Direct Proportion

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Preview AQA GCSE style questions on Direct proportion. Click "Show Solution" to see the step-by-step answer.

EasyQuestion 1

[2 marks]

y is directly proportional to x. When x = 4, y = 12. Find y when x = 7.

MediumQuestion 2

[3 marks]

The cost of printing leaflets is directly proportional to the number printed. 500 leaflets cost £45. Find the cost of 350 leaflets.

HardQuestion 3

[4 marks]

y is directly proportional to x². When x = 2, y = 20. Find x when y = 125.

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About Direct proportion in AQA GCSE

Two quantities are in direct proportion when they increase or decrease at the same rate. If one quantity doubles, the other doubles too. If one halves, the other halves. The relationship can be written as y ∝ x (y is proportional to x) or y = kx, where k is the constant of proportionality. The value of k can be found by dividing y by x for any pair of values. Graphs of directly proportional quantities are straight lines through the origin. The gradient equals the constant of proportionality k. If a straight line doesn't pass through the origin, the quantities are not directly proportional. Common examples include: cost and number of items (at a fixed price), distance and time (at constant speed), weight and volume (for uniform materials). To solve direct proportion problems: identify the constant relationship, set up the proportion equation, and solve. For example, if 5 items cost £20, then k = 20/5 = 4, so cost = 4 × number of items.