Direct and Inverse Proportion. Direct Proportion Example: C is directly proportional to t We are told that when C = 70, t = 14 We can write C t So C =

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Presentation transcript:

Direct and Inverse Proportion

Direct Proportion Example: C is directly proportional to t We are told that when C = 70, t = 14 We can write C t So C = kt where k is a constant To work out k:- Since C = 70 when t = 14, 70 = k x 14 So k = 5 So the formula is C = 5t (a) When t = 5, what is C? (b) When C = 280, what is t?

Direct Proportion Example: A is directly proportional to r squared We are told that when r = 2, A = 68 We can write A r So A = kr To find k: We know that when r = 2, A = 68 So 68 = 2 x k So k = 68 divided by 4 = 17 So the formula is A = 17r (a) What is A when r is 3? (b) What is r when A is

Inverse Proportion M is inversely proportional to R If M = 9 and R =4, find a formula connecting M and R (a) Find M when R = 2 (b) Find R when M = 3

Inverse Proportion P varies inversely with the square of Q If P is 4 when Q is 5, find a formula connecting P and Q (a) work out P when Q is 10 (b) work out Q when P is 25

y is directly proportional to the cube of x. When x = 2, y = 64. (a) Find an expression for y in terms of x. (b) Hence or otherwise, GCSE Grade A Question

GCSE Grade A/A* Question The force, F, between two magnets is inversely proportional to the square of the distance, x, between them. When x = 3, F = 4. (a)Find an expression for F in terms of x. (b)Calculate F when x = 2. (c)Calculate x when F = 64.