SPM Additional Mathematics 2017, Paper 1 (Question 17 – 19)


Question 17 (3 marks):
It is given that 5 ( 2x+3 ) n dx= p ( 2x+3 ) 5 +c , where c, n and p are constants.
Find the value of n and of p.

Solution:
5 ( 2x+3 ) n dx= 5 ( 2x+3 ) n dx = 5 ( 2x+3 ) n+1 ( n+1 )×2 +c = 5 2( 1n ) × 1 ( 2x+3 ) n1 +c = 5 2( 1n ) ( 2x+3 ) n1 +c Compare  5 2( 1n ) ( 2x+3 ) n1 with  p ( 2x+3 ) 5 n1=5 n=6 5 2( 1n ) =p 5 2( 16 ) =p 5 2( 5 ) =p p= 1 2


Question 18 (3 marks):
A straight line passes through P(3, 1) and Q(12, 7). The point R divides the line segment PQ such that 2PQ = 3RQ.
Find the coordinates of R.

Solution:



2PQ=3RQ PQ RQ = 3 2 Point R =( 1( 12 )+2( 3 ) 1+2 , 1( 7 )+2( 1 ) 1+2 ) =( 18 3 , 9 3 ) =( 6,3 )


Question 19 (3 marks):
The variables x and y are related by the equation y=x+ r x 2 , where r is a constant. Diagram 8 shows a straight line graph obtained by plotting ( yx ) against  1 x 2 .

Diagram 8

Express h in terms of p and r.


Solution:

y=x+ r x 2 yx=r( 1 x 2 )+0 Y=mX+c m=r, c=0 m= y 2 y 1 x 2 x 1 r= 5p0 h 2 0 hr 2 =5p hr=10p h= 10p r

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