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JABATAN PELAJARAN NEGERI JOHORPEPERIKSAAN PERCUBAAN SPM 2010
ADDITIONAL MATHEMATICSKertas 2
Kertas soalan ini mengandungi 17 halaman bercetak
3472/2AdditionalMathematicsKertas 2September 2010
2 Jam
MARKING SCHEME
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BAHAGIAN A
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1x = 1 + 2y Or y =
2
1xOr y =
1
4
xOr x = 1
4
y
Eliminate x or y*(1 + 2y)y + y = 4Or
x + 1 =
)2
1(*
4
x)
Or
or equivalent
2y2 + 2y 4 = 0x2 9 = 0
(x 3)(x + 3) = 0(2y 2)(y + 2) = 0
x = 3, - 3y = - 2 , y = 1or
y = - 2 , y = 1or
x = 3, - 3
Note :
OW-1 if the working of solving quadratic equation is not shown.
5
5
Solve the quadraticequation by using thefactorization @quadratic formula @completing the square
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2a)
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
3a) i)
ii)
d = 50
Use Tn = a + (n 1 )d
T6 = 500 + 5(50)
750OR 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 :
Minimum point : (2, -7)
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b) Use Sn =2
n[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 forcorrect answer.
3
8
4a)
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.
17.75Accept in the range (17.50 18.00)
4
3 7
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2
4
6
8
0
2
4
6
8
4.5 9.5 14.5 19.5 24.5 29.5 34.5
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5a)
b) i)
ii)
Use identityCos2x Sin2x = Cos2xOr 2sinxcosx = sin2x
LHS = RHSNo mistake allowed
2
Graph Sin2 period in 0 x 2
Amplitude 2
Max = 2 and min = - 2
Drawing of the straight line from the equation involvingx and y, either gradient OR y intercept of straight
Line must be correct.y = 1 -
2
x
Straight line drawn correctly andNumber of solutions = 4
All must be correct
2
3
3
8
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2
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6a) 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 = x + 6y = - 2x + 16
x + 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)(37
4
)4(1)(3
yOR
x
D (8, 0)
OW 1 for correct answer without working.
3
2
38
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BAHAGIAN B
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7a)
b)
c)
y = 4 x2
dx
dy= - 2x
= -2
mPQ =
01
3
k=
k =
2
5
Integrate (4 - x2 )
Use limit 2*
1in to *[
3
)(4
3x
x ]
A1 =3
5
A2 = find the area ofTrapezium
= (25 + 3)(1) =
411
ORArea of shaded region = A1 + A2.
=12
53 4.42
Integrate x2
[4y - 2
)(2y
] Use limit
4
3 in
*[ 2
)(
4
2y
y ]
3
4
3 10
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1 2 3 4 5 8760
2
4
6
8
10
12
14
16
18
20
xy
x
10
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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
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