gP2 or fi-}JF. 83 : R2 =26P oR R2. =26 P. B2 : log2 R2 = lo1z26 +log2 P OR ,R2 rogz T= 81 ,. l=og'P. or 3log2. log24. 4
._
\
€ l.
ADDTTTONAL Kertasl
rvrArr@arr
cs
Septernber
2 jam
MAJLIS PENGETUA SEKOLAH MALAYSIA CAWANGAI\ PULAU PINANG
MODUL LATIHAN BERFOKUS SPM 2OI4 MARKSCHEME
ADDITIONAT MATHEMATIC Paper
I
Two hours
S
347211
2
ADDITIONAL MATHEMATICS PAPER 1 2AI4 Solution and Mark Scheme
Question
I
2
Marhs
Mark
3, g))
g), (2, 4), t(3 ,
(- 2, 4), (-
(b)
.f :x->*2
oR f(x)=i2
(a)
L7
1
(b)
-14
2
(a)
(b)
m2+6m+11
-2 2
J-
(3)2
2
+ pQ)+
18 = 0
x:6 :
4
11
p:-9
81
3
2
S(r):i2 +2
Bl : (b)
2
1
-3
Bl : g(Y): (V -3)'+ 6U- 3) + (a)
1
f-t (x): +
Bl:
4
Total
(a)
81:
3
Sub
(r-3Xr-6)-0
or 3a:18 or
m1-6, m> 6 B2: (- m)2 -
3+o=
2
4
3
3
(-9)
4QXe) >
Bl :x2 -mx+ 9 = Q
6
(a)
x=3
I
(b)
(3,2)
1
(b)
f(x)= (r- 3)'+2
3472n
I
3
34721r
3
7
/l
3
2
3
3
4
4
3
3
rr,s
2
B2:2x -3
Bl:5b"51 or 1
I
83
: R2 =26P oR R2 =26 P
B2
:
log2 R2
= lo1z26 +log2 P OR rogz
81
,
l=og'P. log24
or 3log2
,R2 T=
24
9
B2:
-1 37
+(n-
0
1X6)
: d-6
B1
10
or fi-}JF
gP2
R
53
(a)
4
I
(b)
20
3
4
3
3
B2: (2n + 4t)(n-2q BI
11
;va)*b-1)4I
-2r 55l-+Ll-4,2 -7
B.2:
1-
2 3
B1
34721I
,-23
0
= 820
3472tI
tz
(a)
1 L*'+4 v
(b)
I
2
p:2,q-7(both)
3
4
3
3
4
4
B2:p-2 or q-7 Bt
: 5 =+p+4 or stz--G) +4 1
r =14,t
13
-+
0oth)
5
82: r =14 or
5
: 8 _z(r)+t(a)
Bt
t7
+-
or
, _20)*3(t)
o-
5
t4
5
2100, 3300
83 : 210o or
3300
B2: (2sinr + l)(sin )c +2)=
Bl :
ls
(a)
(1 -2sin2x)-5sin
0
x=3
t6
2
Bl 1 /. PoR:0.45 (b)
344.576 /344.59/344.6
Bl
16
3472tr
4
2
2
, te6)2(z.6sz)
Ji5 /3.6a6 81
2
:
22
+32
3472n
t7
(a)
-5 a *4b
(b)
2
)=z or 4( L)=t' \3+n) \3+n)
Bz: 5 -s( -L
-6 81 : -3(2x+ t-4 Q)
2t
(a)
-4
(b)
16
81
347211
:
or 5
3472n
Br
23
(a)
: p=ry--($Ef
144
Bl:4!
x3!
72
Bl:31 x2! x3!
24
(a)
(b)
0.1
4AI
Bl : 1.08
u72lt
0.
I3l4
3:47212
ADDITIONAL MATFIEh4ATIC
S
Kertas 2 Septernber Al
z- lam 2" .
MAJLIS PENGETUA SEKOLAH MALAYSIA CAWANGAN PULAU PINAIIG
MODUL LATIHAN BERFOKUS SPM 2OI4
MARKSCHEME
ADI}ITIONAL MATHEMATIC S Paper 2
Two hours and thirty minutes
347212
2
sEcTroN A ( 40 MARKS ) Mark Scheme
Ques
1.
y=2x-6 or x-3+
ry E
or
y=x2-15
_t1Ttiil'_t_:'_: *z
_ *(b_6) -
15
or
.f,
.:r)'-y =
15
Solve the Quadr aticEquation
il;il;;
-(e)*Jt-z)z
-4(rX-9)
2(r)
or
OR
l-e-15)=3 2\
-(8)t
(8)2
- 4(1) (-24)
2(r)
Cqmnletine the sgugfe
(x- i2 - (- D2 -g= Q OR
b, + 4)2
-
42
x = 4.16, -2.16 Qr
y:2,32,-
10.32
OR
y :2.32r-
x:
10.32
or 4.16, -2,16
Notg:
OW-l if
347212
steps to solve quadratic equation arcnot showq.
-24=
o
Sub
TotaI
Marhs
Mark
347212
Mark Scheme
Ques
2
(a)
k+(9-lXx):52A
?Po+
Sub
Total
Marks
Mark
(t z-rX')J =474a
Solve simultaneous linear equations
x-
50
or
k: 120 I I
k- 120 or
x(b)
50
* 120 + (n- 1)*(50)
:
n-
4
5
48 + (n
- I)(74) 2
7
Note : Accept complete listing of the terms
3
(a)
9:t-
ytl!?:-.J
Y -(-3) =*2(x-1)
fllyC- -r/2, fllAD-2
or
-3 : * 2(I)+ c
Y: hc-5 (b)
3
Solve simultaneous equations ?x + 4y:20 and *y:2x - 5 2
D(4,3)
(c)
B (t0, o)
use
A
-%lf )-(
)l
;: i-1ro-iib:i;;:i;i +o *r| 22.5
347212
I
3
8
347212
(a)
I
| Use tTtrx ntz: -
1
I
rl I
substitute
l*r:;,mt:-3
gg-e-gY
x-- 1 into 4
?t:19-l(:-3-) ::
n;(
!)3 =_r
(- r)t
(b)
2- !
Integr ate
\ rrt
3
)c
11 y---+-+C 2xn
x
Substitute to find c
I 17 l)=--+-+'2xax2
s
(a)
of
Shape
sine
2cyclesfor0
