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1/23
\
_
l
ADDTTTONAL
rvrArr@arr
c s
Kertasl
Septernber
2
jam
MAJLIS
PENGETUA SEKOLAH
MALAYSIA
CAWANGAI\
PULAU
PINANG
MODUL
LATIHAN BERFOKUS
SPM 2OI4
MARKSCHEME
ADDITIONAT
MATHEMATIC S
Paper
I
Two
hours
M or e SPM P a p er s a t :
h t t p :/ / spm soa l a n .w o r d p r ess.c om /
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2/23
2
ADDITIONAL MATHEMATICS PAPER
1
2AI4
347211
Question
Solution and
Mark
Scheme
Sub
Marhs
Total
Mark
I
(a)
(b)
t(3
,
g),
(2,
4),
(-
2, 4),
(-
3,
g))
.f
:x->*2 oR
f(x)=i2
1
1
2
2
(a)
(b)
L7
-14
81:
f-t
(x):
+
1
2
3
3
(a)
(b)
-3
Bl:
m2+6m+11
-2
S(r):i2
+2
Bl
:
g(Y):
(V
-3) +
6U- 3)
+
11
2
2
4
4
(a)
(b)
p:-9
Bl
:
(3)2
+
pQ)+
18
=
0
x:6
81 :
(r-3Xr-6)-0
or 3a:18 or
3+o=
(-9)
2
2
4
-
J
m1-6,
m>
6
B2:
(-
m)2
-
4QXe)
>
Bl
:x2
-mx+
9
=
Q
3
3
6
(a)
(b)
(b)
x=3
(3,2)
f(x)=
(r-
3) +2
I
1
I
3
3472n
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3
34721r
7
3
2
/l
rr,s
2
B2:2x
-3
Bl:5b 51
or 53
3
3
I
R
1
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
4
9
24
B2:
-1
37
+(n-
1X6)
0
B1 :
d-6
3 3
10
(a)
(b)
4
20
B2:
(2n
+
4t)(n-2q
-
0
BI
;va)*b-1)4I
=
820
I
3
4
11
-2r
l-+Ll-4,2
55
B.2:
-7
1-
2
3
B1 ,-2
3
3
3
34721I
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3472tI
tz
(a)
(b)
1
v
L* +4
2
p:2,q-7(both)
B2:p-2 or
q-7
Bt
: 5
=+p+4
1
or
s
--G)
+4
z
I
3
4
13
r
=14,t
-+
0oth)
5
82:
r
=14
or
t7
+-
5
ort
:
8
_z(r)+t(a)
5
, _20)*3(t)
o-
5
3
3
t4 2100, 3300
83
:
210o
or
3300
B2:
(2sinr
+
l)(sin
)c
+2)=
0
Bl
:
(1
-2sin2x)-5sin
x=3
4
4
ls
(a)
(b)
t6
Bl 1
/.
PoR:0.45
344.576 /344.59/344.6
Bl
,
te6)2(z.6sz)
2
2
4
16
Ji5
/3.6a6
22 +321
:
2
2
3472tr
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3472n
t7
(a)
(b)
-5
a
*4b
2
Bz:
5
-s(
-L
)=z
or
4(L)=t or
\3+n)
\3+n)
5
-6
81
:
-3(2x+
t-4
Q)
2t
(a)
(b)
-4
16
81
:
347211
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3472n
Br
:
p=ry--($Ef
23
(a)
144
Bl:4
x3
72
Bl:31
x2 x3
24
(a)
(b)
0.1 4AI
Bl
:
0.
I3l4
1.08
u72lt
M or e SPM P a p er s a t :
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7/23
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
M or e SPM P a p er s a t :
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2
sEcTroN
A
(
40
MARKS
)
347212
Ques
Mark Scheme
Sub
Marhs
TotaI
Mark
1.
y=2x-6
or
y=x2-15
or
x-3+
ry
E
_t1Ttiil _t_: _:
*z
_
*(b_6)
or
.f,
.:r) -y
or
-
15
Solve the Quadr
aticEquation
il;il;;
=
15
-(e)*Jt-z)z -4(rX-9)
2(r)
OR
l-e-15)=3
2\
-(8)t
2(r)
Cqmnletine
the
sgugfe
(x-
i2
-
(-
D2 -g=
Q
OR
b,
+ 4)2
-
42
-24=
o
x
=
4.16,
-2.16
Qr
y:2,32,-
10.32
OR
y
:2.32r-
10.32
or
x: 4.16,
-2,16
Notg:
OW-l
if
steps to solve
quadratic
equation
arcnot showq.
