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MATEMATIK TAMBAHAN SKEMA PERCUBAAN SBP KERTAS 2 SBP
Citation preview
1
3472/2
Matematik
Tambahan
Kertas 2
Ogos 2014
2 jam
BAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN
KEMENTERIAN PELAJARAN MALAYSIA
PENTAKSIRAN DIAGNOSTIK AKADEMIK SBP 2014
PERCUBAAN SIJIL PELAJARAN MALAYSIA
ADDITIONAL MATHEMATICS
Paper 2
Skema Pemarkahan ini mengandungi 10 halaman bercetak
MARKING SCHEME
2
No Solution and Mark Scheme Sub
Marks
Total
Marks
1
2
2
6 2
3
6 2 6 25 4 5
3 3
10 7 24 0
( 7) ( 7) 4(10)( 24)
2(10)
1.94, 1.24
0.71, 2.83
yx
y yy y
y y
y
y
x
5
5
2(a)
(b)
(c)
2( ) 2( 1) 2 K1
2 7 6 K1
6 5 N1
h x x m
m k
m k
12
2k m N1, N1
22 (4 ) 8 0x n x K1
2
4 4( 2)( 8) 0n K1
4, 12n N1
3
2
3
8
2
2
6 3 P1
2
6 3 6 35 4 5 K1
2 2
15 53 30 0
( 53) ( 53) 4(15)(30)K1
2(15)
xy
x xx x
x x
x
0.71, 2.83 N1
1.94, 1.24 // 1.25 N1
x
y
OR
3
3(a)
(b)
2 , 2 ( 1), 2 ( 2),......r r r K1
7
2(2 ) 6(2 ) 2162
r K1
15r
length of ribbon 30 N1
30 ,32 ,34 ,...... K1
2d K1
48 30 ( 1)(2 )n
9n N1
3
3
6
4 (a)
(b)
(c)
1m K1
8y x N1
4 5 26
7
x or
4 5 22
7
y K1
11, 3P
N1
8AB K1
2 2
4 4 8x y K1
2 2 8 8 24 0x y x y N1
2
2
3
7
4
5(a)
(b)
y = 2 - x
y = 3 cos 3
2x
2
- 3
0
2
3
x
y
Shape of Cosine 0 2x P1
Period 1.5 cycle P1
Amplitude 3 P1
2x
y
K1
Draw line 2x
y
K1
Number of solutions = 3 N1
3
3
6
6(a)
(b)
15.5 2 25.5 5 35.5 12 45.5 6 55.5 7 K1
32
38.94 N1
Mean
2 2 2 2 2
215.5 2 25.5 5 35.5 12 45.5 6 55.5 7 (38.94) K1K132
134.86 N1
Varian
2
3
8
5
(c)
3
332 19
440.5 10 K1K16
41.33 N1
Q
3
7
LAMPIRAN
8 (a)
(b)
(c)
4 K1dy
xdx
1
4Nm K1
1
5 14
y x
1 21
4 4y x N1
1
2
0
1Area= (4 5)(1) 2 3
2x dx K1
13
0
9 23
2 3
xx
K1
9 23 0
2 3
K1
5
6 N1
5
3
52
3
2 2
3Volume ( )
2
3 K1
4 2
5 3(5) 3 3(3) K1
4 2 4 2
ydy
y y
7 N1
3
4
3
10
6
9(a)
(b)
(c)
BQ BA AQ
Or AC AD DC
K1
(i) 3 6BQ x y
N1
(ii) 3
52
AC y x
N1
35
2AP my mx
K1
3 3 6AP n x ny
K1
Compare and solve
33 3
2m n and 5 6m n K1
3
4m N1
5
8n N1
3
8PD BQ QD
or 1 1
4 2PD AC BQ
K1
9 17
8 4PD x y
N1
3
5
2
10
10(a)
(i)
(ii)
2
10(0.75)
7.5 N1
10(0.75)(0.25)
1.875 N1
10 9 1 10 10 0
9 10
( 9) ( 9) ( 10)
(0.75) (0.25) (0.75) (0.25) K1 K1
0.2440 N1
P X P X P X
C C
2
3
10
7
(b)(i)
(ii)
1.3 1.5 2.5 1.5(1.3 2.5) K1
0.8 0.8
( 0.25 1.25) K1
0.4931 N1
P x P z
P z
Total = 160
0.4931 K1
324 N1
3
2
11(a)
(b)
(c)
1 5sin8
AOB
K1
0.6752AOB rad N1
2 28 5 4FC K1
4 1.571CD K1
Perimeter 2 28 5 4 4 1.571 5 4 8 K1
= 25.53 cm N1
1
5 6.2452
BFO K1
41
4 0.67522
Or 41
4 1.571 0.67522
K1
Area 2 21 1 1
5 6.245 4 0.6752 4 1.571 0.67522 2 2
K1
= 17.38 cm2
N1
2
4
4
10
8
12(a)
(b)
(c)
5 2 0 K1
5
2
t
t
25 14 K1v t t
2
max
5 55 14
2 2
20.25 N1
v
2
2
5 14 0 K1
5 14 0
( 2)( 7) 0 K1
7 N1
t t
t t
t t
t
2 3514 K1
2 3
t ts t
2 3 2 3
7 9
5(7) (7) 5(9) (9)14(7) 14(9) K1
2 3 2 3s or s
1 1 1Total distance 106 106 85 K1
6 6 2
1=127 N1
3
3
3
4
10
9
13(a)
2 2 26.5 3.5 2(6.5)(3.5)cos70EC K1
6.24 cm N1
2 10
(b)
sin sin 70
3.5 6.24
BAC K1
Use 31.81ACD BAC K1
180 62.74ADC K1
117.26 N1
4
(c)(i)
D' D C
A
'AD C must acute angle N1
1
(ii) ' 180 2 62.74D AD K1
1
' 3.7 3.7 sin54.522
ADD K1
5.57 cm2 N1
3
14
LAMPIRAN
10
END OF MARKING SCHEME
15(a)
10
10
12100 125 K1
RM 9.60 N1
Q
Q
2
10
(b)
Use 120 P1
120110 K1
100
132 N1
3
(c)
12
12
100 121 K190
RM108.90 N1
Q
Q
2
(d) 110(8) 136(5) 120 125(4)121 K1
8 5 4
2060 120121 K1
17
3 N1
m
m
m
m
m
3