SPM Additional Mathematics 2017, Paper 1 (Question 4 – 7)


Question 4 (3 marks):
Diagram 4 shows a trapezium ABCD.

Diagram 4

Given  p ˜ =( 3 4 ) and  q ˜ =( k1   2 ) where k is a constant, find value of k.


Solution:

p ˜ =m q ˜ ( 3 4 )=m( k1   2 ) ( 3 4 )=( mkm    2m ) mkm=3 ………. ( 1 ) 2m=4 ……………. ( 2 ) From( 2 ): 2m=4 m=2 Substitute m=2 into ( 1 ): 2k2=3 2k=3+2 2k=5 k= 5 2


Question 5 (3 marks):
Given  25 h+3 125 p1 =1, express p in terms of h.

Solution:
25 h+3 125 p1 =1 25 h+3 = 125 p1 ( 5 2 ) h+3 = ( 5 3 ) p1 5 2h+6 = 5 3p3 2h+6=3p3 3p=2h+9 p= 2h+9 3


Question 6 (3 marks):
Solve the equation: log m 324 log m 2m=2

Solution:
log m 324 log m 2m=2 log m 324 log m 2m log m m 1 2 =2 log m 3242( log m 2m log m m )=2 log m 3242 log m 2m=2 log m 324 log m ( 2m ) 2 =lo g m m 2 log m ( 324 4 m 2 )=lo g m m 2 324 4 m 2 = m 2 4 m 4 =324 m 4 =81 m=±3( 3 is rejected )


Question 7 (2 marks):
It is given that the nth term of a geometric progression is T n = 3 r n1 2 , rk.  
State
(a) the value of k,
(b) the first term of progression.

Solution:
(a)
k = 0, k = 1 or k = -1 (Any one of these answer).

(b)
T n = 3 2 r n1 T 1 = 3 2 r 11   = 3 2 r 0   = 3 2 ( 1 )   = 3 2


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