Inverse Proportion

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

EasyQuestion 1

[2 marks]

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 10.

MediumQuestion 2

[3 marks]

6 workers can build a wall in 10 days. How many days would it take 15 workers?

HardQuestion 3

[4 marks]

y is inversely proportional to x². When x = 2, y = 8. Find x when y = 0.5.

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About Inverse proportion in AQA GCSE

Two quantities are inversely proportional when one increases as the other decreases by the same factor. If one quantity doubles, the other halves. The product of the two quantities stays constant. The relationship can be written as y ∝ 1/x or y = k/x, where k is the constant of proportionality. Alternatively, xy = k (the product is always the same constant). Graphs of inversely proportional quantities are hyperbolas - curved lines that approach but never touch the axes. As x gets very large, y gets very small (and vice versa). Common examples include: speed and time for a fixed distance (faster speed means less time), number of workers and time to complete a job (more workers means less time), pressure and volume of a gas at constant temperature. To solve inverse proportion problems: find k by multiplying corresponding values, then use y = k/x. For example, if 4 workers take 6 days, k = 4 × 6 = 24, so workers × days = 24 always.