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.
Ratio, proportion and rates of change worksheet — GCSE Foundation
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- 1.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.
- 2.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.
- 3.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.
- 4.3 pencils cost £1.20. Work out the cost of 7 pencils.
- 5.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.
- 6.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?
- 7.Write the ratio 4x : 6x in its simplest form, where x is a positive number.
- 8.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.
- 9.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
- 10.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.
- 11.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.
- 12.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
- 13.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
- 14.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
- 15.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
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