : (I to VIII)

    Frequency : (I to VIII)

    Note : Allow two mistakes in frequency, for P1