Proportion AQA Module 3

MAIN MENU 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 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

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

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?

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

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

Direct Proportion Involving squares, cubes and square roots

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 .......

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

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

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

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

Inverse Proportion

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

Time is inversely Proportional to the number of men t ∝

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

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

Inverse Proportion Involving squares, cubes and square roots

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

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