Printable · GCSE Foundation · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Foundation
Fifteen questions across the ratio, proportion and rates of change statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Ratio, proportion and rates of change worksheet — GCSE Foundation
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- 1.A shop's profit, P pounds, is in direct proportion to the number of items sold, n. When 15 items are sold, the profit is £45. Write down the ratio n : P in its simplest form for this shop.
- 2.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.
- 3.Write 400 g : 1.5 kg as a ratio in its simplest form.
- 4.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 5.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.
- 6.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.
- 7.Triangle A and triangle B are mathematically similar. A side of triangle A is 4 cm long and the corresponding side of triangle B is 10 cm long. Write the ratio of the length in triangle A to the length in triangle B in its simplest form.
- 8.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
- 9.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.
- 10.A cyclist travels 45 km in 3 hours at a constant speed. Work out the cyclist's average speed, in km/h.
- 11.Simplify the ratio 45 : 30 : 75 to its simplest form.
- 12.A solution is made by dissolving 50 g of sugar in 200 g of water. Work out the concentration of sugar in the solution as a percentage.
- 13.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.
- 14.A film runs for 2.25 hours. Work out the length of the film in minutes.
- 15.Write 45 minutes : 2 hours as a ratio in its simplest form.
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