1

3472/2

Matematik

Tambahan

Kertas 2

Ogos 2014

2 ½ jam

BAHAGIAN PENGURUSAN

SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN

KEMENTERIAN PELAJARAN MALAYSIA

PENTAKSIRAN DIAGNOSTIK AKADEMIK SBP 2014

PERCUBAAN SIJIL PELAJARAN MALAYSIA

ADDITIONAL MATHEMATICS

Paper 2

Skema Pemarkahan ini mengandungi 10 halaman bercetak

MARKING SCHEME

2

No Solution and Mark Scheme Sub

Marks

Total

Marks

1

2

2

6 2

3

6 2 6 25 4 5

3 3

10 7 24 0

( 7) ( 7) 4(10)( 24)

2(10)

1.94, 1.24

0.71, 2.83

yx

y yy y

y y

y

y

x

5

5

2(a)

(b)

(c)

2( ) 2( 1) 2 K1

2 7 6 K1

6 5 N1

h x x m

m k

m k

12

2k m N1, N1

22 (4 ) 8 0x n x K1

2

4 4( 2)( 8) 0n K1

4, 12n N1

3

2

3

8

2

2

6 3 P1

2

6 3 6 35 4 5 K1

2 2

15 53 30 0

( 53) ( 53) 4(15)(30)K1

2(15)

xy

x xx x

x x

x

0.71, 2.83 N1

1.94, 1.24 // 1.25 N1

x

y

OR

3

3(a)

(b)

2 , 2 ( 1), 2 ( 2),......r r r K1

7

2(2 ) 6(2 ) 2162

r K1

15r

length of ribbon 30 N1

30 ,32 ,34 ,...... K1

2d K1

48 30 ( 1)(2 )n

9n N1

3

3

6

4 (a)

(b)

(c)

1m K1

8y x N1

4 5 26

7

x or

4 5 22

7

y K1

11, 3P

N1

8AB K1

2 2

4 4 8x y K1

2 2 8 8 24 0x y x y N1

2

2

3

7

4

5(a)

(b)

y = 2 - x

y = 3 cos 3

2x

2

- 3

0

2

3

x

y

Shape of Cosine 0 2x P1

Period 1.5 cycle P1

Amplitude 3 P1

2x

y

K1

Draw line 2x

y

K1

Number of solutions = 3 N1

3

3

6

6(a)

(b)

15.5 2 25.5 5 35.5 12 45.5 6 55.5 7 K1

32

38.94 N1

Mean

2 2 2 2 2

215.5 2 25.5 5 35.5 12 45.5 6 55.5 7(38.94) K1K1

32

134.86 N1

Varian

2

3

8

5

(c)

3

332 19

440.5 10 K1K16

41.33 N1

Q

3

7

LAMPIRAN

8 (a)

(b)

(c)

4 K1dy

xdx

1

4Nm K1

1

5 14

y x

1 21

4 4y x N1

1

2

0

1Area= (4 5)(1) 2 3

2x dx K1

13

0

9 23

2 3

xx

K1

9 23 0

2 3

K1

5

6 N1

5

3

52

3

2 2

3Volume ( )

2

3 K1

4 2

5 3(5) 3 3(3) K1

4 2 4 2

ydy

y y

7 N1

3

4

3

10

6

9(a)

(b)

(c)

BQ BA AQ

Or AC AD DC

K1

(i) 3 6BQ x y

N1

(ii) 3

52

AC y x

N1

35

2AP my mx

K1

3 3 6AP n x ny

K1

Compare and solve

33 3

2m n and 5 6m n K1

3

4m N1

5

8n N1

3

8PD BQ QD

or 1 1

4 2PD AC BQ

K1

9 17

8 4PD x y

N1

3

5

2

10

10(a)

(i)

(ii)

2

10(0.75)

7.5 N1

10(0.75)(0.25)

1.875 N1

10 9 1 10 10 0

9 10

( 9) ( 9) ( 10)

(0.75) (0.25) (0.75) (0.25) K1 K1

0.2440 N1

P X P X P X

C C

2

3

10

7

(b)(i)

(ii)

1.3 1.5 2.5 1.5(1.3 2.5) K1

0.8 0.8

( 0.25 1.25) K1

0.4931 N1

P x P z

P z

Total = 160

0.4931 K1

324 N1

3

2

11(a)

(b)

(c)

1 5sin

8AOB

K1

0.6752AOB rad N1

2 28 5 4FC K1

4 1.571CD K1

Perimeter 2 28 5 4 4 1.571 5 4 8 K1

= 25.53 cm N1

1

5 6.2452

BFO K1

414 0.6752

2 Or 41

4 1.571 0.67522

K1

Area 2 21 1 15 6.245 4 0.6752 4 1.571 0.6752

2 2 2 K1

= 17.38 cm2

N1

2

4

4

10

8

12(a)

(b)

(c)

5 2 0 K1

5

2

t

t

25 14 K1v t t

2

max

5 55 14

2 2

20.25 N1

v

2

2

5 14 0 K1

5 14 0

( 2)( 7) 0 K1

7 N1

t t

t t

t t

t

2 3514 K1

2 3

t ts t

2 3 2 3

7 9

5(7) (7) 5(9) (9)14(7) 14(9) K1

2 3 2 3s or s

1 1 1Total distance 106 106 85 K1

6 6 2

1=127 N1

3

3

3

4

10

9

13(a)

2 2 26.5 3.5 2(6.5)(3.5)cos70EC K1

6.24 cm N1

2 10

(b)

sin sin 70

3.5 6.24

BAC K1

Use 31.81ACD BAC K1

180 62.74ADC K1

117.26 N1

4

(c)(i)

D' D C

A

'AD C must acute angle N1

1

(ii) ' 180 2 62.74D AD K1

1

' 3.7 3.7 sin54.522

ADD K1

5.57 cm2 N1

3

14

LAMPIRAN

10

END OF MARKING SCHEME

15(a)

10

10

12100 125 K1

RM 9.60 N1

Q

Q

2

10

(b)

Use 120 P1

120110 K1

100

132 N1

3

(c)

12

12

100 121 K190

RM108.90 N1

Q

Q

2

(d) 110(8) 136(5) 120 125(4)121 K1

8 5 4

2060 120121 K1

17

3 N1

m

m

m

m

m

3