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# SPM Pahang Math P2 2010 Ans

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SULIT 1449/2 1449/2 Matematik Kertas2 Peraturan Pemarkahan September 2010

PEPERIKSAAN BERSAMA SEKOLAH-SEKOLAH NEGERI PAHANG 2010

PEPERIKSAAN PERCUBAAN SPM 2010

MATEMATIK

Kertas 2

PERATURAN PEMARKAHAN

Peraturan pemarkahan ini mengandungi 12 halaman. [Lihat sebelah 1449/2 SULIT

Jumlah Markah = 1 2 100%140

Kertas Kertas

2

Section A [ 52 marks ]

No Marking Scheme Marks

1

a.

b.

P1

P2

3

3

No Marking Scheme Marks

2 (a) 1210631

240

(b) 84012101210631

GC

GC = 5

K1

N1

K1

N1

4

3

Identify EAD or DAE or angle marked on the diagram correctly tan EAD =

123 or equivalent

14.04o or 14o 2

P1

K2

N1

4

4

(a) False (b) Implication 1: If m > n then m – 3 > n – 3 Implication 2 : if m – 3 > n – 3 then m > n (c) Conclusion : 4n + n3 , where n = 1,2,3,4, ……..

P1

P1

P1

P1P1

5

5

2x + 3y = –6 or x –

41 y = 4 or equivalent

7y = –28 y = – 4 x = 3

K1

K1

N1 N1

4

4

No Marking Scheme Marks 6

(a) y = 4 (b) Gradient of JK =

21 or the gradient being used

c )5(213

or

21

)5()3(

xy

21

21

xy or equivalent

yintercept = 21

P1

P1

K1

N1

P1

5

7

0103 2 xx

0)2)(53( xx 2x

35

x or

67.1x

K1

K1

N1

N1

4

8 p =3 , k = 10 1 3 62 4 3

mn

4 3 612 1 34 6

mn

32

32

mn

m = 32

, n = 32

Notes:

1.

32

32

mn

: N1

2. Solution without using matrices method cannot be accepted.

P1P1

P1

K1

N1,N1

6

5

No Marking Scheme Marks

9

(a) 127222

36040

or 137222

36090

12513137222

3609012

7222

36040

81.58

211758

(b) 1212

722

36040

or 1313722

36090

1313722

360901212

722

36040

07.183

141183

K1

K1

N1

K1

K1

N1

6

10

a) (S,A) (S,T) (S,U) (A,S) (A,T) (A,U) (T,S) (T,A) (T,U) (U,S)

(U,A) (U,T) b) (i) (T,S) (T,A) (T,U)

41

123 or

(ii) (S,A) (S,U) (A,S) (A,T) (T,A) (T,U) (U,S) (U,T)

32

128 or

P1

K1

N1

K1

N1

5

11 (a) 45 (b) (i) 8.45 a.m (ii) 70 km (c)

607590

72

P1

P1 P2

K1

N1

6

6

Section B [48 marks]

No Marking Scheme Marks

12(a)

(b)

(c)

(d)

8

-16

Graph Axes are drawn in the correct direction, uniform scale for – 4 x 4 and – 24 y 24 7 points and 2 points* plotted accurately Smooth and continuous curve without straight line(s) and passes through all the 9 correct points for – 4 x 4 Notes : (1) 7 or 8 points plotted correctly, award K1

(2) Other scale being used, subtract 1 mark from the KN marks obtained.

-8.0 < y < -9.0

1.8 < x < 1.9

Note : Do not accept the values of x and y obtained by calculation Identify the equation y = -2x+1 or equivalent The straight line y = -2x+1 drawn correctly

The values of x : 3.6 < x < 3.7

-3.3 < x < -3.1

Notes : (1) Award N mark(s) if the value(s) of x shown on the graph (2) Do not accept the value(s) of x obtained by calculation

K1

K1

K1

K2

N1

P1

P1

K1 K1

N1

N1

12

7

No Marking Scheme Marks 13 (a)

(b)

i) (1 , 8) Notes :

1. (2, 6) : P1

2. Accept answers without bracket. ii) (7 , 5) Notes :

1. (8, 3) : P1

i) (a) V : Enlargement with scale factor 21

centered at point (1, 2).

(b) W : Reflection in the line 3x

Notes:

1. Enlargement, scale factor 21

or

Enlargemant at point (1, 2).: P2

2. Enlargement only : P1

3. Reflection only : P1

ii) 22 20.4 or equivalent 22 20.4 – 20.4 61.2

P2

P2

P3

P2

K1

K1

N1

12

8

No Marking Scheme Marks 14(a)

(b)

(c)

Marks Upper

Boundary Frequency Cumulative Frequency

6 - 10 10.5 0 0 11 - 15 15.5 1 1 16 - 20 20.5 3 4 21 - 25 25.5 6 10 26 - 30 30.5 10 20 31 - 35 35.5 11 31 36 - 40 40.5 7 38 41 - 45 45.5 2 40

Column I (all class interval correct)

Column II (all upper boundary correct)

Column III (all frequency correct)

Column IV(all cumulative frequency correct)

Note : Allow two mistakes in column III for P1 Ogive Axes are drawn in the correct direction, uniform scale for 10.5 x 45.5 and 0 y 40 The horizontal axis labeled with upper boundary or use the values of upper boundary for plotting Plot 7 points* Smooth and continuous curve without straight line(s) and passes through all the 8 correct points for 20.5 x 55.5.

Notes : (1) 5 or 6 points* plotted correctly, award K1

(2) Mark(s) for plotting can be given to a curve which passes through 7 points* and point (10.5, 0)

(3) Other scale being used, subtract 1 mark from the KN marks obtained. First Quartile = 25.5 or Third Quartile = 35 0.5 Interquartile range = 35 – 25.5 = 9.5 0.5

P1

P1

P1

P1

K1

K1

K2

N1

K1

K1 N1

12

9

No Marking Scheme Marks 15 (a)

Correct shape with rectangles VUKJ and GKMB. All solid lines. Note: Ignore straight line JR J and R joined with dashed line to form rectangle JRBG GJ = VU = KM > UK The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1

K1

K1

K1

N1

U

K

R M B

G J

V

10

No Marking Scheme Marks

(b)

(i)

Correct shape with rectangles ADEF and IULF. All solid lines. Semicircle VSU drawn FL> UL > DE=AD The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1

K1

K1

K1

N1

11

No Marking Scheme Marks

(ii)

Correct shape with rectangles USTN, NKLM and EFLH. All solid lines. Note: Ignore straight line HC H and C joined with dashed line to form rectangle HLMC ST = TM > LM > LF > FE = HK =US The measurement is accurate to 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90 1

K1

K1

K1

N1

12

U S

C N M

L

F E

T

K H

12

No Marking Scheme Marks

16.

(a)

(i)

(ii)

(b)

(c)

(d)

750N C(750N, 300E) 750N or 300E : P1 30 x 60 1800 n.m. 20x60xcos 750 : Award K1 for using cos 630 310.58 n.m. (75x2)x60 9000 310.58 + 9000 9310.58

1058.9310

931.058

P1

P2

K1 N1

K1K1 N1

K1

K1

K1

N1

12

13

Graph for number 12

Graph for number 14

14

Graph for number 14

0

5

10

15

20

25

30

35

40

15.5 20.5 25.5 30.5 35.5 40.5 45.5 10.5