SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

1

Additional Mathematics Paper 1

Ogos, 2014

MODUL PENINGKATAN PRESTASI TINGKATAN 5 TAHUN 2014

ANJURAN

MAJLIS PENGETUA SEKOLAH MALAYSIA (KEDAH)

ADDITIONAL MATHEMATICS

MARKING SCHEME

Paper 1

MODUL 2

.

SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

2

PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM 2014

Marking Scheme Module 2

Additional Mathematics Paper 1

Question Solution/ Marking Scheme Answer Marks 1

(a) B1 : 3 2m or n= =

(a) 3m = AND 2n = (b) many – to – one

2

1

2

B2 : ( )6 63 12f orp p

= =

B1 : 1 6 3fp

− =

12

p = 3

3 (a) B1 : 2 3 3y− =

(b) B1 : ( )2 3 3 8k− − =

(a) ( ) 133

g = − (b) 5k =

2

2

4

B2 : ( )( )1 2 0

1 2p p or

p or p− − =

= = B1 : ( ) ( )( )22 4 1 3 2p p− −

1 2p AND p= = 3

5 (a) B1 : 3 5p or q= − = −

(a) 3p = − AND 5q = − (b) 3x = −

2

1

SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

3

Question Solution/ Marking Scheme Answer Marks 6

B2 :

or 52

x = , 3x = −

B1: (2 5)( 3)x x− +

532

x− ≤ ≤

3

7

B2 : 3

2 2 2

2

log 16 log loglog 8

h k+ +

B1 :

32 2

2 2

log 16 loglog log 8

or h ork or

4 33a b+ + 3

8 B2: 6221 −=−+ x

B1 : ( )22( 1) 37(7) 7x or− −

25

−

3

9 B3 : ( )2 14 3+

B2 :

( ) ( )26 182 2 25 2 2 17 5322 2

3

d d

or d

+ − + =

=

B1 :

( ) ( )26 182 2 25 2 2 172 2

d or d + +

44 4

52 3−

SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

4

Question Solution/ Marking Scheme Answer Marks 10

(a) B1: 1

9

3 =mm

(b) B1:

911

91181

5

5

−

−

=S

(a) 3 3m AND m= = − (b) 91.123

2

2

11

B1: 13

r =

272

2

12 (a) B1: 2xy ax b= +

(b) B1 : ( )

( )

13 7* 2

3 2* 2

bor

b

= +

= +

(a) 2 (b) 1b = −

2

2

13 B2 :

( ) ( ) ( )2 2 224 3 2 4x y x y − + − = + − B1 :

( ) ( ) ( ) ( )2 2 2 23 2 0 4x y or x y− + − − + −

2 23 3 24 8 36 0x y x y+ − − + = 3

14 B1:

( ) ( ) ( ) ( ) ( ) ( )1 11 4 3 2 8 8 3 4 11 2 02

k k × + × + × − × + × + × =

OR

8 4 4 211 3 3 k− −

=− −

1k = −

2

SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

5

Question Solution/ Marking Scheme Answer Marks 15

(b) B1 : 5 or 22 43 +

(a) ji 43 +

(b) 5

43 ji +

1

2

16 B3 : 6 2 0 12 4 0m OR m+ = + =

B2 : 3 3 6 08 4 12 03

m + + =

B1 : 6

12OB

=

3m = − 4

17 B3 : 41 81 138 19x or x= ⋅ = ⋅

B2 :

26sin 8sin 8 02sin 2 sin3

x x or

x or x

− − + =

= − =

B1 : ( )23 1 2sin 8sin 5x x− = −

41 81

138 19

xAND

x

= ⋅

= ⋅

4

18

(b) B2: ( ) ( ) ( )( )21 112 * 1.047 6 10.3922 2

−

B1: ( ) ( ) ( )( )21 112 * 1.047 6 10.3922 2

or

(a) 1.047rad

(b) 44.21

1

3

SULIT 3472/1

3472/1 Additional Mathematics Paper 1 SULIT

6

Question Solution/ Marking Scheme Answer Marks 19

(b) B1: 70 118

k∗ +=

(a) 70

(b) 18k =

1

2

20 B2 : (1) 24 8h′′ = − B1 : 1812)( 2 +−=′ xxxh

16

3

21 B2 : 2 8 2 3k or x− = − =

B1 : 2 8x −

3k = 3

22

B2 : ( ) ( )22

0

3 11 1 49 15 1 5

xor

x +

− − −

B1 : ( ) ( ) 23 11

xh x dx

x+

=−∫

10 3

23

(b) B1: 2 3 2 3 515 5 7 5 7

or + × − ×

(a) 25

(b) 47

1

2

24 (b) B1 : 4 3 5

3 2 3C C C× ×

(a) 495 (b) 120

1

2

25 B2 : p( z>k ) = 0.0608 B1 : P(z > 0. 14) = 0.4443

k = 1.548

3

END OF MARKING SCHEME