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ProportionProportion OCR Module 9
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Direct Proportion involving Squares, Cubes & Roots Direct Proportion Inverse Proportion involving Squares, Cubes & Roots MAIN MENU
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Direct Proportion
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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
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Or... Wages = k x Hours k is the “constant of proportionality”
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If he works for 12 hours, he earns £72. What will he earn if he works 32 hours?
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Reverse Calculation If James earned £84, for how many hours did he work?
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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
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Direct Proportion Involving squares, cubes and square roots
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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
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Find a)the cost of a table 18cm wide b)The width of a table costing £882
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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
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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
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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
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Inverse Proportion
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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
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Time is inversely Proportional to Men t ∝t ∝
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t =t = t =t = If we have 20 men, m = 20 t =t = = 2 days
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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
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Inverse Proportion Involving squares, cubes and square roots
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What’s the difference? Essentially, these are similar to the problems seen in the previous section on Inverse Proportion. Try the questions overleaf
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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
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