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 Additional  Mathematics  Paper 1 Au gust, 2016

PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM

2016

ANJURAN MAJLIS PENGETUA SEKOLAH MALAYSIA (KEDAH)

ADDITIONAL MATHEMATICS MARKING SCHEME Paper 1

MODULE 1

.

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Additi onal M athematics athematics Pape Paperr 1 

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PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM 2015 Marking Scheme Additional Mathematics Paper 1 MODUL 1 Question

Solution/ Marking Scheme

1

B1: No or many to one relation

2

B2:  p  2 or q  B1:

 p



3 x

1

or 

3

Answer

Marks

 No AND many to one relation

2

1 3 2

1

 p  2   and q 

3

3x  3q

3

3 B1:  x  2  x  5

 x 2  3x  10  0

4

(a)

2 or 

(b) B1 :

2 3

q   4

2 1

(b) 2 and 

2 3

2

5 (a) B1 :  x    2

6

B2 :

3 x  1 25

 p  2

2

(b) k   10

1

(a)

  x 1

B1 :

7

B2:

B1 :

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 x

log 2 25



2

3

log 2 4

5

 2   20 2 2 x

2

2 x

2

or 

22 x 2

 x 

3 2

3

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B3:

B2:

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15

 2  2 r   14  2    270  2 

15 2

2a  14(2 ) 

15

or

2

4 r  14 d 

2  

4

B1: a  2 r or d   2  9 B2:

a 1  0.9

25

12

14.49

B1:

 x



8

54 5

 x

or

y



8, 7 

7

B1:

(8  4) 2  (0  ( 3) 2

(a)

(b)

B1:

( y  4) 2  ( x  ( 3)) 2

(b)  x 2   y  6 x  8 y  0

2

3

or d   2 x

(a)

5

3

r   0.9

5

2

2

2

 or c  3

B2 : log 3  y  log 3  x B1 : log 3  y   log 3 3472/1

25 1  r 7   9 0.1

   1  4   1       3   B2: 16 x  a 1   1   3     

B3: k   13

or 

or

9

B1: S 4  16 x

11



1  0.9

B1: a 

10

7

2 k 

 log 3 27

k  

5 2

 and c  3

4

 x 2 k  27

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 3    3  

B2: 

B1:

15

4 k   4 k  

 3  q     3 

3

B2: 2v 

4

RQ

u 

or

B1:  PN  PR  RN

16

1 4

QR

1

B1:

(37  5m) 8 (37  5m) 8

B1:

18

v



3

3



4

3 4

u

3

k   7  and m  4 4

7

 k   or 2k   3

17 (b) B2:

2

or PN  PQ  QN 

B3: k   7  or m  4 B2:

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 y 2  36 2

(a) 9

1

(b)  y  6 , y   6

3

2

1158  9   y   9  y 

B3: 90 x  15  x2  0

6

B2:   x 2 (45  5 x)

4

B1: r  x

B3:   M   16  0.02 19 B2:

dM  dk 

 16

0.64

B1:  k   0.04 or

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dM  dk 



4

8k  (3  k 2 ) 2

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20

(a) 337.38°

(b) B2: B1:

 5  12     13  13 

2

sin    

(b) 

5

120

1

3

169

13

21 B2:

B1:

22

1 2 1 2

(20 2 )(2.6211)  -

(7 2 )(2.6211)  or

1 2

25

(7 2 )(2.6211)

1 2

( 20 2 )(2.6211)

9

  y 3   B3 :     6 y 2  27 y   3 6

or 

9

14

3

 (3)  2 3

or 

 4  (3)3    3 

  x dy or 9 or (0,6) (0,9)

or r  3

 B 2 :

 y

2

3

 12 y  27 dy

6

18  

  

4

9

 B1:

2

6

23 (a)

 1 1  (b) B1 :     6 6 

(b)

24

1

1

6

5 2

36

(a)

252

1

(b)

30 240

1

25 B2: B1 :

C4 p4q 0  0.3702

4

4

78 %

3

C 4 p 4 q 0

END OF MARKING SCHEME 3472/1

Additi onal M athematics Paper 1 

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