[spmsoalan]Skema Addmath K1,2 P.Pinang 2014.pdf

7/24/2019 [spmsoalan]Skema Addmath K1,2 P.Pinang 2014.pdf

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 /
http://spmsoalan.wordpress.com/http://spmsoalan.wordpress.com/


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




3/23

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




4/23

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




5/23

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




6/23

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




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




8/23

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




9/23

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




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


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




12/23

347

347




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




14/23

347

logro

347




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




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




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




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




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




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




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




22/23

t6

347212

Mark Scheme

x

+

y

S

8 or

equivalent

x

600x

+

2A0y

[spmsoalan]Skema Addmath K1,2 P.Pinang 2014.pdf

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