trial penang 2014 spm matematik tambahan k1 k2 skema [scan]
DESCRIPTION
Bahan Pecutan Akhir Add Math SPMTRANSCRIPT
\._€
l.
ADDTTTONAL rvrArr@arr c sKertaslSepternber2 jam
MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAI\ PULAU PINANG
MODUL LATIHAN BERFOKUS SPM 2OI4
MARKSCHEME
ADDITIONAT MATHEMATIC S
Paper I
Two hours
2
ADDITIONAL MATHEMATICS PAPER 1 2AI4
347211
Question Solution and Mark SchemeSub
MarhsTotalMark
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
3 34721r
7 3
2/l rr,s
2
B2:2x -3
Bl:5b"51 or 53
3 3
IR
1gP2 or fi-}JF
83 : R2 =26P oR R2 =26
P
B2 : log2 R2 = lo1z26 +log2 P OR,R2rogz T=
81 , l=og'P. or 3log2log24
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-4,255
B.2: -71- 2
3
B1 ,-23
3 3
34721I
3472tI
tz (a)
(b)
1v
L*'+42
p:2,q-7(both)
B2:p-2 or q-7
Bt : 5 =+p+41or s --G) +4tz
I
3 4
13 r =14,t -+ 0oth)5
82: r =14 ort7+-
5
orBt : 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 +3281 :
2 2
3472tr
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
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
3:47212
ADDITIONAL MATFIEh4ATIC S
Kertas 2SepternberAl .z- lam2"
MAJLIS PENGETUA SEKOLAH MALAYSIACAWANGAN PULAU PINAIIG
MODUL LATIHAN BERFOKUS SPM 2OI4
MARKSCHEME
ADI}ITIONAL MATHEMATIC S
Paper 2
Two hours and thirty minutes
2
sEcTroN A ( 40 MARKS )
347212
Ques Mark SchemeSub
MarhsTotaIMark
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)=32\-(8)t
2(r)
Cqmnletine the sgugfe
(x- i2 - (- D2 -g= Q
OR
b, + 4)2 - 42 -24= o
x = 4.16, -2.16Qr
y:2,32,- 10.32
OR
y :2.32r- 10.32or
x: 4.16, -2,16
Notg:
OW-l if steps to solve quadratic equation arcnot showq.
(8)2 - 4(1) (-24)
347212
Ques Mark SchemeSub
MarksTotalMark
2 (a)
(b)
k+(9-lXx):52A?Po+
(t z-rX')J =474a
Solve simultaneouslinear equations
x- 50
ork: 120
k- 120or
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!?:-.JfllyC- -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
347212
I
(a) | Use tTtrx ntz: - 1
I
Irll*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---+-+C2xn x
Substitute (- I ,2) into tyto find c
I 17l)=--+-+-'2xax2
3
3 6
s (a)
(b)
Shape of sine
2cyclesfor0<x32n
Arnplitude - 3
Modulus
EE]EIE)Accept
cosine
graph
v
3
2
I
.r 3xy-5--1T
Sketch the straight line
Number of solutions =
4
3 7
347212
It
347212
Ques Mark SchemeSub
MarksTotaIMark
(a) | Height of the bars proportional
I to the frequenciesI
I ruUel the class bound afies or
I midpoints of the classe s orI the class interval
EE
Method to find mode
26
(b)1" @ F: 14 @
*14
"f*
l
-9 EIu0)
; g
22.83
4
347212
347212
347212
7
sEcrroNB(40MARKS)
347212
Ques Mark SchemeSub
MarksFull
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 EUse *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 usingthe scales given or not using the graph paper
347212
347212
logro
347212
347212
Ques Mark SchemeSub
MarksFull
Mark
(a) (i) &(ii) Use Triangle Law for 0R or OS
fr:4q-6v
OS - 4u +3v
(b) 9l: _qetsl_11ry:_"_ ${ _9_T _
Or -9u-4v-3-
se QT = lQR
I
(c) | (i) &(ii)
I tubstitute u =3iandt-I Y - -21+ liinto 'r ffi
OS = 6r_+ lSi
4 6t+Lsj?_a- - -
"llao 4 10
3472n
t0 347212
Mark Scheme
Solve simultaneous equationsy:(x-3)2andy--x*9.
