5.4 SPM Practice (Short Questions)

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 α \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 α \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 α \frac{1}{\sqrt[3]{Q}} \\ P α \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:

\begin{array}{l} y α \frac{1}{x^{3}} \\ y = \frac{k}{x^{3}} \\ When y = 16, x = \frac{1}{2} \\ 16 = \frac{k}{{(\frac{1}{2})}^{3}} \\ 16 = \frac{k}{\frac{1}{8}} \\ k = 2 \\ y = \frac{2}{x^{3}} \end{array}

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 α \frac{X}{\sqrt{Y}} \\ W = \frac{k X}{\sqrt{Y}} \\ W = \frac{k X}{Y^{^{\frac{1}{2}}}} \end{array}