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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
4*7*9*5*6*4*
4*627*579*525*476*424*37
Note :
1. Allow *midpoint for K1
2. Allow two mistakes for the multiplication of midpoint and *frequency
for K1.
50
Note :
Correct answer from incomplete working, award KK2.
e.g. 5035
1750(without table)
P1
P1
P2
K2
N1
4
3
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
13
(c)
(d)
Frequency polygon
Axes drawn in correct directions, uniform scales for 6732 x and
9*0 y .
*8 points correctly plotted using the correct midpoint
Note: *6 or *7 points correctly plotted, award K1.
Frequency polygon passes through all 8 correct points using the given scales
for 6732 x and 90 y
*20 from * frequency polygon
Note: Do not accept answer without a frequency polygon.
P1
K2
N1
K1
4
1
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
14
15
Note:
(1) Accept drawing only (not sketch).
(2) Accept diagrams without labels and ignore wrong labels.
(3) Accept correct rotation of diagrams.
(4) Lateral inversions are not accepted.
(5) If more than 1 diagrams are drawn, award mark to the correct ones only.
(6) For extra lines(dotted/dashed or solid) except construction lines, no KN mark is awarded.
(7) If other scales are used with accuracy of 2.0 cm one way, deduct 1 mark from the N mark obtained, for each part attempted.
(8) Accept small gaps or extensions at the corners. For each part attempted:
(i) If 4.0 cm, deduct 1 mark from the N mark obtained.
(ii) If >0.4 cm, no N mark is awarded.
(9) If construction lines cannot be differentiated from the actual 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 KN mark is
awarded.
(10) For double lines or non collinear or bold lines, crooked lines,
deduct 1 mark from the N mark obtained, for each part attempted.
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
15
15 (a)
Correct shape with hexagon ABCDEF.
All solid lines.
DECDFEBCAB
Measurement correct to 2.0 cm (one way) and all angles at the vertices of
rectangles are 190 .
K1
K1
N1
3
A
F
E D
C B
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
16
(b) (i)
Correct shape with rectangles AHGF and FGLD and semicircle AD.
All solid lines.
Note: Accept semicircle drawn not using compass.
FDAFADAH and semicircle AD drawn correctly (use compass).
Measurement correct to 2.0 cm (one way) and
DLHA ,,, 901.
K1
K1
N2
4
A H
G
L D
F
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
17
(b) (ii)
Correct shape with rectangles FGLD, DLKC and QCSR.
All solid lines.
Note:
Ignore straight line AH
A and H joined with dashed line to from rectangle AHLD
QDCQLKGLGKFG
Measurement correct to 2.0 cm (one way) and
all angles at vertices of rectangles 190
K1
K1
K1
N2
5
F G
A H
D L
K C
Q R
S
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
18
16
(a)(i)
(ii)
(b)
(c)
80 S
Note: 80 award P1.
(80 N, 84E) // (80 U, 84T)
Note: 80 N / 84 E // 80 U / 84 T, award P1.
80cos60136
Note:
cos 80 or 136 seen, award K1.
1416.97
80cos6044
60160
500
60160)80cos6044(
20 hour 7 min
P2
P2
K2
N1
K1
K1
K2
N1
2
2
3
5
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
19
-3 -2 -1 1 2 3 4 -4 0
10
20
30
40
y
-10
-20
-30
-40
x
y = 10x + 20
0.65
-2.65 -0.65
11
Question 12
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
20
5
1
2
3
4
6
7
8
9
Question 14
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1449 SULIT Marking Scheme
Peperiksaan Percubaan SPM
1449/1 SULIT
21
32 37 42 47 52 57 62 67
0