._

\

€ l.

[email protected]

cs

Septernber

2 jam

MAJLIS PENGETUA SEKOLAH MALAYSIA CAWANGAI\ PULAU PINANG

MODUL LATIHAN BERFOKUS SPM 2OI4 MARKSCHEME

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

S

Kertas 2 Septernber Al

z- lam 2" .

MAJLIS PENGETUA SEKOLAH MALAYSIA CAWANGAN PULAU PINAIIG

MODUL LATIHAN BERFOKUS SPM 2OI4

MARKSCHEME

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

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)

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
v

-

3

(- I ,2) into ty

3

6

E

E] EI E)

Accept cosine graph 4

3

2

I

.r 3x y-5-1T

Sketch the straight line

Number of solutions =

347212

3

7

347212 It

Mark

Ques

(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

Scheme

Sub

Marks Mark

E E

Method to find mode

26

(b)1"

@

F: 14

@

0)

*14

Iu;

g

22.83

347212

"f* -9

l

4

E

TotaI

347212

347212

347212

7

sEcrroNB(40MARKS)

(a)

x-I

1

2

3

4

5

6

logroy

0.44

0.63

0.82

1.03

1.20

L.40

(b)

Plot logt \$/ against ( x

Full Marks Mark Sub

Mark Scheme

Ques

E E

- 1)

& 6 *points plotted correctly

(c)

Line of best fit

log;,oy= logr ok + ( r

- 1) logrch

E Use

;Use

*c

*m: logoh

h

- 1.56

lg-

Note : SS-1 if part of the scale'is not uniform or not using the scales given or not using the graph paper

347212

log1s fr

1.74

10

347212

logro

347212

347212

Sub

Mark Scheme

Ques

(i) &(ii)

(a)

Marks

Use Triangle Law for

Full Mark

0R or OS

fr:4q-6v OS

9l: _qetsl_11ry:_"_ \${ Or -9u-4v

(b)

- 4u +3v

_9_T_

-3-

se QT = lQR

I

(c)

| (i) &(ii)

I tI

tubstitute u =3iand Y

- -21+ liinto 'r ffi

OS

=

6r_+

lSi

6t+Lsj 4 ?_a- - "llao

3472n

4

10

t0

Mark

347212

Scheme

Solve simultaneous equations

y:(x-3)2andy--x*9.

B(5,4)

A(0,9)

Integrate (x

- 3)'wrt x

6xz ,+ Ar:t9x 32

At\/'

(* -3)3 3

,f5

Uselimit

t

in Ar

OR

Az

Find the arcaof tapezium

Az=

or

At

*(e 4)x *(5) l-. 2\ +

l+-'{: r25

/Do1/lzo.B3

Integrate n(x - 3)o wrt x

v:rry 3

Use

Iin

0

243

n

ll48:- n //

48.6n

o(ry-sf 5

341212

11

Mark

Use ^r - r0 to

Scheme

find arc

DC or EC

Arc DC-s

(Z\ \2)

AC:

+72

or arc EC - 5(1.2

AC*arcDC+2

19.45

/l

/

= Y, fg to find area of sector CBE

Use

15.5

Use

A- Yrfe b find

area

of sector DBE

I

Use *

A,: *Of(;-Lz4)

bxh

22

find

lo|sin

Ar:LABC or A3: or A+: L EBC

Az= 17.5', At

A+: Il,82

/-

OR

*15.5

A

Cto

ABE

- 5 .687 ;

+As-At-A+

OR

A- A2-Ar-A+* (*t5.5 -A+)

5.22

347212

ll

5.23

t2

347212

Mark Scheme

8p:2

(i)

DL4

1 ll o.z5

(ii)

Use

* (0.25), (0.75)n-r

P(X -

1

Write P(X>Z): 3) + P(X - 4) +.. .+ P(X: 8) OR

P(X:

0)

-

P(X - 1) - P(X= 2)

0.3015

(i) z- 2.50.8-1.6

0.13029

ll

0,1303

fn -1.6 -''r' =1.175 .

0.8

m=2,54

347212

347212

13

SECTTON C (20 MARKS)

Mark

Integr

Scheme

ate Izt - 8 dt

v- f

8t +

v-

find Use

t:

Substitute 12 in *

c

0 and

y to

c

c: 12

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

Find total distance travelled

use

fi"at arll:"dtl

t6

347212

I:

or I:

in

*s

347212

L4

Mark

Scheme

use Qt x loo Qo

)c

I=

-

y=

125

* I2s(27) + l2s(34) + 137 .5(10) + 1s0(10) 27 +34+10+10+19

127.8

use Qn 26A0

x loo = *127 .8

RM

118

x *1 27 .B

100

150.8

347212

3322.8

t2o(1e)

l5

3472/2

t.

Mark Scheme

Ques

1,4

(a)

(i)

Yr-'-: :rlt 19 lt ! 4! 9- ly -!\$BC

2

= 82

+lz2 -

BC:

(ii) y::

2(8)

B

Sub

FUII

Marks Mark

c

(lz) cos 25'

5.83

:ir :l:11 y:?

::.1i

C sin 25 12 =-5.83

::

::o

sin

60.450

I 19.550

(b) I

G)

(ii)

(iii)

Z DAfi:59. use

1o

|olez)sin

(*5e.1

47 "75

347212

+ 25)

10

t6

Mark

x + y S 8 or

Scheme

equivalent

x 600x +

2A0y < 3 000

or

equivalent

Draw coffectly at least one straight line from the *inequalities which involves xand y Draw coffectly all the three *straight lines

Note : Accept dashed lines

(i)

I

(ii)

Maxirnum

point:

(4, 3)

Use 3bc + 7y

for point in the *region R

Note:

ss-l

if

in (a), the symbol 63-" is not used at all or rnore than three inequalities are given

in (b), does not use the scale given or does not use graph paper or interchange between r-anis and y-axis

347212

347212

E E E

t7

END OF N{ARK SCHEME 347212

347212

## Skema Penang K1+K2.pdf

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. Page 3 of 23. Skema Penang K1+K2.

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