1. Proportion
AQA Module 3

2. MAIN MENU Direct Proportion
Direct Proportion involving Squares, Cubes & Roots
Inverse Proportion
Inverse Proportion involving Squares, Cubes & Roots
MAIN MENU

3. Direct Proportion

4. There is Direct Proportion between two variables if one is a simple multiple of the other
E.g. “Jim’s wages are directly proportional to the hours he works”
The more hours he works, the more money he earns
Direct Proportion

5. Or... Wages = k x Hours k is the “constant of proportionality”

6. If he works for 12 hours, he earns £72
If he works for 12 hours, he earns £72. What will he earn if he works 32 hours?

7. If James earned £84, for how many hours did he work?
Reverse Calculation

8. Try these - y ∝ x If F = 20 when M = 5 If P = 150 when Q = 2
Find F when M =3
Find M when F = 28
If P = 150 when Q = 2
Find P when Q = 6
Find Q when P = 750
If R = 17.5 when T = 7
Find R when T = 9
Find T when R = 50
Try these - y ∝ x
Main Menu

9. Direct Proportion
Involving squares, cubes and square roots

10. Directly proportional to the square of .......
The cost of a square table is directly proportional to the square of its width.
The cost of table 10cm wide is £200
Directly proportional to the square of

11. Find
the cost of a table 18cm wide
The width of a table costing £882

12. F is directly proportional to M If F = 40 when M = 2
Find F when M =5
Find M when F = 250
P is directly proportional to Q If P = 100 when Q = 5
Find P when Q = 4
Find Q when P = 400
R is directly proportional to T If R = 96 when T = 4
Find R when T = 5
Find T when R = 24
Try these – y ∝ x²
Main Menu

13. P is directly proportional to Q If P = 400 when Q = 10
Find P when Q =4
Find Q when P = 50
T is directly proportional to S If T = 40 when S = 2
Find T when S = 6
Find S when T = 48
Try these – y ∝ x3
Main Menu

14. Y is directly proportional to √X If Y = 36 when X = 144
Find Y when X =81
Find X when Y =147
T is directly proportional to √S If T = 4 when S = 64
Find T when S = 144
Find S when T = 7
Try these – y ∝ √x
Main Menu

15. Inverse Proportion

16. There is Inverse Proportion between two variables if one increases at the rate at which the other decreases
E.g. “It takes 4 men 10 days to build a brick wall. How many days will it take 20 men?”
The more men employed, the less time it takes to build the wall
Inverse Proportion

17. Time is inversely
Proportional to the
number of men
t ∝

18. t =
If we have 20 men, m = 20
t =
t =
= 2 days

19. M is inversely proportional to R If M = 9 when R = 4
Find M when R =2
Find R when M = 3
T is inversely proportional to m If T = 7 when m = 4
Find T when m = 5
Find m when T = 56
W is inversely proportional to x. If W = 6 when x = 15
Find W when x = 3
Find x when W = 10
Try these – y ∝ 1/x
Main Menu

20. Inverse Proportion
Involving squares, cubes and square roots

21. Essentially, these are similar to the problems seen in the previous section on Inverse Proportion.
Try the questions overleaf
What’s the difference?

22. F is inversely proportional to M If F = 20 when M = 3
Find F when M =5
Find M when F = 720
P is inversely proportional to √Q If P = 20 when Q = 16
Find P when Q = 1.25
Find Q when P = 40
Try these – y ∝ 1/xn
Main Menu