# 5.4 Variations, SPM Paper 1 (Short Question)

Question 5:
It is given that R varies directly as the square root of S and inversely as the square of T. Find the relation between R, S and T.

Solution:
$R\text{}\alpha \text{}\frac{\sqrt{S}}{{T}^{2}}$

Question 6:
It is given that P varies directly as the square of Q and inversely as the square root of R. Given that the constant is k, find the relation between P, Q and R.

Solution:

$\begin{array}{l}P\text{}\alpha \text{}\frac{{Q}^{2}}{\sqrt{R}}\\ P=\frac{k{Q}^{2}}{\sqrt{R}}\end{array}$

Question 7:
Given that P varies inversely as the cube root of Q. The relationship between P and Q is

Solution:
$\begin{array}{l}P\text{}\alpha \text{}\frac{1}{\sqrt[3]{Q}}\\ P\text{}\alpha \text{}\frac{1}{{Q}^{\frac{1}{3}}}\end{array}$

Question 8:
Given that y varies inversely as the cube of x and y = 16 when x = ½. Express y in terms of x.

Solution:

Question 9:
W varies directly with X and inversely with the square root of Y. Given that k is a constant, find the relation between W, X and Y.

Solution:
$\begin{array}{l}W\text{}\alpha \text{}\frac{X}{\sqrt{Y}}\\ W\text{=}\frac{kX}{\sqrt{Y}}\\ W\text{=}\frac{kX}{{Y}^{{}^{\frac{1}{2}}}}\end{array}$