1. ProportionProportion OCR Module 9

2. Direct Proportion involving Squares, Cubes & Roots Direct 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

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

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

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

8. Try these - y ∝ x 1. If F = 20 when M = 5 a.Find F when M =3 b.Find M when F = 28 2. If P = 150 when Q = 2 a)Find P when Q = 6 b)Find Q when P = 750 3. If R = 17.5 when T = 7 a)Find R when T = 9 b)Find T when R = 50 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

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

12. Try these – y ∝ x ² Main Menu 1. F is directly proportional to M² If F = 40 when M = 2 a.Find F when M =5 b.Find M when F = 250 2. P is directly proportional to Q² If P = 100 when Q = 5 a)Find P when Q = 4 b)Find Q when P = 400 3. R is directly proportional to T² If R = 96 when T = 4 a)Find R when T = 5 b)Find T when R = 24

13. Try these – y ∝ x 3 Main Menu 1. P is directly proportional to Q³ If P = 400 when Q = 10 a.Find P when Q =4 b.Find Q when P = 50 2. T is directly proportional to S³ If T = 40 when S = 2 a)Find T when S = 6 b)Find S when T = 48

14. Try these – y ∝ √x Main Menu 1. Y is directly proportional to √X If Y = 36 when X = 144 a.Find Y when X =81 b.Find X when Y =147 2. T is directly proportional to √S If T = 4 when S = 64 a)Find T when S = 144 b)Find S when T = 7

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

17. Time is inversely Proportional to Men t ∝t ∝

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

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

20. Inverse Proportion Involving squares, cubes and square roots

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

22. Try these – y ∝ 1/x n 1. F is inversely proportional to M² If F = 20 when M = 3 a.Find F when M =5 b.Find M when F = 720 2. P is inversely proportional to √Q If P = 20 when Q = 16 a)Find P when Q = 0.64 b)Find Q when P = 40 Main Menu