SKEMA Matematik Kertas 2 T5 Pahang

SKEMA PEMARKAHAN
PENILAIAN PERCUBAAN SPM NEGERI PAHANG 2017
MATHEMATICS 1449/2

SECTION A

Mark Scheme

Question

1

[52 MARKS]

(a)

Sub Total
Mark Mark

L
M

1

N
(b)

L
M
2

N
Note : (M  N) is correctly shaded award K1.

3

2

x  8 x  273  0

1

2

x  21x  13  0

1

x = 21 or x = 13

1

 The length of the paper = 21 cm
3

Volume of cone =

1

1 22
3
×

× 142 × 48 ×
3
7
4

1

7392
or 1232
6

1

22
× 72 × t = 1232
7

1
1

8 cm

4

y = 3x

or

4

x + y = 60

4

1

4x = 60

1

OR

 3  1  x   0 
   =  

 1 1   y   60 

 x
1
  =
 y  3(1)  (1)(1)

 1 1  0 
  

  1 3   60 

(2)

x = 15

1

y = 45

1

 x   15 
Note :   =   award 1 mark
 y   45 

2

4

5

(a)

Palsu / False

1
/ If x2  1 = 8, then x = 3

(b) Jika x2  1 = 8, maka x = 3
Palsu / False
(c)

1
1

Sudut pedalamannya bukan 108.

/ The interior angle is not

1

108.

(d) (4 × n2)  n, n = 1, 2, 3, 4, ……..

6

(a)

1,1

 FAG

1

tan FAG =

(b)

180
250

or equivalent

270
22
× 2 ×
× 21
360
7

(a)

[

3
7

or 165.43 or

270
22
×
× 212

360
7

(b)

[

or

270
22
×2×
×9
360
7

270
270
22
22

×2 ×
× 21] + 12 + [
×2×
× 9] + 12
360
360
7
7
165

270
22
×
× 212 ]
360
7
848

4
7

or

1
1

35.75 or 35 45’

7

6

1158
7



848.57

[

1

1

1

270 22
×
× 92
360 7

1

270 22
×
× 92 ]
360
7

1

or

or

3

3

5940
7

1

6

8

(a)

(A,N) (A,D) (A,S) (A,H)
(C,N) (C,D) (C,S) (C,H)
2
(K,N) (K,D) (K,S) (K,H)
(F,N) (F,D) (F,S) (F,H)

(b)

(i)

(ii)

(A,H) (C,H)

1

2
16

1

1
8

(A,N) (A,D) (A,S) (C,N) (C,D) (C,S) (K,H) (F,H)

8
16

9

or

or

1
2

1
1

(a)

y = 10

(b)

y =

5
x + c
3

1

10 =

5
(9) + c
3

1

y =

(c)

6

1

5
x  5
3

1

Pintasan-y / y-intercept = 5

4

1

5

10

(a)

250A + 320B = 21600

1

280A + 310B = 22740

(b)

 250 320   A   21600 
   = 


 280 310   B   22740 
 A
1
  =
 B  (250)(310)  (320)(280)

1

 310  320   21600 
 


  280 250   22740 

1

Grade A = RM48
Grade B

Note :

11

(a)
(b)

1

= RM30

5

 48 
  award 1 mark
 30 

17 minutes

1

28  12
8

1

2
(c)

1

1

[ ½ x (12 + 28) x 8] + [17 x 28] + [ ½ x (28 + V) x 15] = 1116

2

V = 36

1

5

6

Section B
Question

12

Mark Scheme

(a)
x
y

(b)

2.5

19.2

2

Sub Total
Mark Mark

1,1

24

Refer to the graph.
Note:
1)
2)

if points are correctly marked on the graph.
the curve passes exactly through the points.

Graph :





Axes are drawn in the correct direction with uniform scale in
the range  3  x  4 and  48  y  48.
All 6 points and 2 points* are correctly marked

Smooth curve and continuously in range of 3  x  4
with no straight line part and passing through all the correct
8 points.

