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


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

Solution:
5(2x+3)ndx=5(2x+3)ndx=5(2x+3)n+1(n+1)×2+c=52(1n)×1(2x+3)n1+c=52(1n)(2x+3)n1+cCompare 52(1n)(2x+3)n1with p(2x+3)5n1=5n=652(1n)=p52(16)=p52(5)=pp=12


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=3RQPQRQ=32Point R=(1(12)+2(3)1+2,1(7)+2(1)1+2)=(183,93)=(6,3)


Question 19 (3 marks):
The variables x and y are related by the equation y=x+rx2 , where r is a constant. Diagram 8 shows a straight line graph obtained by plotting (yx) against 1x2.

Diagram 8

Express h in terms of p and r.


Solution:

y=x+rx2yx=r(1x2)+0Y=mX+cm=r, c=0m=y2y1x2x1r=5p0h20hr2=5phr=10ph=10pr

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