Revision
Direct and Inverse Proportions
Question 1:
A train moves on a circular track of radius, r metres. The safe speed of the train v m/s, is
directly proportional to the square root of r. If the safe speed for a radius of 121 m is
22 m/s, calculate
a) the safe speed for a radius of 81 m,
b) the radius if the safe speed is 28 m/s.
Revision
Direct and Inverse Proportions
Question 2:
The volume of a cylinder, V is directly proportional to the square of its radius, r.
When the radius is 3 cm, its volume is 120 cm3.
a) Find an equation connecting the V and r.
b) Find the volume of the cylinder if its radius is 8 cm, giving your answer to the
nearest whole number.
Revision
Direct and Inverse Proportions
Question 3:
In an experiment, the speed v, of the wheel of a car is directly proportional to the
square root of the tyre pressure, p. Given that v = 40 when p = 25, find
a) the equation connecting v and p,
b) the value of v when p is 36.
Revision
Direct and Inverse Proportions
Question 4:
y is directly proportional to x3.
When x has a certain value, y = 5. Find the value of y when x is halved.
Revision
Direct and Inverse Proportions
Question 5:
It is given that y is directly proportional to x2. When x has a certain value, y = 8.
Find the value of y when x is halved.
Revision
Direct and Inverse Proportions
Question 6:
y is proportional to x2 and y = 8 and x = 4.
a) Find the value of y when x = 10.
b) What happens to y when x is doubled.
Revision
Direct and Inverse Proportions
Question 7:
p is directly proportional to q3. When q has a certain value, p = 24. Find the value of p
when this value of q is doubled
Revision
Direct and Inverse Proportions
Question 8:
y is proportional to x 2 . x is increased by 100%. Find the percentage increase in y.
Revision
Direct and Inverse Proportions
Question 9:
It is given that y is directly proportional to x2. When x is reduced by 50%, calculate the
percentage decrease in y.
Revision
Direct and Inverse Proportions
Question 10:
The surface area, A cm2 of a container varies directly as the square of its radius r cm.
a) Describe the effect on A when r is halved.
b) Find the percentage increase in r when A increases by 300%.
Revision
Direct and Inverse Proportions
Question 11:
W is directly proportional to I2. I is increased by 150%.
Find the percentage increase in W.
Revision
Direct and Inverse Proportions
Question 12:
It is given that y varies inversely as the square of x and y = 16 when x = 2.
Find an expression for the relationship between y and x.
Revision
Direct and Inverse Proportions
Question 13:
y is inversely proportional to the square of x. It is know that y = 4 for a particular value
of x. Find the value of y when this value of x is halved.
Revision
Direct and Inverse Proportions
Question 14:
It is given that y is inversely proportional to x3, and that y = 640 for a particular value of
x. Find the value of y when this value of x is doubled.
Revision
Direct and Inverse Proportions
Question 15:
The resistance of a wire of constant length varies inversely to the square of its diameter.
The resistance is 23 ohms when the diameter is d mm. Find the resistance of the wire
when the diameter is halved.
Revision
Direct and Inverse Proportions
Question 16:
y is inversely proportional to x3. It is known that y = 32 for a particular value of x.
Find the value of y when this value of x is halved.
Revision
Direct and Inverse Proportions
Question 17:
m is inversely proportional to the square root of n.
At a certain value of n, the value of m is 20.
a) Write down an equation involving m and n.
b) Find the value of m when n is four times its original value.
Revision
Direct and Inverse Proportions
Question 18:
The period of a pendulum, T, varies inversely as the square root of the acceleration due
to gravity, g.
a) Write down an expression for T in terms of g, and a constant k.
b) Find the percentage change in T, when g is doubled.
Revision
Direct and Inverse Proportions
Question 19:
y is inversely proportional to x2. It is known that y = 500 for a particular x. Find the
value of y when this value of x is doubled.
Revision
Direct and Inverse Proportions
Revision Accomplished!