(8)2
-
4(1)
(-24)
347212
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Ques
Mark Scheme
Sub
Marks
Total
Mark
2
(a)
(b)
k+(9-lXx):52A
?Po+
(t
z-rX')J
=474a
Solve
simultaneous
linear
equations
x-
50
or
k:
120
k-
120
or
x- 50
*
120
+
(n-
1)*(50)
:
48
+
(n
-
I)(74)
n-
4
Note :
Accept complete
listing of
the
terms
I
I
5
2
7
3
(a)
(b)
(c)
9:t-
ytl ?:-.J
fllyC-
-r/2,
fllAD-2
Y
-(-3)
=*2(x-1)
or
-3
:
*
2(I)+
c
Y:
hc-5
Solve simultaneous equations
?x
+
4y:20
and
*y:2x
-
5
D(4,3)
B
(t0,
o)
use
A
-%lf
)-(
)l
;:
i-1ro-iib:i;;:i;i +o
*r|
22.5
3
2
3
I
8
347212
347212
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10/23
347212
I
(a)
|
Use
tTtrx ntz:
-
1
I
I
rl
l*r:;,mt:-3
substitute
x--
1
into
4
gg-e-gY
?t:19-l(:-3-)
::
n;(
)3
=_r
(-
r)t
(b)
Integr
ate
2-
\
rrt
)c
11y---+-+C
2xn
x
Substitute
(-
I
,2)
into
ty
to
find
c
I 17
l)=--+-+-
'2xax2
3
3
6
s
(a)
(b)
Shape
of
sine
2cyclesfor0
7/24/2019 [spmsoalan]Skema Addmath K1,2 P.Pinang 2014.pdf
11/23
It
347212
Ques
Mark
Scheme
Sub
Marks
TotaI
Mark
(a)
|
Height
of
the bars
proportional
I
to
the frequencies
I
I ruUel the class bound
afies or
I
midpoints
of
the
classe s
or
I the
class
interval
E
E
Method to
find
mode
26
(b)1
@
F:
14
@
*14
f*
l
-9
E
Iu
0)
;
g
22.83
4
347212
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12/23
347
347
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13/23
7
sEcrroNB(40MARKS)
347212
Ques
Mark Scheme
Sub
Marks
Full
Mark
x-I 1
2
3
4
5
6
logroy
0.44
0.63 0.82
1.03
1.20
L.40
(a)
EE
(b)
&
(c)
Plot
logt
/
against
(
x
-
1)
6
*points
plotted
correctly
Line
of best
fit
log;,oy=
logr
ok
+
(
r
-
1) logrch
E
Use
*c
log1s
fr
;Use
*m:
logoh
h
-
1.56
lg-
1.74
10
Note
: SS-1 if
part
of
the
scale'is
not
uniform
or
not using
the
scales
given
or
not
using
the
graph paper
347212
M or e SPM P a p er s a t :
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347
logro
347
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15/23
347212
Ques
Mark
Scheme
Sub
Marks
Full
Mark
(a)
(i)
&(ii)
Use
Triangle
Law for
0R
or
OS
fr:4q-6v
OS
-
4u
+3v
(b)
9l:
_qetsl_11ry:_ _ ${
_9_T
Or
-9u-4v
-3-
se
QT
=
lQR
I
(c)
|
(i) &(ii)
I
tubstitute
u
=3iand
t-
I
Y
-
-21+
liinto 'r
ffi
OS
=
6r_+ lSi
4
6t+Lsj
?_a-
-
-
llao
4 10
3472n
M or e SPM P a p er s a t :
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16/23
t0
347212
Mark Scheme
Solve
simultaneous
equations
y:(x-3)2andy--x*9.
