Math Selangor K2 Skema Jawapan Set A

SKEMA JAWAPAN
MATEMATIK KERTAS 2 1449/2
PERCUBAAN SPM 2017
Marks

Marking Scheme / Skema markah
1

Submarks

Total Marks

(a)
y
6

4

2

x

−2

−4

0

2

−2

3 marks

4
y = 3− x

−4

Draw the straight dotted line 2x− y = 0
Region shaded correctly

1 mark
1 mark

(b) No
1 mark

22  x + 1 
×
 × 7 = 88
7  2 
� 2 + 2x – 15 = 0
( x − 3) ( x + 5 ) = 0

1 mark
1 mark

radius= 2

1 mark

M + N = 78 or M − N = 24

1 mark
1 mark
1 mark

2

2

3

2M=102 or equivalent

4

5.

51

Years of service = 58 − 51
=7
(a) θ =∠ ACD or ∠ DCA
36
(b) tan θ =
20
θ = 60∙95˚ or 60˚57'
2

(a) If x > 25, then x> 5.
False
(b) 2 m> 0
(c) The number of subsets for set A = 24
Bilangan subset bagi set A ialah = 24

4 marks
1 mark

4 marks

1 mark
1 mark
1 mark

3 marks

1 mark
1 mark
1 mark
2 marks

5 marks

1 mark

Marking Scheme / Skema markah
6.

(a) CD = 10 − 8
2

x=6

1 mark

4
3
4
3 = (−6) + c or c = 11
3
4
y = x +11or equivalent
3

1 mark

1

×
2

1
2

22
7

×

7

1

2

2

5 marks
1 mark
1 mark

× � �2 × 5 and ×(5+17)×5×7 been seen

22
7

7

1

2

2

× � �2 × 5 + ×(5+17)×5×7

1925
1
@481 @481.25
4
4

8.

108 x+100y=990
120 x+56y=852

x
1
56
−100 990
�y� =
�
��
�
−120
108 852
108(56)−120(100)
x = 5, y = 4.5
9

240

22

(a) 2× � � × 2× � � ×7 or 4 × 7
360
7

2× �
260
3

240
�
360

22
7

× 2× � � ×7 + 4 × 7

2

240

22

1

� × � 7 � ×7 2 or 2 ×7×6.0622
360

2× �

240
�
360

22

1

7

2

× � � ×7 2 − 2× ×7×6.0622

616
3
(a) { ( R1, B ) , ( R1, R2) , (R1 , R3) , ( R1 , Y) , ( R2 , R1) ,

205∙33 or
10

1 mark
4 marks
1 mark
1 mark
1 mark

6 marks
1 mark

2 marks
1 mark
1 mark
1 mark

@86 3 @86.67 cm

(b) �

2 marks

1 mark

100 x
990
�� �= �
�
56 y
852

108
�
120

Total Marks

1 mark

2

(b) m=

7.

Marks
Submarks

1 mark

6 marks

1 mark
1 mark
2 marks

( R2 , R3) , ( R2 , B ) , ( R1 , Y ) , ( R3 , R1 ) , ( R3 , R2) ,
( R3 , B) , ( R3 , Y ) , ( B , R1 ) , ( B , R2 ) , ( B , R3 ) ,
( B , Y ) , ( Y , R1 ) , ( Y , R2 ) , ( Y , R3 ) , ( Y , B )}
(b) (i) {(R1,R2), (R1,R3), (R2,R1), (R2,R3), (R3,R1), ( R3,R2)}

6
3
=
20 10
(ii) { ( Y , B ) }

1 mark
1 mark
1 mark

1
20

1 mark

6 marks

Marking Scheme / Skema markah

11

2

Marks
Submarks

(a) (i) 3 // 0.67

1 mark

(b)(i) 11.20 a.m.

1 mark
1 mark
1 mark

(ii) 100 km
c) 80 ÷ 1

20
or equivalent
60

1 mark

Total Marks

6 marks

1 mark

180
2.5
60 km h-1
12.

(a)

x

2

6

V

392

216

(b) Graph
Axes are drawn in the correct direction, uniform scale for
0≤x ≤8 and 0≤V≤450.

1 mark
1 mark

1 mark

7 points and 2 points* plotted accurately

2 marks

Smooth and continuous curve without straight line(s) and
passes through all the 9 correct points 0≤x ≤8 and 0≤V≤450.

