### GCSE Variation paper (H)

#### Year 10/11 maths revision

1. The force F on a mass is directly proportional (∝) to the acceleration 'a' of the mass
When a = 350, F = 850
a) Find a formula for F in terms of a.
b) Find F when a = 140

2. The resistance R (ohms) of a wire is directly ∝ to the length l (cm) of the wire
When l = 150, R = 750
a) Find R when l = 450

3. The energy E (Joules) of a gas is directly ∝ to it's temperature T ( °Kelvin).
When T = 280, E = 40
a) Find a formula for E in terms of T
b) Calculate T when E = 9

4. The energy (E) released when matter is converted to energy is ∝ to mass of that object (m).
When E = 1.0 × 1016 Joules, m = 0.111 kg
a) Find a formula for E in terms of m giving your answer in standard form
b) Calculate the mass, in kg when E is 1.8 million Joules

ANS

1. x is inversely proportional to y.
x = 5 when y = 12
a) Work out the value of x when y = 3
b) Work out the value of y when x = 4

2. The gravitational force F (Newtons) between two masses is inversely proportional to the square of the distance d between them.
When d = 8, F = 10
a) Find a formula for F in terms of d.
b) Calculate F when d = 10

3. The time T (hours), required to build a brick wall is inversely proportional to the number of men M laying bricks.
When 6 men are laying bricks the wall takes 4 hours to build.
a) Find the time taken if 8 men were building the wall.
b) If it took ¾ hour to build the wall how many men would there be?

4. The resistance R ohms of a wire is inversely proportional to the cross sectional area A cm2 of the wire.
When A = 0.1, R = 180
a) Find R when A = 0.09
b) Find A when R = 15

ANS

###### Inversely proportional to square  Menu

1. The time in minutes (T) for meals to be served at a busy restaurant is inversely proportional to the square of the number of waiters (W) working at that time.
It takes 20 minutes for meals to be served when 12 waiters are working.
a) Find an equation connecting T and W.

2. The force F (Newtons) between two point charges is inversely proportional to the square of the distance d between them.
If F = 2 × 10–10 N when d = 2 × 10–3 m
a) Find an expression for F in terms of d.
b) Calculate F when d = 4 × 10–3 m giving your answer in standard form

ANS

###### Proportional to the square  Menu

1. The mass m of a liquid in a cylindrical container is proportional to the square of the radius r
When r = 7, m = 16
a) Write an equation that shows how m varies with r
b) Find r when m = 9

ANS

###### Directly proportional to cubed  Menu

1. The mass of a solid sphere (M gm) is proportional to its radius (R cm) cubed.
When R = 6, M = 7560 gms
a) Find a formula for M in terms of R
b) Find the value of M when R = 5

ANS