Upload
others
View
10
Download
0
Embed Size (px)
Citation preview
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
PERATURAN PERMARKAHAN ADDITIONAL MATHEMATICS PAPER 1
NO MARKING SCHEME MARKS FULL MARKS
1
(a) –5
(b) 0 ≤ f(x) ≤ 13
1
1
2
2
a) 5,5
3)(1
x
x
xxf or equivalent
5
3
1
35
y
yxory
x
x
b) 1,1
5)(1
x
x
xxgf or equivalent
572
372
x
x
or follow through from (a)
2
B1
2
B1
4
3
qp
3
4
42 – 4p(3 – q) = 0
px2 + 6x + 3 = 2x + q
3
B2
B1
3
4
–57
52)5(134
5
por
p
2
B1
2
5
a) 45
p + 30 = 75
b) 100 cm
2
B1
1
3
6
2.047 [Accept : 2.045 – 2.048]
x(2log106 - log1015) = log106 or equivalent
x log105 or x log103 or x log1015 or (2x – 1) log106
3
B2
B1
3
7
3
2
p
p
2
2
log33
2log2
log2 p2 – log24
3
B2
B1
3
2
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
NO MARKING SCHEME MARKS FULL MARKS
8 a) 6400x2, 1600x
2, 400x
2
b) 6.25x2
6400x2 (0.25)
5
1
2
B1
3
9 a) 146 2 4
S7 = )]12(6)86(2[
2
7
B1
b) 194 2
86 + (10 – 1)(12) B1
10 a) xy
b) 4
1
1
2
11
2
qp
63
qp
1
B1
2
12 –2
102 – 8k = 118 or 102 – 8k = –118
)6)(4(10)3(2[)2()4)(3()10(62
1 kk
or equivalent
3
B2
B1
3
13 a) 3
b) 2
c) 2
1
1
1
3
3
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
NO MARKING SCHEME MARKS FULL MARKS
14 a)
b)
1 3
Sekiranya rajah betul dan terdapat semua anak panah
Sekiranya rajah betul tanpa anak panah
2
B1
15 a) ( )
1 3
b) – 3 , 5
2
√ ( )
B1
16
4 4
( ) ( )
B3
[ ] *
+
B2
∫
∫ ( )
B1
17 28
4 4
64 – 36
B3
*
+
or 36
B2
∫
B1
18 a) 1.855
2 4
or
or
B1
b) 1118.89
2
( ) ( )
( )
B1
4
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
NO MARKING SCHEME MARKS FULL MARKS
19 a) 37.5
1 4
b) 37.17
3
B2
30.5
B1
20 a) and
3 4
or
B2
√
or
√
B1
b) Student B
1
21 3
2 2
B1
22
3 3
(
) (
) (
) (
)
B2
( ) ( ) ( ) ( ) or
(
) or (
) or (
) or (
)
B1
23 a) 720
1 4
b) 192
3
or
B2
or
or
or
B1
5
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
NO MARKING SCHEME MARKS FULL MARKS
24 0, -2
4 4
( ) B3
( ) ( ) B2
or
B1
25 a)
2
4
B1
b)
2
B1
6
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
PERATURAN PEMARKAHAN ADDITIONAL MATHEMATICS PAPER 2
Number Solution and marking scheme Sub Marks Full Marks
1
2
11 2
11 2 2 11 2 15 0
4 4 17 0
174 ,
4
53 ,
2
5 173, 4 ,
2 4
x y
y y y
y y
y y
x x
and
P1
K1
K1
N1
(both values of
y or x)
N1
(both points)
5
2(a)
(b)
42
22 pq
px
44
2
p
q or 32
p
5q 6p
7
4
0344482
k
kkk
N1
K1
N1N1
P1
(shape of
minimum
graph)
P1
(minimum point
and y-intercept)
K1
N1
8
x
y
7
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
3(a)
(b)
xxAQPA
xy
yx
x
3649
364
4
9
Katakan z = PA+AQ
6
0361 2
x
xdx
dz
1254.100
5.088
8
scmdt
dA
dt
dA
jdj
dA
K1
N1
K1
K1
N1
K1
K1
N1
8
4(a)
(b)
Number of questions
Bilangan soalan
Frequency
Kekerapan
1 – 5 2
6 – 10 9
11 – 15 10
16 – 20 8
21 – 25 8
26 – 30 3
( )
or
( )
(
( )
) (
( )
)
11.18
11
P1
(Table)
K1
K1
N1
N1
5
8
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
5(a)
(b)
2
1
2
xy
Number of solutions = 3
P1
(shape of
graph)
P1
(2 period)
P1
(amplitude)
K1
(straight line)
K1
N1
6
6(a)
(b)(i)
(ii)
dhahOE
ODAOhOEAO
1
5
1
5
3
3
12
32
k
h
kh
hk
dkakOE
3:2:
5
3
EADE
ADAE
K1
N1
K1
K1
(solve the
simultaneous
equations)
N1
N1
K1
N1
8
2
-1
1
1
2
9
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
7
(a)
(b) (i)
(ii)
log10 x 0.62 0.86 1.02 1.20 1.32 1.66
log10 y 0.18 0.38 0.52 0.66 0.78 1.04
Refer to graph
log10 y = q log10 x + log10 p
log10 p = y-intercept = - 0.33
p = 0.4677 ± 0.05
q = gradient
q = 0.825 ± 0.1
P1
P1
P1
K1
N1
K1
N1
10
8(a)(i)
(ii)
(b)
2
2 4
3 3
0 28 8x dx or x dx
2 44 4
0 2
8 84 4
x xx or x
4 44 4 22
8 2 0 8 4 8 24 4 4
56
0 016 3
k k
dy or y dy
2
0
0
316
2
k
k yy or
23 1
16 0 0 342 2
kk
232 32 4 3 69
2 3
3
k
k
N1
K1
K1
K1
N1
K1
K1
K1
K1
N1
10
10
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
9 (a)
(b)
(c)
6 5
1 2
1 942
. rad
. rad
2 2 0
2 2 0
5 1 942 9 71
5 44 5
1 2
4 5 4 5 2 4 5 4 5 111 27 7 429
5 45 1 942 2 5
1 2
4 5 4 5 2 4 5 4 5 111 27
18 139
QR . or .