1 mark

Notes : (1) 7 or 8 points plotted correctly, award 1 mark
(2) Other scale being used, subtract 1 mark

13

(c) 432 ≤V≤ 435
2∙9 ≤x≤ 3∙1
Note: Do not accept the values of x and y obtained by calculation

1 mark
1 mark

(d) ) Identify the equation V = 140 correctly drawn
0∙4≤x ≤0∙6
6∙6≤x ≤6∙8

2 marks
1 mark
1 mark
2 marks
2 marks

(a) (i) ( −3 , −2 )
(ii) ( −3 , −2 )
(b) (i) H is Reflection in the line � = � + 2
H ialah pantulan pada garis y = x +2.

(ii) M ia an enlargement with a scale factor 2 and centre O (3,3).
Mialah pembesaran dengan factor skala 2 pada O (3,3)

(c) )

Area of image = 22 x area of object = 64
=16

12 marks

2 marks

3 marks
2 mark
1 mark

12 marks

Marks

Marking Scheme / Skema markah

Submarks

Total Marks

14
Column I
Age (years)
Umur (tahun)

Column II

Column III

Upper
FrequencyKek
boundrySempadan
erapan
atas

Column IV
Cummulative Frequency
Kekerapan longgokan

20 – 24

24.5

0

0

25– 29

29.5

10

10

30 – 34

34.5

20

30

35– 39

39.5

40

70

40– 44

44.5

50

120

45 – 49

49.5

30

150

50 – 54

54.5

10

160

Column I
1 mark
Column II
1 mark
Column II
1 mark
Column II
1 mark

(a)
(b) Mean =
= 40.13 or

27(10) + 32(20) + 37(40) + 42(50) + 47(30) + 52(10)
160

321
8

1 mark

(c) Axes are drawn in the correct direction, uniform scale for
0 ≤ vertical axis ≤ 160 and 24.5 ≤ horizontal axis ≤ 54.5

1 mark

All points plotted accurately.
Smooth and continuous curve.

2 marks
1 mark
2 marks

(d) 48
15

2 marks

(a)

H

E

C

7 cm

F

3 cm

G

3 cm

B

Correct shape rectangles EFGH and BCHG.
All lines are solid.

1 mark

BC>BF >FG =GB

1 mark

Measurements accurate up to ± 0.2 cm (one way) and all right
angles = 90o± 1o

1 mark

12 marks

Marks

Marking Scheme / Skema markah

15

Submarks

Total Marks

(b)

N

4 cm
3 cm

K

L

2 cm
A

3 cm

R

P

3 cm

1 mark

Correct shape rectangle ARLK and triangle NPR.
NP >NR >RP=AR>KA.

1 mark

Measurements accurate up to ± 0.2 cm (one way) and all right
angles = 90o± 1o

15

2 marks

(b)

N

H

4 cm

M

L

I
2 cm

R

3 cm

P

4 cm

C

Correct shape rectangles LMPR, MICP and NHCP. All solid lines.

1 mark

M –I is joined by a dashed line.

1 mark

RC >HC>HI = MI >LM >LR.
Measurements accurate up to ± 0.2 cm (one way) and all right
angles = 90o± 1o

1 mark
2 marks

12

Marking Scheme / Skema markah
16

Marks
Submarks

2 marks

(a) 144° E / T
Note: Award 1 mark for 144° or �° E / T is seen
(b) (70 °S, 144° E )
Award 2 marksfor( θ °S, 144° E )
Award 1 marksfor( θ °N, 144° E )

3 marks

(c) (180°– 70° – 70°) × 60

1 mark

2400 nautical miles

1 mark

(d) 144°× 60 × cos 70°

1 mark

(70° + 70°) × 60

1 mark

144 × 60 × kos70 (70  + 70) × 60
or
50
550

1 mark

144 × 60 × kos70
(70  + 70) × 60
+
50
550

1 mark

12

1 mark
21.18

Total Marks

Graph for Question 12
Graf untukSoalan 12
V
450

400

350

300

250

200

150

100

50

O

1

2

3

4

5

6

7

8

x

Graph for Question 14
Graf untukSoalan 14

Cumulative Frequency

160

140

120

100

80

60

40

20

O
24.5

29.5

34.5

39.5

44.5

39.5

54.5

Ages (Years)
Umur(Tahun)