A(0,9)
Integrate
(x
-
3) wrt x
B(5,4)
Ar:t-
6xz
,+
9x
32
(*
-3)3
t\/
3
,f5
Uselimit
t
in Ar
OR
Find the arcaof
tapezium
Az At
Az=
l-.
*(e
+
4)x
*(5)
2\
l+- {:
r
r25
/Do1/lzo.B3
Integrate n(x
-
3)o
wrt
x
v:rry
Use
3
Iin
0
o(ry-sf
5
243
n ll48:- n
// 48.6n
M or e SPM P a p er s a t :
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17/23
11 341212
Mark Scheme
Use
^r
-
r0
to
find arc
DC
or
EC
AC:
AC*arcDC+2
19.45
/l
Use
/
=
Y, fg
to
find
area
of
sector CBE
15.5
Use A- Yrfe
b
find
area
of sector DBE
A,:
*Of(;-Lz4)
Use
I
*
bxh OR
lo|sin
Cto
22
find
Ar:LABC
or A3: A
ABE
or
A+: L
EBC
Az=
17.5 ,
At
-
5
.687
;
A+: Il,82
/-
*15.5
+As-At-A+
OR
Arc
DC-s
(Z\
\2)
or
arc EC
-
5(1.2
+72
5.22 ll 5.23
A- A2-Ar-A+*
(*t5.5
-A+)
347212
M or e SPM P a p er s a t :
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18/23
t2
347212
Mark
Scheme
(i)
8p:2
D-
1
ll
o.z5
4
(ii)
Use
*
(0.25), (0.75)n-r
Write
P(X>Z):
P(X
-
3)
+
P(X
-
4)
+..
.+ P(X:
8)
OR
1 P(X:
0)
-
P(X
-
1)
-
P(X=
2)
(i)
z-
2.5
-1.6
0.8
0.13029 ll
0,1303
fn
-1.6
.
r
- -
=1.175
0.8
0.3015
m=2,54
347212
M or e SPM P a p er s a t :
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19/23
13
SECTTON
C
(20
MARKS)
347212
Mark
Scheme
Integr
ate
Izt
-
8
dt
v-
f 8t
+
c
Substitute
t:
0
and
v- 12 in
*
y
to
find c
c: 12
Use
a
-0tofindr
t
-4
Solvev.0tofindr
(t-2)(t-6)-0
t:2,
6
t'
-8r+12
dt
s
=
t-
-
4t2
+r2t
3
Substitute
t
=
*2
or
t
-
4 into
*s
OR
use
I:
or
I:
in
*s
Find
total
distance
travelled
fi"at
arll:"dtl
t6
347212
M or e SPM P a p er s a t :
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20/23
L4
347212
Mark
Scheme
use
Qt
x
loo
Qo
)c
-
125
y=
I=
*
I2s 27)
+
l2s 34)
+
137
.5 10)
+
1s0 10)
27 +34+10+10+19
127.8
use
Qn
x
loo
26A0
=
*127
.8
RM 3322.8
118
x
*1
27
.B
100
t2o 1e)
150.8
347212
M or e SPM P a p er s a t :
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21/23
t.
l5
3472/2
Ques
Mark Scheme
Sub
Marks
FUII
Mark
1,4
(a)
(i)
Yr-'-:
:rlt
19
lt
4
9-
ly
- $-
B c
BC
2
=
82 +lz2
-
2(8)
(lz)
cos
25'
BC:
5.83
(ii)
y::
:ir
:l:11
y:?
::.1i
: :
::o
sin
C
sin
25
=-
12 5.83
60.450
(b)
I
G)
I
19.550
(ii)
ADB
=
60,45o
(iii)
Z
DAfi:59.
1o
use
|olez)sin
(*5e.1
+
25)
47
"75
10
347212
M or e SPM P a p er s a t :
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22/23
t6
347212
Mark Scheme
x
+
y
S
8 or
equivalent
x
600x
+
2A0y