Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM...

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Page 1: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 3: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 4: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 5: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 6: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 7: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 8: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 9: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 10: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 11: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 12: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 13: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 14: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 15: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 16: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 17: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 18: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 19: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 20: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 21: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 22: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 23: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 24: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 25: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 26: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 27: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 29: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 30: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 31: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 34: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 35: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 37: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

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Page 39: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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No Marking Scheme Marks 1.

The line x = 3 correctly drawn. The region correctly shaded Note : Award P1 to shaded region, which satisfy any two inequalities. (Check one vertex from any two correct lines)

K1 P2

2.

32

28141229

−==

==+

nm

mnm

K1 K1 N1 N1 4

3.

( )( ) 03120352 2

=+−=−+

xxxx

21

=x 3−=x

K1 K1 N1 N1

4 4.

3154

85.35.3722

21

cm

××××

( )

( )3

16887

3228785.35.3722

21

==××

=×+××××

hh

h

K1 N1 K1 K1 N1

5

(a)

(b)

2

2

x =3

y

x

3y = 2x + 6 2y = -x +2

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Page 40: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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5.

(a) i) 4² < 8 ii) - 6 > - 5 (b) Conclusion : 13 have only two factors. (c) nn 32 + , where n = 1, 2, 3, ……

P1 P1 P1 P1 P1 5

6. (a) 3=RSM

( ) cx += 234 or 324=

−−

xy or equivalent

23 −= xy

(b) 023 =−x or 32

04=

−−

x or ( )

erceptx int23

−−

−=

32

=x

P1 K1 N1 K1 N1 5

7.

2158

2121217222

36045

217222

36045

=

++×××

×××

41110

77217

722

3609021

722

36045 22

=

××−

××−

××

K1 K1 N1 K1 K1 N1 6

8.

( ) ( )

−−

−−−=

4231

32411L

=

−−

4231

21

K1 N1

(b)

(a)

(a)

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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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=

−−

35

1234

kh

−−

=

35

4231

21

kh

12

==

kh

P1 K1 N1 N1

6 9. (a) 30 minutes

1

1

80212

200

= kmh

kmh

1100

2200

−= kmh

120

80100−=

kmh

P1 K1 N1 K1 N1 5

10. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ){ }TYSYYYTXSXXXTS ,,,,8,,5,,,,,,8,,5,,,3,,3,8,3,5,3

(a) ( ) ( ) ( ) ( ) ( ) ( ){ }8,,,,,,8,,5,,8,3 YTXSXXX

( )21

126==aP

(b) ( ) ( ){ }8,3,5,3

( )61

122==aP

P1 P1 P1 P1 P1 5

11. (a) ∠ AHD or ∠ DHA

(b) Sin ∠ AHD = 1712

∠ AHD = 44.90°

P1 K1 N1 3

(b)

(b)

(c)

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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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12. (a)

x -2 3

y -1 -16

(b) Graph (Refer graph on Lampiran 1)

Axes drawn in correct direction, uniform scales in 5.34 ≤≤− x and 531 ≤≤− y .

7 points and ∗2 points correctly plotted or curve passses through these points for 43 ≤≤− x .

Smooth and continuous curve without any straight line and passes through all 9 correct points for 43 ≤≤− x .

Note: 7 or 8 points correctly plotted for 5.34 ≤≤− x , award K1

(c) i) 5.25.1 ≤≤ y

ii) 9.37.3 ≤≤ x (d) Identify equation 6−= xy Straight line 6−= xy correctly drawn Values of x 0.28.1 ≤≤ x

8.20.3 −≤≤− x

K1 K1 K1 K2 N1 P1 P1 K1 K1 N1 N1

12 13.

(a) i) ( 2 , 0 ) ii) ( -1 , 5 ) iii) ( -1 , -1) (b) i) a) W = Rotation 90° anticlockwise at centre ( -0.5 , -1.5 ). b) V = Enlargement about centre ( - 4 , 1 ) with scale factor = 2. ii) x×= 2284 21=x 84 – 21 = 263cm

P1 P1 P2 P3 P3 K1 N1

12

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Page 43: Tutor Mansor Burhan – Mathematics & Additional Mathematics...PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2 PERLIS 14. (a) Marks Frequency Upper boundary Cumulative frequency

PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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14. (a)

Marks Frequency Upper boundary

Cumulative frequency

1 – 10 0 10.5 0 11 – 20 2 20.5 2 21 – 30 3 30.5 5 31 – 40 5 40.5 10 41 – 50 10 50.5 20 51 – 60 11 60.5 31 61 – 70 5 70.5 36 71 – 80 3 80.5 39 81 – 90 1 90.5 40

All frequencies correct All upper boundaries correct All cumulative frequencies correct (b) Mean =

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )40

15.8535.7555.65115.55105.4555.3535.2525.15 +++++++

or 40

1990

= 49.75 (c) Ogive

Axes drawn in correct direction , uniform scales for 5.905.10 ≤≤ x and 400 ≤≤ y

*9 points correctly plotted Note: 7 or 8 points correctly plotted, award K1. Smooth and continous curve without any straight line passes all 9 correct points for 5.905.10 ≤≤ x . Note : If other scales are used, deduct 1 marks from KN marks obtained.

(d) 59.5

P2 P1 P1 K2 N1 P1 K2 N1 N1 12

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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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15. (a)

Correct shape with rectangles EFGH, GHJK and JKLM. All solid lines. FL > LM > HJ = JM > EH Measurements correct to ( )cm2.0± One way and all angles at edges of rectangles = °±° 190

(b)(i)

Correct shape with pentagon AFGKR and rectangle KLBR. All solid lines. AB > FA > AR > LB > KL > FG Measurements correct to ( )cm2.0± One way and all angles at edges of rectangle, ∠ F, ∠ A, ∠ R = °±° 190 (b) ii)

K1 K1 dep K1 N1 dep K1K1 K1 K1 dep K1 N2 dep K1K1

E H J M

F G K L

2 cm 3 cm 3 cm

7 cm

F

L K 6 cm

G

B R A

6 cm

4 cm

3 cm

2 cm

5 cm

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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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Correct shape with rectangles GHML and LMCB. All solid lines. Note : Ignore NP N and P joined with dotted line to form rectangle NPCM BC > CH, CM > NM = LN > GL Measurements correct to cm2.0± ( one way) and all angles at the vertices of rectangles = °±° 190

K1 K1 dep K1 K1 dep K1K1 N2 dep K1K1K1 12

2 cm

4 cm

3.5 cm 3.5 cm

G H

L M N

B P C

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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2

PERLIS

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16.

( )W

W°=

°−105

75180

ii) ( )606363180 −− = 3240 nautical mile.

°= 4860

2880

V = ( )N°−° 4863 = N°15 (c) i) 63cos6055 ×× = 1498.17 nautical mile.

660

288017.1498 +

= 6.634 hours.

P2 K1 N1 K1 K1 N1 K1 N1 K2 N1 12

(a) i)

(b)

ii)

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