Skema Matematik kertas 2 percubaan SPM

Skema Matematik kertas 2 percubaan SPM

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SKEMA PEMARKAHAN
PEPERIKSAAN PERCUBAAN SPM 2011
MATHEMATICS 1449/2
SECTION A
Question
[52 MARKS]
Sub
Mark
Mark Scheme
1
Total
Mark
y
x = -3
y
4
x4
3
4
0
x
4
Dotted line x + y = 4 drawn
Line x + y = 4 must touch the point (– 3, 7)
Region shaded correctly
1
1
1
3
Note : Accept ‘multiple hatching’
2
2 m2  m  6  0
1
2m  3m  2  0
1
m=
3
2
m=−2
Note: Do not accept any other method.
1
1
4
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3
6p – 2q = 18
or
5p = 10

or
2p  4q = 16
or equivalent
10
q  1 0 or equivalent
3
1
1
OR
p=3+
1
q
3
q = 3p  9
5p = 10
or
or
p = 8 + 2q
or
q=

or
1
p -4
2
10
q = 10
3
or equivalent
( 1)
( 1)
OR
2

 2   p    6 
3    

q
8
 1  2    

 p
1
 2
  
 q  2(2)  1( 2 )   1
3
(1)
2  6 

3  
2  8 
(1)
p=2
1
q = 3
 p  2 
Note : If      award 1 mark
 q   - 3
Identify  PRQ or  QRP
4
tan PRQ =
(ii)
(b)
4
1
12
or equivalent
5
1
1
67.38 or 67.4 or 67 23’
5 (a) (i) False /
1
3
Palsu
1
True / Benar
1
If n > 7, then n > 12
Jika n > 7, maka n > 12
Note: Do not accept ‘than’ (spelling)
1
False
1
/ Palsu
(c)
PQRS is a square
PQRS ialah segi empat sama
1
2
5
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6 (a)
75
1  (3)
=
(b)
(c)
1
1
2
1
1
1
( – 4) + c ( seen m = )
2
2
c=–2
1
y=
x–2
2
–4=
(b)
1
1
d=5
e=–4
1
1
 2  1   x  11

   =  
 3  4  y   9 
 x
1
  =
(2)(4)  (3)(1)
 y
1
  4 1  11

  
  3 2  9 
x=7
y=3
Note :
8.
1
1
x–2=0
2
x-intercept = 4
7 (a)
1
6
1
1
1
6
7
  award 1 mark
 3
22
×7 × 7 × 15
7
1
1 22
×
×7×7×6
3
7
1
22
1 22
× 7 × 7 × 15 – ×
×7×7×6
7
3
7
1
2002
1
3
4
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4
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9(a)
( b)
{ (4,5), (4,6)}
2
1
or
24
12
{(S,4), (5,P) (5,Q) (5,R) (T,4) (6,P) (6,Q) (6,R) (U,4) (V,4)}
10
5
or
24
12
10
(a)
Note: If all sample space listed, accept the direct answer.
30
22
60
22
× 2 ×
× 14 or
×2×
× 21
360
7
360
7
21 +
60
22
30
22
×2×
× 21 +7 +
× 2 ×
× 14 + 14
360
7
360
7
71 13 or 71.33
(b)
11 (a)
(b)
60
×
360
60
×
360
1
2
1
5
1
1
1
1
1
205 13 or 205.3 or 205.33
1
4
1
15  30
30  15
or
02
20
–
(c)
22
15
22
× 21 × 21 or
×
× 14 × 14
7
360
7
22
15
22
× 21 × 21 –
×
× 14 × 14
7
360
7
1
15
or –7.5
2
4
1
1
(30 + 15) × 2 or
(25 + 15) ( x – 6) or ( 4×15)
2
2
3
4
1
1
(30 + 15) × 2 + (4 × 15) + (25 + 15) ( x – 6) = 145
2
2
3
x=6
6
1
1
1
1
1
6
52
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Section B
Question
12 (a)
Mark Scheme
x
y
– 1.5
16
3
–8
Marks
1
1
(b)
 Axes drawn in the correct directions with uniform scales.
 All 7 points and *2 points correctly plotted or curve passes through
all the points.
(7 or 8 points correctly plotted award 1 mark).
 2 smooth and continuous curve without any straight line passes
through all 9 correct points using the given scales.
(c) (i)
ii)
(d)
1
2
2
8.4  y  8.8
 1.9  x  2.1
1
1
Identify equation of y  5  2 x
Straight line y  5  2 x correctly drawn
 2.25  x  2.65
1
1
1
12
5
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Question
13(a) (i)
Scheme of marks
(4, 1)
Marks
2
Note: Point (1, 4) award 1 mark
(ii)
( – 1, 6)
2
Note: Point (1, 3) award 1 mark
(b) (i)
(a)
V = Rotation, 90o anti clockwise , about centre (3, 5).
3
(b)
U = Enlargement , scale factor 3, at centre Q(5, 4)
3
Note: Do not accept wrong spellings for rotation and enlargement.
(b) (ii)
32  24 – 24
1
192
1
12
6
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Question
Scheme of marks
14 (a)
(b) (i)
(ii)
Mass (kg)
Jisim (kg)
30 - 34
35 – 39
40 – 44
45 – 49
50 – 54
55 – 59
60 - 64
Frequency
Kekerapan
1
2
5
6
8
5
3
Marks
Midpoint
Titik tengah
32
37
42
47
52
57
62
1
1
1
50 – 54
1
1(32)  2(37)  5(42)  6(47)  8(52)  5(57)  3(62)
1 2  5  6  8  5  3
= 49.5
2
Mean =
1
(c)

Axes drawn in the correct directions with uniform scales.
 All 7 points correctly plotted
 Point (27, 0) and (67, 0) correctly plotted
 All the 7 points starting from (27, 0) until (67, 0) are connected
correctly with straight line
1
2
1
1
12
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Question
15 (a)
Scheme of marks
marks
Plan:
The shape must be right with the rectangles. All lines must be fully drawn.
3
2 cm
3 cm
6 cm
b (i)
Measurement must be accurate to  0.2 cm and all angles at rectangle
vertex = 90o  1
Note: The shape is correctly drawn award 1 mark
Elevation X:
The shape must be right . All lines must be fully drawn.
4
1 cm
1 cm
3 cm
4 cm
2 cm
2 cm
5 cm
1 cm
b (ii)
Measurement must be accurate to  0.2 cm and all angles at rectangle
vertex = 90o  1
Note: The shape is correctly drawn award 1 mark
Elevation Y:
The shape must be right with the rectangles. All lines included the dotted
lines must be shown completely.
5
1 cm
1 cm
1 cm
2 cm
6 cm
Measurement must be accurate to  0.2 cm and all angles at rectangle
vertex = 90o  1
Note: The shape is correctly drawn award 1 mark
8
12
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Question
16. (a)
(b) (i)
(c) (i)
(ii)
Scheme of marks
Marks
145oW or 145o B
Note : 145o or  o W or  o B award 1 mark
2
70o
700 × 60
1
1
4 200
1
5220
60
1
5220
– 55
60
1
32oS
1
Using cos 55
1
180  60  cos 55
1
180  60  cos 55 o  5220
650
1
1
17.56
12
9