Johor Addmaths SPM 2010 Trial P2 Marking Scheme
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Transcript of Johor Addmaths SPM 2010 Trial P2 Marking Scheme
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
JABATAN PELAJARAN NEGERI JOHOR PEPERIKSAAN PERCUBAAN SPM 2010
ADDITIONAL MATHEMATICS Kertas 2
Kertas soalan ini mengandungi 17 halaman bercetak
3472/2 Additional Mathematics Kertas 2 September 2010 2 ½ Jam
MARKING SCHEME
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
2
BAHAGIAN A
No Solution Sub marks
Total marks
1
x = 1 + 2y Or y = 2
1x Or y =
14x
Or x = 14
y
Eliminate x or y *(1 + 2y)y + y = 4 Or
x + 1 = )
21(*
4x
)
Or or equivalent 2y2 + 2y – 4 = 0 x2 – 9 = 0 (x – 3)(x + 3) = 0 (2y – 2)(y + 2) = 0 x = 3, - 3 y = - 2 , y = 1 or y = - 2 , y = 1 or x = 3, - 3 Note : OW-1 if the working of solving quadratic equation is not shown.
5
5
Solve the quadratic equation by using the factorization @ quadratic formula @ completing the square
P1
K1
K1
N1
N1
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
3
No Solution Sub marks
Total marks
2 a)
b)
c)
2( x – 2)2 – 7 m = 2 k = - 7. OR equivalent method -2(x – 2 )2 + 7 Or equivalent
3
2
1
6
3
a) i)
ii)
d = 50 Use Tn = a + (n – 1 )d T6 = 500 + 5(50) 750 OR other valid method. Use Tn = a + (n – 1 )d = 1000
150
5001000
11. Or November 2009.
1
2
2
1 x
y
(2, - 7)
Shape : Ụ
Minimum point : (2, -7)
N1
P1
P1
K1
N1
N1
N1
N1
K1
K1
P1
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
4
No Solution Sub marks
Total marks
b) Use Sn =
2n
[2a + (n – 1 )d]
2
12 [2(500) + (11)(50)]
9300 *9300 x 0.08 = RM 744 Note : If listing method is used all terms must be correctly listed, accept for correct answer.
3
8
4 a)
b)
*L = 19.5 or *F = 21 + p or *fm = 10 Use median formula
21.5 = *19.5 + 5)10*
)21(*)2
55((
pp
With *fm and F corresponding to *L 8 = 13 – p p = 5 Draw histogram with scale given. Sekurang-kurangnya 6 bars. Find the mode from his histogram. 17.75 Accept in the range (17.50 – 18.00)
4
3
7
N1
N1
K1
N1
K1
P1
K1
K1
K1
N1
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
5
2
4
6
8
10
12
14
16
18
4.5 9.5 14.5 19.5 24.5 29.5 34.5
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
6
No Solution Sub
marks Total
marks
5 a)
b) i)
ii)
Use identity Cos2x – Sin2x = Cos2x Or 2sinxcosx = sin2x LHS = RHS No mistake allowed
2 Graph Sin
2 period in 0 ≤ x ≤ 2 Amplitude 2 Max = 2 and min = - 2 Drawing of the straight line from the equation involving x and y, either gradient OR y intercept of straight Line must be correct.
y = 1 - 2x
Straight line drawn correctly and Number of solutions = 4 All must be correct
2
3
3
8
K1
N1
0
2
P1
P1
K1
N1
N1
-2
P1
1
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
7
No Solution Sub
marks Total
marks
6 a) i)
ii)
b)
MBC = - 2 Use y – y1 = m(x – x1) Or equivalent method, and substitute x = 7 and y = 2 y - 2 = - 2(x – 7) y = - 2x + 16 Solve simultaneous equation y = ½x + 6 y = - 2x + 16 ½x + 6 = - 2x + 16 x = 4, y = 8 B (4, 8)
Use C (7, 2) = ]4
)8(1)(3,4
)4(1)(3[ yx
24
)8(1)(374
)4(1)(3
yORx
D (8, 0) OW – 1 for correct answer without working.
3
2
3
8
P1
N1
K1
K1
N1
N1
K1
K1
SULIT 3472/2
3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
8
BAHAGIAN B
No Solution Sub
marks Total
marks
7 a)
b)
c)
y = 4 – x2
dxdy
= - 2x
= -2 mPQ = ½
013 k
= ½
k = 25
Integrate (4 - x2 )
Use limit 2*
1in to *[
3)(4
3xx ]
A1 = 35
A2 = find the area of Trapezium
= ½ (25
+ 3)(1) = 4
11
OR Area of shaded region = A1 + A2.
= 1253
⁄⁄ 4.42
Integrate x2
[4y - 2)( 2y
] Use limit 4
3in *[
2)(4
2yy ]
½
3
4
3
10
K1
K1
K1
K1
N1
K1
K1
N1
K1
N1
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9
16.500
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9
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1 2 3 4 5 8 7 6 0
2
4
6
8
10
12
14
16
18
20
xy
x
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4n – 5m = -1
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- 1.281 // - 1.282
P(Z>10160h
) = -1.281 // -1.282
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0.3085
13
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100
y = 45.36
15
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3472/2 Hak Cipta JPNJ 2010 [Lihat sebelah SULIT
<BAD = 35.42°
16
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20 40 60 80 100 120 140 160
20
40
60
80
100
120
140
160
180
200
180 200
x = 120
(60, 140)
R
18