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15 (a)
1449
SULITMarking Scheme
Peperiksaan Percubaan SPM PAGE 71449
SULITMarking Scheme
Peperiksaan Percubaan SPM
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2011
MATHEMATICS 1449MARKING SCHEME
Paper 1
1A11A21B31A
2B12D22B32D
3C13D23D33D
4C14D24D34D
5D15B25C35B
6B16A26C36C
7A17A27B37B
8B18D28C38C
9B19A29C39A
10A20D30C40D
A - 9 , B - 10, C - 9, D - 12
Paper 21 (a)Straight dotted line correctly drawn.
Region correctly shaded.Note:
1. Accept solid line for K1.
2. Award P1 to the shaded region bounded by two correct lines. (Must include part of region R)
K1
P23
2 (a) (b) or
or equivalent
20.56 or 2033
P1K1
N1
3
3 3n2 7n 6 = 0 or equivalent
( 3n + 2 )( n 3 ) = 0 or equivalentOR
or equivalent (K1)
n = n = 3 Note:
1. Accept without = 0 .
2. Accept three terms on the same side, in any order.
3. Accept with n = or n = 3 for Kk2.
K1K1
N1
N14
4 or or equivalentNote
Attempt to equate the coefficient of one of the unknowns, award K1.
or or equivalent
OR
or or or
or equivalent. (K1)Note
Attempt to make one of the unknowns as the subject, with 2 terms on the other side, award K1
or or equivalent . (K1)
OR
(K2)Note
Attempt to write the matrix equation, award K1.
Note:
as final answer, award N1.
K1
K1N1
N1
4
5
+
389.72 389.74Note:
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
N14
6 (a) (b)
(c)and 10km = 104m
OR50 = 5 or (P1)
OR 50 = 5 or 10km = 104m (P1)If , then . // Jika , maka .
False // Palsu
3 is a factor of 12 // 3 adalah faktor bagi 12
P1
P1
P1
K25
7 (a)
(b)
(c)
or
or Note: Accept * using ( -3 , 0) and ( *k , 4) only
or equivalent
Note:
Do not accept
P1
P1
K1
N1
N15
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) }
or
or
P1
N2
N2
5
9 (a)
(b)
or
+ + 28 +28 + 14
or or 121.31 121.33
or
EMBED Equation.3
EMBED Equation.3
or 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
33
10 (a) (b)
(c)4
or equivalent
50
or or equivalentd = 648
P1
K1
N1
K2
N16
11(a)
(b)
Note : Determinant or 2, award P1.
or
or or 2.5
or or
Note:
1. Do not accept or
2. as final answer, award N1.
3. Do not accept any solutions solved not using matrices.
P1
P2
P1
K1
N1
N13
4
12 (a) (b)
(c)
(d)
6.4
Graph
Axes drawn in correct directions with uniform scales for and .
All 7 points and *2 points correctly plotted or the curve passes through all the points for .
A smooth and continuous curve without any straight line and passes through all 9 correct points using the given scale for .
Note:
1. 7 or 8 points correctly plotted, award K1.
2. Ignore curve out of range.
(i)
(ii) 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.
Identify equation
Straight line correctly drawn.
(Check any two points (0, 20), (1, 30), (2, 40), and accurate to square grid vertically)
Note:
1. Allow N marks if values of x are shown on the graph.
2. Values of x obtained by calculation, award N0.
P1
P1
P1
K2
N1
P1
P1
K1
K1
N1
N1
2
4
2
4
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.
Note:
or or equivalent, give K1
P1
P2
P3
P3
K2
N1
3
6
3
14 (a) (b)
(c)
(d)
Class IntervalSelang KelasMidpointTitik Tengah
Frequency
Kekerapan
I
30 34 320II
35 39 37
4III
40 44
42
6IV
45 49
47
5V
50 54
52
9VI
55 59
57
7VII
60 64
62
4VIII65 69
67
0Class Interval : (II to VII)
Midpoint : (I to VIII)
Frequency : (I to VIII)
Note : Allow two mistakes in frequency, for P1
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. (without table)
Frequency polygon Axes drawn in correct directions, uniform scales for and .
*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 and
*20 from * frequency polygon
Note: Do not accept answer without a frequency polygon.
P1
P1
P2
K2
N1
P1
K2
N1
K1
4
3
4
1
15
15 (a)
(b) (i)
(b) (ii)
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 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 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.
Correct shape with hexagon ABCDEF.All solid lines.
Measurement correct to cm (one way) and all angles at the vertices of rectangles are .
Correct shape with rectangles AHGF and FGLD and semicircle AD.
All solid lines.
Note: Accept semicircle drawn not using compass.
and semicircle AD drawn correctly (use compass).
Measurement correct to cm (one way) and
901.
Correct shape with rectangles FGLD, DLKC and QCSR.
All solid lines.
Note:
Ignore straight line AHA and H joined with dashed line to from rectangle AHLD
Measurement correct to cm (one way) and
all angles at vertices of rectangles
K1
K1
N1
K1
K1
N2
K1
K1
K1
N2
3
45
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.
Note:
cos 80 or 136 seen, award K1.
1416.97
20 hour 7 min
P2
P2
K2
N1
K1
K1
K2
N12
2
3
5
(
(
(
(
(
(
-2
-3
-1
1
2
3
4
-4
10
20
30
40
y
-10
-20
9
8
7
-30
-40
0
x
(
(
47
42
37
32
(
6
4
3
2
1
5
0
67
62
57
52
(
(
(
(
(
(
(
(
(
y = 10x + 20
0.65
-2.65
-0.65
11
Question 12
y
EMBED Equation.DSMT4
EMBED Equation.DSMT4
x
(6
4
0
(
(
Question 14
A
F
E
D
C
B
A
H
G
L
D
F
F
G
A
H
D
L
K
C
Q
R
S
PAGE 1449/1
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