2010 pspm kedah mm12 w ans

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    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH

    NEGERI KEDAH DARUL AMAN

    PEPERIKSAAN PERCUBAAN SPM 2010 1449/1MATHEMATICS

    ANSWER FOR PAPER 1

    1 B 11 C 21 C 31 D

    2 A 12 D 22 A 32 B

    3 D 13 A 23 A 33 B

    4 B 14 B 24 B 34 D

    5 C 15 C 25 B 35 C

    6 B 16 B 26 D 36 B

    7 C 17 D 27 A 37 D

    8 C 18 C 28 D 38 C

    9 A 19 A 29 A 39 D

    10 B 20 A 30 C 40 A

    ANALISIS

    A 10

    B 11

    C 10

    D 9

    NOTA: MARKAH PELAJAR = 100140

    )21( +KK

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    1449/2 (PP)

    Matematik

    Kertas 2

    Peraturan

    Pemarkahan

    19 September2010

    PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

    SEKOLAH MENENGAH

    NEGERI KEDAH DARUL AMAN.

    PEPERIKSAAN PERCUBAAN SPM 2010

    UNTUK KEGUNAAN PEMERIKSA SAHAJA

    Peraturan pemarkahan ini mengandungi 19 halaman bercetak

    MATHEMATICS

    Kertas 2

    PERATURAN PEMARKAHAN

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    2

    Section A

    [ 52marks]

    Question Solution and Mark Scheme Marks

    1(a)

    (b)

    Note :

    P R correctly shaded, award K1

    K1

    K2 3

    P R

    Q

    P R

    Q

    P R

    Q

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    3

    Question Solution and Mark Scheme Marks

    2 24 3 7 0 =x x

    ( ) ( )1 4 7 0+ =x x or equivalent

    OR2( 3) ( 3) 4(4)( 7)

    2(4)

    =x (K1)

    1= x

    7 31 1 75

    4 4= x or or

    Note : 1. Accept without = 0.2. Accept three terms on the same side, in any order.3. Accept correct answer from the correct term without

    factorisation for Kk2.

    K1

    K1

    N1

    N1 4

    3 33 21

    2

    p q = or 3 2 18p q+ = or equivalent

    Note:

    Attempt to equate the coefficient of one of the unknowns award

    K1

    4 12q = or 4 32p = or equivalent

    OR

    14 2p q= + or14

    2

    pq

    = or equivalent (K1)

    2(9 )

    3

    qp

    = or

    39

    2q p= or equivalent (K1)

    Note:

    Attempt to make one of the unknowns as the subject, award K1

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    4

    Question Solution and Mark Scheme Marks

    OR

    ( ) ( )

    1 2141

    33 911 1 2 22

    p

    q

    =

    or equivalent (K2)

    8p =

    3q =

    Note :

    Accept

    1.8

    3

    p

    q

    =

    as final answer, award N1

    2.

    ( ) ( )

    1 2141

    33 91

    1 1 2 22

    or equivalent seen, award (K1)

    N1

    N1

    4(a)

    (b)

    PTQ or QTP

    2 2

    12tan

    6 8=

    +

    or equivalent

    50 19 or 50 11' or 50 12 '

    P1

    K1

    N1 3

    5(a)(i)

    (ii)

    (b)

    False // Palsu

    True // Benar

    If 2 0x > , then 0 or 0x x> < //

    Jika 2 0x > , maka 0 atau 0x x> <

    P1

    P1

    P1

    4

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    5

    Question Solution and Mark Scheme Marks

    (c)

    If 0 or 0x x> < , then 2 0x > //

    Jika 0 atau 0x x> < , maka 2 0x >

    5 and 9 are odd numbers // 5 dan 9 adalah nombor ganjil

    P1

    K1 5

    6(a)

    (b)

    0 2 5x= or equivalent

    5

    2

    x = or1

    2

    2

    or 2 5

    mQR = 2

    6

    4

    y

    x

    =

    *mQR or 6 =

    *mQR (4) + c or equivalent

    2 14y x= + or equivalent

    K1

    N1

    P1

    K1

    N1 5

    7(a)

    (b)

    p = 14

    q = 4

    2 3 13

    4 1 5

    x

    y

    =

    1 3 1314 2 2(2)(1) ( 3)(4)

    xy

    =

    or

    *13

    2

    x inverse

    y matrix

    =

    2x =

    3y =

    P1

    P1

    P1

    K1

    N1

    N1

    2

    4

    6

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    6

    Question Solution and Mark Scheme Marks

    Note:

    1. Do not accept

    *2 3 1 0

    4 1 0 1

    inverseor

    matrix

    =

    .

    2.2

    3

    x

    y

    =

    as final answer, award N1.