A(0,9)
Integrate (x - 3)'wrt x
B(5,4)
Ar:t- 6xz ,+ 9x32(* -3)3At\/'
3
,f5
Uselimit t
in Ar
OR
Find the arcaof tapezium Az At
Az= l-. *(e + 4)x *(5)2\
l+-'{:or
r25 /Do1/lzo.B3
Integrate n(x - 3)o wrt x
v:rry
Use3
Iin0
o(ry-sf5
243 n ll48:- n // 48.6n
11 341212
Mark Scheme
Use ^r - r0 to find arc
DC or EC
AC:
AC*arcDC+2
19.45 /l
Use / = Y, fg to findarea of sector CBE
15.5
Use A- Yrfe b findarea of sector DBE
A,: *Of(;-Lz4)Use
I * bxh OR lo|sin Cto22
find Ar:LABC or A3: A ABEor A+: L EBC
Az= 17.5', At - 5 .687 ;A+: Il,82
/- *15.5 +As-At-A+
OR
Arc DC-s (Z\\2)
or arc EC - 5(1.2
+72
5.22 ll 5.23
A- A2-Ar-A+* (*t5.5 -A+)
347212
t2 347212
Mark Scheme
(i) 8p:2
D- 1 ll o.z5L4
(ii) Use
* (0.25), (0.75)n-r
Write P(X>Z):P(X - 3) + P(X - 4) +.. .+ P(X: 8)
OR1 P(X: 0) - P(X - 1) - P(X= 2)
(i) z- 2.5 -1.60.8
0.13029 ll 0,1303
fn -1.6 .'r' -'- =1.175
0.8
0.3015
m=2,54
347212
13
SECTTON C (20 MARKS)
347212
Mark Scheme
Integr ate Izt - 8 dt
v- f 8t + c Substitute t: 0 and
v- 12 in * y tofind c
c: 12
Use a -0tofindr
t -4
Solvev.0tofindr
(t-2)(t-6)-0
t:2, 6
!t' -8r+12 dt
s = t- - 4t2 +r2t3 Substitute t = *2 or t - 4 into *s
OR
use I: or I: in *s
Find total distance travelled
fi"at arll:"dtl
t6
347212
L4 347212
Mark Scheme
use Qt x looQo
)c - 125 y=
I=* I2s(27) + l2s(34) + 137 .5(10) + 1s0(10)
27 +34+10+10+19
127.8
use Qn x loo26A0
= *127 .8
RM 3322.8
118 x *1 27 .B
100
t2o(1e)
150.8
347212
t.
l5 3472/2
Ques Mark SchemeSub
MarksFUII
Mark
1,4 (a) (i) Yr-'-: :rlt 19 lt ! 4! 9- ly -!$- B c
BC 2 = 82 +lz2 - 2(8) (lz) cos 25'
BC: 5.83
(ii) y:: :ir :l:11 y:? ::.1i : : ::osin 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 "7510
347212
t6 347212
Mark Scheme
x + y S 8 or equivalent
x
600x + 2A0y < 3 000 or equivalent
EEE
Draw coffectly at least one straight linefrom the *inequalities which involvesxand y
Draw coffectly all the three*straight linesNote : Accept dashed lines
The correct region shaded
(i) I
(ii) Maxirnum point: (4, 3)
Use 3bc + 7yfor point in the *region R
Note:ss-l ifin (a), the symbol 63-" is not used at all orrnore than three inequalities are given
in (b), does not use the scale given ordoes not use graph paper orinterchange between r-anis and y-axis
347212
t7 347212
END OF N{ARK SCHEME
347212