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Matematik Tambahan Kertas 2 Ogos 2012 2 ½ jam
BAHAGIAN PENGURUSANSEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN
KEMENTERIAN PELAJARAN MALAYSIA
PENTAKSIRAN DIAGNOSTIK AKADEMIK SBP 2012PERCUBAAN SIJIL PELAJARAN MALAYSIA
ADDITIONAL MATHEMATICS
Paper 2
Skema Pemarkahan ini mengandungi 10 halaman bercetak
MARKING SCHEME
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2
No Solution and Mark SchemeSub
MarksTotal Marks
1 8 32
yx OR P1
2 8 33 6 02
yy y OR28 2 8 23 6 0
3 3x xx K1
Replace a, b & c into formula K1
2( 24) ( 24) 4(7)( 12)2(7)
y OR2( 20) ( 20) 4(7)( 59)
2(7)x
OR N1OR N1
5 5
2 (a)
kxykxxy31)1(
322
2
1431
kk
(b)
3
3
6
(1,4)
3
3 -1
-Maximum shape P1-*Maximum point K1-Another 1 point y-intercept / x-intercept K1
K1K1N1
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3
3(a) OR 12
rP1
116 12
30.5112
n
K1
K1
N1
4 7
(b)OR 1
4r P1
64114
S
K1
= 1853
or 85.33 N1
3
4(a)(i) Change or 1
3BCm
OR 3ABm K1
5 3 ( 6)y x OR any correct method K1
N1
5 7
(ii) Use simultaneous equation to find point B
and K1
B = 15 1,2 2
N1
(b)K1
D = 39 25,4 4
N1
2
Use rraS
nn 1
)1(
Use 1
aSr
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4
5(a)
(b)
Amplitude = 3 [ Maximum = 3 and Minimum = 3 ] P1Sine shape correct P1Two full cycle in 0 x 2 P1Negative sine shape correct(reflect) P1
4 7
or N1
Draw the straight line K1
Number of solutions is 3 N1
3
6(a) L = 79.5 OR F = 24 OR fm = 4 P13 (36) 24479.5 10
4K1
N1
3 8
(b) (i)(44.5 4) (54.5 5) (64.5 6) (74.5 9) (84.5 4) (94.5 8)
36X
260236
= 72.28
5
y
3
3
2 x
K1
N1
OR
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5
(ii)2 2 2 2 2 2(44.5) 4 (54.5) 5 (64.5) 6 (74.5) 9 (84.5) 4 (94.5) 8
K1
2197689 (*72.28)36 K1
N1
7 Rujuk Lampiran
8(a)
(b)
2
2
25
21
5
1 1
2 2
2 21
2( 2) 2( 5)2( 2) 2( 5)1 1
dxx
x x
3
3
10
(c )2
22
5
23 1
5
22 3 13 1
5 5
2( ) Volume ( 2)
4 8 43 1
4 5 8 54( 2) 8( 2) 4 2 4 53 1 3 1
14.56
i dxx
x x x
4
K1
N1
K1
K1
N1
K1
K1
K1
N1
K1
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6
9(a)
(b)
(c)
yx
yxxOD
yxAC
415
47
)57(437
57
3 7 157 5 54 4 421 74 4
3
15 1554 4
3
x y h y k x y
k
k
h k
h
5
452150
t
t
3
5
2
10
10(a) (i) 6 410 6= 0.03676
(ii)
9 1 10 010 109 10
= 0.0001437
5
5
10
N1
K1
N1
K1N1
K1
N1
K1
N1
K1
K1
N1
K1
N1
K1
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7
(b)5.34548
5.345404840 )( ZPXPi
= 0.7278
( ) 0.745 0.524
3.543.166
ii P X mm
m
11(a)
(b)
(c)
7tan 1
0.78554
OR RQ PR cm
rad rad
2 2
7(1.571) 7(2.3565)
7 7 2(7)(7)(cos135 )oOR
2 27 7 7(1.571) 7(2.3565) ( 7 7 2(7)(7)(cos135 )
54.4268
o
Perimeter
21 74
2 21 17 2.3565 7 sin1352 2
o
2 2 21 1 17 7 2.3565 7 sin1354 2 2
78.8996
oArea
2
4
4
10
K1
N1
N1
K1
K1
K1
N1
K1K1
K1
N1
K1
K1
K1
N1
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8
No Solution and Mark SchemeSub
MarksTotal Marks
12(a)a = 10 - 5t = 0
t = 2 s2
2
c = 302
2
= 40 ms- 1
4 10
(b)2 0
2 6 0t t
0 6t
3
(c)
32
s = 0, t = 0 , c = 0
ttts 30655 32
32 or 32
= 180 = 133.33
Total distance = 180 + 33.133180= 226.67 m
OR
3
Use v > 0
Integrate and substitute t = 2
Use a = 0
Integrate a to find v
K1
K1
N1
K1
N1
K1
K1
Integrate v dt K1
K1
N1
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9
67.226
67.46180
30251030
2510
8
6
26
0
2 dtttdttt
13(a)12510055
10P
P10 = RM 44
2 10
(b)
* h = 1
2
(c)115100
2011P
P07 = RM 23
2
(d)
I S =
= 122.86
4
Integrate v
+
K1
K1
N1
N1
K1
N1
K1
K1
N1
See 125 P1K1
K1
N1
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10
14 Rujuk Lampiran
15(a) Using sine rule to find BAC .sin sin 30
27 14
oBAC
74.64oBAC (obtuse) 180 74.64
105.36
o o
o
BAC
3 10
(b) 105.36 30 or 6o oDCB DC cm
Use cosine rule to find BD.
22 26 27 2 6 27 cos135.3631.55
BDBD
3
(c) Use formula correctly to find area of triangle ABC or ACD.180 30 105.36
44.64
o o o
o
ABC
22 227 14 2 27 14 cos 44.6419.67
ACAC
o or
o
Use Area ABCD = sum of two areas
Area ABCD = 189.7 cm2 .
4
END OF MARKING SCHEME
N1
N1
K1
P1
K1
N1
K1
K1
K1
N1
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Pentaksiran Diagnostik Akademik SBP 2012 Paper 2 ADM
0.1 0.3 0.4 0.6
10
20
30
40
50
60
70
80
x
x
0.5
No.7(a)
0.70
x
0.2
x
x
Plot against K1
(at least one point)
6 points plotted correctly K1
Line of best fit N1
0.1 0.2 0.25 0.4 0.5 0.8
y 62 54 50 38 29 4
1 2ny mm x
N1
P1
N1
. 80miin K1
N1
1. 0.37iiix K1
N1
0.8
x
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Answer for question 14
(a) I.
II.
III.
(b) Refer to the graph,
1 graph correct3 graphs correct
Correct area
(c) max point ( 50,120 )
i) k = 100x + 80yMax fees = 100(50) + 80(120)
= RM 14, 600
ii)
10 20 30 40 50 60 700 80
20
40
140
120
100
160
180
80
60
(50,120)
10
N1
N1
N1
N1
N1
N1
K1
N1
K1
N1
y
x