1
2

1

Note:
(i)
6 @ 7 points are correctly plotted, award 1 mark
(ii) Other scale used, deduct 1 mark.

(c)

(i)
(ii)

(d)

12.5 ≤ y ≤ 14.5

1

1.4 ≤ x ≤ 1.6

1

Identify equation of

1

Straight line

correctly drawn

1

2.0 ≤ x ≤ 2.2

1

3.7 ≤ x ≤ 3.9

1

6

12

13

(a)

(i)

( 6, 4)

1

(ii)

( 6,  1)

2

Note: Point (6, 1) award 1 mark

(iii)

( 10,  2)

2

Note: Point (6, 1) award 1 mark

(b)

(i)

(a)

Y = Reflection in the line y = x

2

(b)

X = Enlargement of scale factor 2 with centre (0,2).

3

(ii)
1

PQRS =

1
PQRS = 42

14

(a)

(i)

1

Berat (kg)
Mass (kg)

Kekerapan
Frequency

Titik Tengah
Midpoint

31 - 40

2

35.5

41 - 50

3

45.5

51 - 60

6

55.5

61 - 70

9

65.5

71 - 80

8

75.5

81 - 90

4

85.5

91 - 100

2

95.5

101 - 110

1

105.5

7

1
2
1

12

2(35.5)  3(45.5)  6(55.5)  9(65.5)  8(75.5)  4(85.5)  2(95.5)  1(105.5)
2  3  6  9  8  4  2 1

(ii)

2

1

67.79
(b) Refer to the graph.

 Uniform scales and correct axes, using class intervals, midpoints or
class boundries (30.5  x  110.5)

 All *8 bars correctly drawn.

 Histogram with 8 correct bars.

1
1

(c) Kelas mod / Modal class = 61 – 70

15

(a) (i)

I/H/D

5 cm

2

1

G

C

6 cm

J/E/A

F

3 cm

B

Correct shape with rectangle AFBCGD and a semicircle . All solid lines.

1

JI > EF > FB

1

Measurement correct to ± 0.2 cm (one way) and all angles

2

A, B, C and D = 900 ±10

8

12

a)

(ii)
3 cm

J/I

E/H

5 cm

F/G

8 cm

A/D

8 cm

B/C

Correct shape with rectangle 8 cm x 3 cm and trapezium ABFE. All solid
lines
AB = AJ > EF  EJ

1

1

Measurement correct to ± 0.2 cm (one way) and all angles 900 ±10
(except EFB & ABF)

9

1

6 cm

J

(b)

I
2 cm

F/E

1 cm

4 cm

1 cm

G/H

6 cm

B/A

C/D

Correct shape with rectangle BCGH and FGIJ. All solid lines

1

Note : Ignore dashed lines.

16

Dashed lines.

1

BC = CG > GI

1

Measurement correct to ± 0.2 cm (one way) and all angles 900 ±10.

2

(a)

3

( 30º N , 60º W)
Note:

60º W award P2 OR 60o or  ° W , award P1

10

12

(b)

(90  30) x 60’

2

3600 nautical miles

1

4500
60

1

Note: 60 or ( 90 – 30 ) seen , award K1

(c)

 (75 – 30) or (30 – 75)

1

45o N

(d)

1

4500  50 x 60' kos 30
600

2

11.83

1

Note : (*50 x 60) ) or cos 30 award K1

11

12

y

50
X

40

30
X
20
X
y= 13.5

X

10

3

x=2.1

2

x=1.5

X
1

O

1

10 X

X
y = 6x - 10

20

-30

40
50

12

2

3

x=3.8

x

4

Frequency

10

9

8

7

6

5

4

3

2

1

0
35.5

45.5

55.5

65.5

13

75.5

85.5

95.5

105.5

Mass
(kg)