SULIT

3472/1

Additional

Mathematics

Paper 1

Sept

2010

PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA

SEKOLAH MENENGAH MALAYSIA (PKPSM) CAWANGAN MELAKA

DENGAN KERJASAMA

JABATAN PELAJARAN MELAKA

PEPERIKSAAN PERCUBAAN

SIJIL PELAJARAN MALAYSIA 2010

ADDITIONAL MATHEMATICS

Paper 1

MARKING SCHEME

This marking scheme consists of 5 printed pages

PAPER1

QUESTION

NUMBERS WORKING MARKS

FULL

MARKS

1

a) -2

b) one to one

1

1

2

2

(a) -3

𝑔−1 𝑥 =𝑥−5

2 @ 2x + 5 = -1

(b) 1

3𝑥 +

23

6

1

6 2𝑥 + 5 + 3

2

1

2

1

4

3

h(x) = 2x + 3

h(y) = 2(y+4) – 5

h(x-4) = 2x - 5

3

B2

B1

3

4

3.609 , -1.109 @ 3.608 , -1.108

𝑥 =−(−5)± (−5)2−4 2 (−8)

2(2) or 3.609 @ -1.109

2x2 - 5x -8 = 0

3

B2

B1

3

5

-7 < k < 5

or (k+7)(k-5) < 0 or -7 and 5 ( seen)

(1+k)2 – 4 (1)(9) < 0

3

B2

B1

3

6

(a) q = -3

(b) x = 3

(c) (3, -4)

1

1

1

3

7

x = 6

2x + 9 = 3x + 3

2( 22(x+4)) - (23 )(x+1)

3

B2

B1

3

-7 5

QUESTION

NUMBERS WORKING MARKS

FULL

MARKS

8

R = 𝑃2

34 or R = 𝑃2

81

Log3 𝑃2

34 =

log 3 R

2log3 R or log3 P – log3 3

2 = log3 𝑅

1

2

log2 P – 2 = 𝑙𝑜𝑔 2 𝑅

𝑙𝑜𝑔39

3

B2

B1

3

9

2𝑛 15

2 𝑜𝑟 15 2𝑛−1

2𝑛 22 − 1 + 9

2

2𝑛(22) − 2𝑛 + 9(2𝑛

21 )

3

B2

B1

3

10

(a) p = 14

(b) 204

S6 = 6

2 [2(9)+(6-1)10] or a=9 and d = 10 seen @

9+19+29+39+49+59

1

B2

B1

3

11

(a) r =2

(b) n= 10

Sn = 1(2𝑛−1

2−1 = 1023

1

2

B1

3

12

9

6

1 −13

𝑟3 = 2

96

3

B2

B1

3

13

p = 10-2 @ p= 0.01 and q = 0.5

q = 0.5 @ log p = -2

log y = log p + q loq x

y = 0.224

3

B2

B1

1

4

14 (a) r =14,

8 =2 𝑟 + 3(4)

5

(a) s=17

5

𝑠 =2 7 +3(1)

5

2

B1

2

B1

4

QUESTION

NUMBERS WORKING MARKS

FULL

MARKS

15 (a) -5 x+3y

(b) 4x+ 3

5 y

1

5(-5x+3y) * + 5 x * answer from part a

1

2

B1

3

16 (a) 𝑃𝑄 = 11𝑖 + 2𝑗

−(−5𝑖 − 4𝑗 ) + 6𝑖 − 2𝑗 .

(b) 𝑃𝑄

𝑃𝑄 =

1

5 5 (11𝑖 + 2𝑗 ) @

𝑃𝑄

𝑃𝑄 =

1

125 (11𝑖 + 2𝑗 )

112 + 52 𝑜𝑟 5 5 𝑜𝑟 125

2

B1

2

B1

4

17 41˚ 25′ , 318˚25′ @ 41.41˚, 318.59˚

cos θ = 0.75

(4cosθ -3)(cosθ+2)=0

Change cos2θ = 2cos2θ -1

4

B3

B2

B1

4

18 64.08

16 + 8(2л – 0.2736 )

2л – 0.2736

3

B2

B1

3

19 x = 3

𝑑2𝑦

𝑑𝑥2= 2 − 162𝑥−2 = 0

𝑑𝑦

𝑑𝑥= 2𝑥 + 54𝑥−3

3

B2

B1

3

20 4

2𝑝 1 − 3

(1)2 = 5

2𝑝𝑥 − 3

𝑥2

3

B2

B1

3

21 2

3

𝑡 52

2−

12

2 − 10 = −3𝑡

𝑡𝑥2

2 𝑜𝑟 𝑡𝑥 𝑑𝑥 − 2 𝑔(𝑥)𝑑𝑥

5

1

5

1

3

B2

B1

3

QUESTION

NUMBERS WORKING MARKS

FULL

MARKS

22 (a) p = 5, p = -7

5+ 2𝑝−1 +8+5+(𝑝2−2)

5 = 10

(b) Mod = 5

Med = 8

2

B1

1

1

4

23 (a)

9

2

(b) 45

23

(3

5x

5

9) + (

4

9x

2

5)

1

2

B1

3

24 (a) 924

(b) 60

𝐶14 x 𝐶4

5 x 𝐶13

1

2

B1

3

25 (a) 1.7273

(b) 0.3986 @ 0.3985 (cal)

P( 4.2−4.2

1.21 ≤Z ≤

5.6−4.2

1.21) or

1

2

B1

3