SULIT 2 14492(GMP) Question Solution and Mark Scheme Marks 1
SULIT 1449/2(GMP) 1449/2(GMP) Mathematics Kertas 2 Peraturan Pemarkahan 2014 SKEMA PRAKTIS BESTARI PROJEK JAWAB UNTUK JAYA (JUJ) 2014 MATHEMATICS Kertas 2 SET 1 PERATURAN PEMARKAHAN UNTUK KEGUNAAN GURU MATA PELAJARAN SAHAJA
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1449/2(GMP) SULIT
SULIT 2 1449/2(GMP)
Question Solution and Mark Scheme Marks1 y
10 y = x + 3
8
6
4 y = 6
- – x
2
x O
2
4
6
8
10 The line x = 6 correctly drawn. K1 The region correctly shaded. P2 Note: Award P1 to shaded region bounded by two correct lines satisfy any two inequalities. (Check one vertex from any two correct lines)
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1449/2(GMP) SULIT
SULIT 3 1449/2(GMP) Question Solution and Mark Scheme Marks 2 2x + 12y = 24 or
6
3 39 or equivalent K1
x y
Note Attempt to equate the coefficient one the unknowns, award K1
11 11 y 11 or x 33 or equivalent
K1
2 OR 13 y
x or y 13 2 x or equivalent (K1)
2 Note Attempt to make one of the unknowns as the subject, with two terms on other side, award K1
11 or 33 or equivalent (K1)
11 y 11 x
2 OR 3
1
x
13 1
1 or equivalent (K2)
1
2
y
6
( 2 3 ) ( 1 ) 2
2 Note N1
Attempt to write matrix equation, award K1
x
6 N1
y
1 Note:
x
6
If as final answer, award N1
4
y
1
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1449/2(GMP) SULIT
SULIT 4 1449/2(GMP) Question Solution and Mark Scheme Marks 2
3 K1
2 m m 11 12 K1
( 2 m 3 ) ( m 4 ) or equivalent
OR 2 ( 11 ) ( 11 ) 4 ( 2 )( 12 )
m or equivqlent (K1)
2 ( 2 )
3
m
N1
2
m
4 N1
Note:
1. Accept without “ = 0” 2.
Accept three terms on the same side, in any order
3
3
3. Accept ( m ) ( m 4 ) with m , m
4
2
2 for Kk2
4. Accept correct answers from three correct terms without factorization for Kk2.
4
JGP or PGJ
4(a)
P1
3 K1
(b) =
tan or equivalent
10
o o
N1
16.70 or 16
42
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1449/2(GMP) SULIT
SULIT 5 1449/2(GMP) Question Solution and Mark Scheme Marks 5(a)
2
2
1 ( *
x y or equivalent award K1
5
2
1 x y or equivalent
( 5 )
1 y
2
5 y
31 8.13 am atau iam 0813
50
60 100 80
48 P1 P1 K1 N1 K1 N1 P1 P1 P1 K1 N1
6
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1 ( * or ) 10 )(
) 10 )(
(b) (ii) x = 10
2
PS
m QR m
2
10
4
8
or
1
c
c )
10 )(
2
1 ( or ) 10 )(
2
1 ( x y or equivalent
Note :
SULIT (c) 6(a) (b) (i) (c)
SULIT 6 1449/2(GMP) Question Solution and Mark Scheme Marks 7(a) (i) Sebilangan
P1
(ii) Semua
P1
(b)
P1
P Q P
K1
2
2n + 2 ,
(c) n = 1, 2, 3, 4, ...
N1
5
1
8(a) k
P1
11 m = 1 P1 2
3 x
12
(b)
3 1 y
7
P1
x
1
3
12 1
K1
y (
2 )( 1 ) ( 3 )( 3 )
3
2
7
N1
x
3 y
2 N1
Note: *
inverse
2
3 1 . Do not accept or
matrix
3
1
inverse
1 * .
matrix
1
x
3 2 . as final answer, award N1 .
y
2 3 . Do not accept solutions solved not using matrix method.
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1449/2(GMP) SULIT
SULIT 7 1449/2(GMP) Question Solution and Mark Scheme Marks
9 K1
1 ( 4 10 ) 8
7
2 K1
1
22 2 3 . 5
10
2
7
1
1
22 2 K1 ( 4 10 ) 8 7 + 3 .
5
10
2
2
7 1 1169 N1 584 or or 584.5
2
2
4 10(a) 160
22 K1 2
10 360
7 160
22 2 10 + 10 + 10 + 16
K1 360
7 59 4028 N1 63 or or 63.94
63
63 160
22 2
1 (b)
10 or 6
16 360
7
2 K1 160
22
1 2 –
10
6
16 K1 360
7
2 43 5776 91 or or 91.68
63
63 N1
6 Note:
1. Accept for mark.
2. Accept correct value from incomplete substitution for K mark.
3. Correct answer from incomplete working, award Kk2
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1449/2(GMP) SULIT
SULIT 8 1449/2(GMP)
Question Solution and Mark Scheme Marks 11(a) Sampel space,S = {HH, HO, HU, HS, HE, OH, OO, OU, OS, OE, P2 UH, UO, UU, US, UE, SH, SO, SU, SS, SE , EH, EO, EU, ES, EE }
Note : Allow one mistake in listing the sample space for P1
(b)(i) { SH, SO, SU, SS, SE } K1
5
1 or N1
25
5
(ii)
K1 { HH, HS, OO, OU, OE, UO, UU, UE, SH, SS, EO, EU, EE }
13 N1
25
6 Note:
1. Accept answer without working for K1N1
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1449/2(GMP) SULIT
SULIT 9 1449/2(GMP) Question Solution and Mark Scheme Marks 12(a)
2.4 K1
- 2
K1
2 (b) Graph
Axes drawn in the correct directions with uniform scale for
4 x 4 and 10 y
10 P1
All 8 points and *2 point correctly plotted or curve passes K2 through all the points for
4 x 4 and 10 y
10 A smooth and continuous curve without any straight line passes
N1
4
through all 10 correct points using the given scale for
4 x 4 and 10 y
10 Note:
1. 8 or 9 points plotted correctly, award K1 2. Ignore curve out of range.