.OT or .
.
TU . . . . cos . or .
.Perimeter .
.
. . . . cos .
Perimeter . cm
2 2 01 15 1 942 4 5 111 27
2 2. or . sin .
2 2 01 15 1 942 4 5 111 27
2 2. . sin .
14.84
K1
K1
N1
K1
K1
K1
N1
K1
K1
N1
10
11
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
10(a)
(b)
(c)
(d)
41
3Nm
3
0 34
y x
3 9
4 4y x
92
2 0 43 0
1 2 1 2
yx
, ,
93 0
3 2
xor y
99
2,
2
2 42
9)09(
9.014
2
2 99 3
2x y
2 24 4 72 36 369 0x y x y
K1
K1
N1
K1
K1
N1
K1
N1
K1
N1
10
12
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
11
(a)( i)
(ii)
(b) (i)
(ii)
2
9 1 10 010 10
9 10
0 7 10 0 7 0 3 10
7
2 1
9 10
0 7 0 3 0 7 0 3
0 1493
63 52
12
0 82043
520 8
12
520 842
12
41 896
. or . .
.
P X P X or
C . . C . .
.
P Z
.
tP Z .
t.
t .
K1
N1
N1
K1
N1
K1
N1
K1
K1
N1
10
13
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full
Marks
12(a)(i)
(ii)
(iii)
(b)
s
(c)
6
2 7 6t t < 0 @ ( 6)( 1)t t < 0
1 < t < 6
2 7dv
a tdt
t > 3.5
3 27
63 2
t tt
1
3 2 3 2 3 2
0
1 7(1) 6 7(6) 1 7(1)6(1) 6(6) 6(1)
3 2 3 2 3 2
23.67
N1
K1
N1
K1
N1
K1 shape
K1 follow
the range
K1
K1
N1
10
14
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
-14
-16
-18
-20
-20 -15 -10 -5 5 10 15 20 25 30 35 40
f x = x2-7x +6
6 1
14
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
13(a) 11.20 100
1.15
or
120100
115
K1
104.35 N1
(b)
65100
48.20y @ 2012 100 125
48.20
P
K1
(i) 134.85y N1
(ii) 2012 60.25P N1
(c) 2 (1 125) (115 3)
2 1 3
x
K1
2 (1 125) (115 3)113.5
2 1 3
x
K1
105.5x N1
(d) 2010
175.40100 113.5
P
K1
2010 154.54P N1 10
14(a)
12.3
sin85 sin 29
PR
K1
25.27PR N1
(b) (b) 66SRP P1
2 2 225.27 3.6 2(25.27)(3.6)cos66PS K1
24.03PS N1
(c)
25.27 24.03
sin sin66RSP
K1
73.88RSP K1
106.12RSP N1
(d) 1(3.6)(25.27)sin66
2
K1
41.55 N1 10
15
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
Number Solution and marking scheme Sub Marks Full Marks
15(a) 5 4 1000y x N1
0.4 0.3 300x y N1
N1
(b)
graph
one line correct
P1
three lines correct P1
shaded region P1
(c)(i) 500 P1
(ii) (340, 540) P1
3.5(340) + 2.4(540) K1
RM 2486 N1 10
16
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
0 0.2 0.4 0.6 0.8 1.0 1.2
0
log10x
- 0.2
0.4
0.2
0.6
0.8
1.0
4
1.2
1.4
6
X
X
X
X
X
1.4 1.6
-0.4
log10 y
Question No. 7 One point plotted correctly with correct scale P1
All 6 points plotted correctly P1
Line of best fit P1
10 20 30 40 50 60 70x
1.8
X
17
SULIT 3472/1 & 3472/2
[Lihat halaman sebelah 3472/1 & 3472/2 © 2016 Hak Cipta MPSM Negeri Sembilan SULIT
100
400
y
200
500
600
700
800
100 200 300 400 500 600 x
Question No. 15
300
900
1000
700 800
R
18
REGULATION OF MARKING END