    3. Do not accept any solutions solved not using matrix method.

    8 21 223 5 6

    3 7

    2225 4

    7

    2 21 22 223 5 6 5 4

    3 7 7

    +

    2739

    7 or

    2391

    7 or 391 3

    Note :

    1. Accept for K mark.2. Correct answer from incomplete working, award Kk2.

    K1

    K1

    K1

    N1 4

    9(a)

    (b)(i)

    {(S,C), (S,O), (S,R), (S,E), (C,S), (C,O), (C,R), (C,E), (O,S),

    (O,C), (O,R), (O,E), (R,S), (R,C), (R,O), (R,E), (E,S), (E,C),

    (E,O), (E,R)}

    Note :

    1. Accept correct tree diagram or grid for P22. Accept 10 correct listings for P1

    {(C,S), (C,O), (C,R), (C,E)}

    4

    20 or

    1

    5

    P2

    K1

    N1

    2

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    7

    Question Solution and Mark Scheme Marks

    (ii) {(S,C), (S,R), (C,S), (C,R), (O,E), (R,S), (R,C), (E,O)}

    8

    20

    or2

    5

    Note :

    Accept answer without working from correct listing,

    tree diagram or grid.

    K1

    N1 4

    6

    10(a)

    (b)

    90 222 14360 7

    or 120 222 7360 7

    90 222 14

    360 7 +

    120 222 7

    360 7 + 14 + 7 + 7 or equivalent

    194

    3 or

    264

    3 or 64 67

    290 2214

    360 7 or

    2120 227

    360 7

    290 2214

    360 7

    2120 227

    360 7 or equivalent

    308

    3 or

    2102

    3 or 102 7

    Note :

    1. Accept for K mark.2. Correct answer from incomplete working, award KK2.

    K1

    K1

    N1

    K1

    K1

    N1 6

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    8

    Question Solution and Mark Scheme Marks

    11(a)

    (b)

    (c)

    45915.3

    30=

    11 28

    10

    or

    17

    10

    71

    10 or 1 7

    Note : Without working, award K1N1

    ( ) ( ) ( )1 111 28 10 11 12 11 8 4592 2

    v + + + + =

    or equivalent method

    Note:

    1. ( )1 11 28 102

    + or ( )11 12 or ( )1

    11 82

    v +

    or equivalent, award K1

    2. Accept 195 or 132 for K1

    22

    P1

    K1

    N1

    K2

    N1 6

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    9

    Question Solution and Mark Scheme Marks

    12(a)

    (b)

    (c)(i)

    (ii)

    (d)

    7

    2

    Note : K only meant for table value.

    Graph

    Axes drawn in correct direction, uniform scales in 3 5 4x

    and 8 28y .

    All 7 points and *2 points correctly plotted or curve passes

    through these points for 3 5 4x and 8 28y .

    A smooth and continuous curve without any straight line and passes

    through all 9 correct points using the given scale for 3 5 4x .

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

    2. Ignore curve out of range.

    10 0 11 0y

    3 20 3 10x

    Identify equation 2 9y x= + or equivalent.

    Straight line 2 9y x= + correctly drawn.

    Values ofx : 2 65 2 55x

    3 05 3 15x

    Note : 1. Allow N marks if values ofx shown on the graph.

    2. Valuesx obtained by calculation, award N0.

    K1

    K1

    P1

    K2(does not

    depend on P)

    N1(depends on

    P and K)

    P1

    P1

    K1

    K1

    N1(dep 2nd K1)

    N1(dep 2nd K1)

    2

    4

    2

    4

    12

    Note:

    1. Allow P mark if value of x and y areshown on the graph.

    2. Value ofx and y obtained by calculation,award P0.

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    10

    y = 2x + 9

    22 3 7y x x=

    2 1 O 1

    20

    15

    10

    5

    5

    10

    2 3 4 x

    25

    30

    y

    3 4

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    11

    Question Solution and Mark Scheme Marks

    13(a)(i) (6, 1) P2

    Note: (6, 1) marked or (1, 4) seen or (1, 4) marked, award P1

    (ii) (8, 5) P2 4

    Note: (8, 5) marked or (3, 8) seen or (3, 8) marked, award P1

    (b)(i)(a) W: Reflection in the linex = 1 P2

    Note :

    1. P1 : Reflection // Pantulan.

    (b) V: Enlargement at centre K or (6, 10) with scale factor3

    2 P3

    Note :

    1. P2 : Enlargement at centre K or(2, 1) or

    Enlargement scale factor3

    2

    2. P1 : Enlargement.

    (ii) * 2388

    2

    K1

    * 23

    88 882

    K1

    110 N1 8

    12

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    12

    Question Solution and Mark Scheme Marks

    14(a)

    (b)

    Frequency : (I to VIII)

    Cumulative frequency : (I to VIII)

    Upper Boundary : (I to VIII)

    Note: Allow one mistake in frequency for P1

    * * * * * * *

    * * * * * * *

    ( 34 5 2) ( 44 5 3) ( 54 5 8) ( 64 5 10) ( 74 5 11) ( 84 5 4) ( 94 5 2)

    2 3 8 10 11 4 2

    + + + + + +

    + + + + + +

    Note :

    1. Allow *midpoint for K12. Allow two mistakes for the multiplication of midpoint

    and*frequency, for K1

    65 75

    Note :

    Correct answer from incomplete working, award Kk2

    e.g.2630

    65 7540

    = (without table)

    P2

    P1

    P1

    K2

    N1

    4

    3

    Marks

    Markah

    Frequency

    Kekerapan

    Cumulative

    Frequency

    Kekerapan

    Longgokan

    Upper

    Boundary

    Sempadan

    Atas

    20 29 0 0 29.5 I30 39 2 2 39.5 II

    40 49 3 5 49.5 III

    50 59 8 13 59.5 IV

    60 69 10 23 69.5 V

    70 79 11 34 79.5 VI

    80 89 4 38 89.5 VII

    90 - 99 2 40 99.5 VIII

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    13

    Question Solution and Mark Scheme Marks

    (c)

    (d)

    Axes drawn in correct direction and uniform scale for

    29 5 99 5x and 0 y 40

    Note :Do not accept wrong label

    *8 points correctly plotted

    Note :

    *6 or

    *7 points correctly plotted or curve passes through

    using at least 6 correct upper boundary, award K1

    Smooth and continuous curve without any straight line passes

    through 8 correct points for using given scales 29 5 99 5x

    Any true statement from the ogive

    Note :

    Do not accept answer without an ogive

    P1

    K2

    N1

    K1

    4

    1

    12

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    14

    0

    5

    10

    15

    20

    25

    30

    35

    40

    29.5 39.5 49.5 59.5 69.5 79.5 89.5

    Marks

    Frequency

    45

    99.5

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    15

    Question Solution and Mark Scheme Marks

    15 Note :

    (1) Accept drawing only (not sketch).(2) Accept diagrams with wrong labels and ignore wrong labels.(3) Accept correct rotation of diagrams.(4) Lateral inversions are not accepted.(5) If more than 3 diagrams are drawn, award mark to the

    correct ones only.

    (6) For extra lines (dotted or solid) except construction lines, nomark is awarded.

    (7) If other scales are used with accuracy of 0.2 cm one way,deduct 1 mark from the N mark obtained, for each part

    attempted.

    (8) Accept small gaps extensions at the corners.For each part attempted :

    (i) If 0 4 cm, deduct 1 mark from the N mark obtained.

    (ii) If > 0 4 cm, no N mark is awarded.

    (9) If the construction lines cannot be differentiated from theactual lines:

    (i) Dotted line :If outside the diagram, award the N mark.

    If inside the diagram, award N0.

    (ii) Solid line :

    If outside the diagram, award N0.

    If inside the diagram, no mark is awarded.

    (10) For double lines or non-collinear or bold lines, deduct 1mark from the N mark obtained, for each part attempted.

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    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    16

    Question Solution and Mark Scheme Marks

    15(a)

    Correct shape with pentagonABHGF

    All solid lines.

    BA>AF>HG >BH

    Measurement correct to 0 2 cm (one way) and all angles

    at vertices of rectangles = 90 1

    K1

    K1

    dep K1

    N1 dep

    K1K1 3

    F

    G H

    BA

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    SULIT 1449/2(PP)

    [Lihat halaman sebelah

    1449/2(PP) SULIT

    17

    Question Solution and Mark Scheme Marks

    15(b)(i)

    Correct shape with rectangles PNML, FPLG, GLJHand FPJHAll solid lines

    FN > FH >HJ = FP >MN = FG >LJ = GH = LM

    Measurement correct to 0 2 cm (one way) and all angles at the

    vertices of rectangles = 90 1

    K1

    K1

    dep K1

    N2 dep

    K1K1 4

    N M

    L J

    HGF

    P

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  • 8/8/2019 2010 Pspm Kedah Mm12 w Ans

    83/84

    SULIT 1449/2(PP)

    1449/2(PP) SULIT

    18

    Question Solution and Mark Scheme Marks

    15(b)(ii)

    Correct shape with rectangles QNPD andADEFAll solid lines

    Note : Ignore straight line KG

    Kand G joined with dashed line to form rectanglesADKG and

    GKEF

    QN= QA >AF>EF=AD > KE= GF >NP = QD >

    EP = AG = DK

    Measurement correct to 0 2 cm (one way) and all angles at

    the vertices of rectangles = 90 1

    K1

    K1

    dep K1

    K1 dep

    K1K1

    N2 dep

    K1K1K15

    12

    N P

    Q

    GK

    FE

    DA

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  • 8/8/2019 2010 Pspm Kedah Mm12 w Ans

    84/84

    SULIT 1449/2(PP)19

    Question Solution and Mark Scheme Marks

    16 (a)

    (b)

    (c)

    (d)

    (75S, 100E) // (75S, 100T)

    Note: 1. 100E or 100T , award P2

    2. 100 or E or T , award P1

    6420

    60 or 107

    642075

    60

    32 S

    ( )80 20 60 cos 75+ or 100 60 cos 75

    Note: ( )80 20+ or 100 or using cos75 correctly, award K1

    1552 91

    180 60

    550

    or equivalent

    Note:( )

    *180 60

    550

    , award K1

    19 64 hours or 19 hours 38 minutes

    P3

    K1

    K1

    N1

    K2

    N1

    K2

    N1

    3

    3

    3

    3

    SMKDarulaman j*k