1. 
Two variables x and y
are related by the equation . Given that 

the variable x is increasing at the rate
of 0.1 unit/s, find the rate at which variable 

y changes when x = 2. 

2.  The area of a circular disc increases at a constant
rate of 0.05 cm^{2}/s. Find the 

rate at which its radius is increasing when the
area is 25 cm^{2}. Give your 

answer correct to 3 significant figures. 

3.  Water is being poured into a container at a rate
of 3 cm^{3}/s. The volume, V cm^{3}, of 

the water in the container, when the depth is
x cm, is given by 

V = 0.005x^{3} + 1.2x^{2}. Find 

(a) the rate of increase in the depth of water
when x = 5 cm, 

(b) the depth of water when the rate of increase
in the depth is 0.15 cm/s. 

Give your answers correct to 2 decimal places. 

4.  A circular ink blot starts with a radius of 3 cm. As the ink soaks into the paper, the 

blot expands so that after t seconds, the radius, r cm, is given by r = 3 + 0.1t. 

(i) Write down an expression for the area, A cm^{2}, of the blot after t seconds. 

(ii) Find the rate of increase of the area of the blot that after 4 seconds, leaving 

your answer in terms of . 