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SPM TRIAL EXAM 2012 Marking Scheme
Additional mathematics Paper I
Number Solution and marking scheme Sub Marks Full
Marks 1
(a) {p, r, s} (b) {a , b, c, d} (c) Many to One
1 1 1
3
2
(a) 27
B1: 2x – 5 = 2 atau f(x) = 25+x
2
2
3
(a) 5 (b) 42 +x
B2: ( ) 7653 −−=+− xxf B1 : ( ) 53 +− xf
1 3
4
4
p = − 7 , q = − 10 ( both ) B2: p = − 7 or q = −10
B1: 33
7 p−= or
3310 q
=− or 01073 2 =−− xx
or 3(−1)2 + p(1)+q = 0, 3(10/3)2 + p(10/3) + q = 0
3
3
5
h =2 and k = 3 B2 : h = 2 atau k = 3
B1 : 13=
h or 922 =++ kh
3
3
6
45 ≤≤− x B2: ( ) 0)5(4 ≤+− xx or B1 : x2 + x – 20 ≤ 0
3
3
4 -5
-
2
7
pr12
+ or prrp +2
B3: mm 33
2
2
log3log
2log
2log+
B2: log m2 + 2logm3or mm 3
23
2
2
log3log
log2log+
B1 : log 2 + log32 or 2logm3 or mlog2log
ormlog3log
4
4
8 158 += px B2: )32(43 +=− px B1: 32 or )32(42 +p
3 3
9 a) 3
b) 360
B1: [ ]18 2(3) (18 1)22
+ −
1 2
3
10 13−=a , 4=d (both) B2: 13−=a or 4=d B1: 52 −=+ da or 157 =+ da
3 3
11 (a) r = x2
(b) 31
B1: 2
2
181
xx−
=
1 2
3
12 a) qpx
xy
+= 2
b) 2−=p , 8=q B2 : 2−=p or 8=q
B1: 4204
−
−=p or q+−= )4)(2(0 or 4 = p(2) + q
1 3
4
-
3
13
2,12
B2: 110)1(3
473
−=⎟⎠
⎞⎜⎝
⎛−
−−×⎟⎠
⎞⎜⎝
⎛−
−
hh or form equation using Pythagoras theorem
B1: 473
−
−
h or
10)1(3
−
−−
h of find the lengths of AB, BC and AC using distance formula
3
3
14 (a) w
1
(b) −2w 1−w2 B1: 21 w− or θcos2w
1 2
3
15
26.57 ° ,116.57 ° , 206.57 ° , 296.57 ° B3: 26.57 ° and 116.57 ° B2: )2)(tan1tan2( +− xx B1: 02tan3tan2 2 =−+ xx
4
4
16
(a) 13 (b) k = −13
B1: ⎟⎟⎠
⎞⎜⎜⎝
⎛
+−
++
25112 k
or jik )25()112( +−+++
1 2
3
17 (a) 4a + 4b (b) ba 42 +−
B1: )44(6 baa ++−
1 2
3
18 8 B2: 9.42)3()3()3(3.13.1 =−+−+−+++ rrrrrr B1: r3.1 or )3(3.1 −r
3 3
19 512
B2: ⎟⎠
⎞⎜⎝
⎛ −+
012)2(32 2
B1:2
02 132 ⎥⎦
⎤⎢⎣
⎡+xx
3 3
-
4
20
122 −+ aa
B2: [ ]))4()4(()( 22 −+−−+ aa B1: [ ]xx +2
3
3
21 k= 8 B3: (k+1)(k−8) = 0
B2: 22 2 22 5 2 5 6
3 3k k+ + + +⎛ ⎞− =⎜ ⎟
⎝ ⎠
B1: 352 kx ++= or 2222 52 kx ++=∑
4 4
22 1 2( , )3 3−
B2 : x = 13
, y = 2(⅓)(3×⅓−2)
B1 : 12x – 4 = 0
3 3
23 (a) 1 (b) i) 5040
ii) 288 B1: 2 × 3! × 4!
1 1 2
4
24 (a)
154
(b) 35
B1 : 3 2 2 1 3 1 2 21 or 5 3 5 3 5 3 5 3⎛ ⎞⎛ ⎞− × + × + ×⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
1 2
3
25 (a)
53
(b) 625144
B1: 32
25
52
53
⎟⎠
⎞⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛C
1 2
3
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