# 5.4 Variations, SPM Paper 1 (Short Question)

Question 1:
It is given that y varies directly as the cube of x and y = 192 when x = 4. Calculate the value of x when y 24.

Solution:

y α x³
y = kx³
192 = k (4)³
192 = 64 k
k = 3

y = 3 x³
when y = – 24
– 24 = 3 x³
x³ = – 8
x = – 2

Question 2:
It is given that y varies directly as the square of x and y = 9 when x = 2. Calculate the value of x when y = 16.

Solution:
y α x²
y = kx²
9 = k (2)²

Question 3:
Given that y varies inversely as w and x and y = 45 when w = 2 and x = $\frac{1}{6}$ . Find the value of x when y = 15 and w = $\frac{1}{3}$

Solution:

Question 4:
Given that   $p\text{}\alpha \text{}\frac{1}{q\sqrt{r}}$ and p = 3 when q = 2 and r = 16, find the value of p when q = 3 and r = 4.

Solution: