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Proportion

Proportion. OCR Module 9. Direct Proportion. Direct Proportion involving Squares, Cubes & Roots. Inverse Proportion. Inverse Proportion involving Squares, Cubes & Roots. MAIN MENU. Direct Proportion. There is Direct Proportion between two variables if one is a simple multiple of the other

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Proportion

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  1. Proportion OCR Module 9

  2. 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. What will he earn if he works 32 hours?

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

  8. If F = 20 when M = 5 • 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. 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 M² If F = 40 when M = 2 • Find F when M =5 • Find M when F = 250 • P is directly proportional to Q² If P = 100 when Q = 5 • Find P when Q = 4 • Find Q when P = 400 • R is directly proportional to T² 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 Q³ If P = 400 when Q = 10 • Find P when Q =4 • Find Q when P = 50 • T is directly proportional to S³ 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 Men t∝

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

  19. M is inversely proportional to RIf 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 M² 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 = 0.64 • Find Q when P = 40 Try these – y ∝ 1/xn Main Menu

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