4 . 6 y 4 .
8 P1
(c)(i)
1 . 7 x 1 .
8
(ii)
P1
2
6 Identify equation y = -2x + 2 or
2
2 x
K1
x (d)
Straight line y
2 x 2 correctly drawn
K1 Values of x :
N1
1 . 25 x 1 .
35 N1
4 2 .
25 x 2 .
35 Note:
12 1. Allow N marks if values of x are shown on the graph.
2. Values of x obtained by calculation, award N0
SULIT 10 1449/2(GMP) y
10
8
6
4
2
x
- 4 - 2
- 3 - 1
1
2
3
4
- 2
- 4
- 6 <
- 10
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SULIT 11 1449/2(GMP)
Question Solution and Mark Scheme Marks 13(a)(i) ( -8 , 6 )P2 ( -5, 4 ) or point (-8,6) marked or point (-5, 4) marked, award P1
(ii) ( 5, -1 )
P2 Note: (-1, 1) or point (5,-1) marked or point (-1, 1) marked, award P1
4 (b)(i)(a) Reflection on line x = -1
P2 Note: 1. Reflection award P1
(b) Enlargement with scale factor ½ at centre E or ( -3,2 ) P3
Note: 1.
Enlargement centre E or ( -3,2 ) or Enlargement scale factor 2, award P2 .
2. Enlargement, award P1 . 2
(ii)
- * 1
24.5 = luas objek
2
2
24.4 x 2 - 24.5 K2
73.5 N1
8
12
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1449/2(GMP) SULIT
SULIT 12 1449/2(GMP
Question Solution and Mark Scheme Marks
14(a)Class Midpoint Frequency Interval Titik Kekerapan Selang Kelas tengah
35
37
2
- – 39
I
40
42
9 II – 44
45
47
10 III – 49
50
52
6
- – 54
IV
55
57
7 V – 59
VI
60
62
4
- – 64
65
67
2 VII – 69
Class interval : (II to VII ) P1
Midpoint : (II to VII) P1 frequency : (II to VIII) P2
4 Note: Allow one mistake frequency for P1.
- * * * * * * * 37 (
2 ) 42 ( 9 ) 47 ( 10 ) 52 ( 6 ) 57 ( 7 ) 62 ( 4 ) 67 ( 4 )
(b)
K2
40 53.725
N1
3 (c)
Frequency polygon Axes drawn in correct directions with uniform scale for
37 x 67 and y
40 P1
Horizontal axes labeled with values of midpoint K2 * 7 points plotted using midpoint.
Note: * 5 or * 6 points plotted correctly, award K1 N1
4 Smooth curve passes all 7 correct points and (34, 0) and ( 72,0 )
19
(d)
K1
1 Note: Do not accept answer without frequency polygon
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1449/2 SULIT
SULIT 13 1449/2(GMP)
y
10
9
8
7
6
5
4
3
2
1 x
34
37
42 47 .52
57
62
67
72
© 2014 Hak Cipta JUJ Pahang
1449/2(GMP) SULIT
SULIT 14 1449/2(GMP Question Solution and Mark Scheme Marks 15(a)
J C D G A B
Correct shape with rectangles ADJG and BCJG. K1 All solid lines.
DJ < JC < DA
K1 Measurements correct to ± 0.2 cm (one way) and
o o
all angles at vertices = 90 ± 1 N1
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1449/2 SULIT
SULIT 15 1449/2(GMP Question Solution and Mark Scheme Marks (b)(i)
F G Q H L M B A Correct shape ABHQMLGF K1 All solid lines.
FA > BH = HQ = LM K1
Measurements correct to ± 0.2 cm (one way) and N2
4 o o
A , B , H , M, Q, L = 90 ± 1
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1449/2 SULIT
SULIT 16 1449/2(GMP Question Solution and Mark Scheme Marks (ii)
E F
I H M N C B
Correct shape with rectangles FEIH and HICB. K1 All solid lines.
Note: Ignore MN
M and N joined with dashed line to form rectangle BCNM K1
M and N lies between HB and IC.BC > BF > BM = MH=HF K1
Measurements correct to ± 0.2 cm (one way) and
o o
All angles at vertices of rectangles = 90 ± 1 N2
5
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1449/2 SULIT
SULIT 17 1449/2(GMP
Question Solution and Mark Scheme Marks o16(a) 100 W
P2
2 Note: o
100 or ° W , award P1
(b)
K2 180 x 60 x cos 55 N1
6194.63
o
3 Note: 180 or using cos 55 , award K1 (c)(i)
K2 (180 -110 ) x 60 + 5400
N1 9600
3 (ii)
K2 9600 ÷ 580 N1
16.55 N1 2253 hour
4 Note : *(180 -110 ) x 60 + 5400 award K1
12