tutor mansor burhan – mathematics & additional mathematics...peperiksaan percubaan bersama spm...
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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2
PERLIS
www.cikgurohaiza.com
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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PEPERIKSAAN PERCUBAAN BERSAMA SPM 2009 MATHEMATICS 1449/2
PERLIS
www.cikgurohaiza.com
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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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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