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

Question 17 (3 marks):
It is given that $\int \frac{5}{{\left(2x+3\right)}^{n}}dx=\frac{p}{{\left(2x+3\right)}^{5}}+c$ , where c, n and p are constants.
Find the value of n and of p.

Solution:

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:

Question 19 (3 marks):
The variables x and y are related by the equation $y=x+\frac{r}{{x}^{2}}$ , where r is a constant. Diagram 8 shows a straight line graph obtained by plotting

Diagram 8

Express h in terms of p and r.

Solution: