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.
Non-calculator
Ratio, proportion and rates of change worksheet — GCSE Foundation
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- 1.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
- 2.Two mathematically similar logos are printed on a poster. They have areas 20 cm² and 45 cm². Nadia says that the length scale factor from the smaller logo to the larger logo is 45 ÷ 20 = 2.25. Give a reason why Nadia is incorrect, and work out the correct length scale factor.
- 3.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
- 4.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?
- 5.A tin of beans has a mass of 400 g. A tin of soup has a mass of 500 g. Write the mass of the tin of beans as a fraction of the mass of the tin of soup, giving your answer in its simplest form.
- 6.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
- 7.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
- 8.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.
- 9.1 litre = 100 centilitres. Work out how many centilitres there are in 6 litres.
- 10.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.
- 11.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?
- 12.Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.
- 13.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
- 14.A section of a kitchen wall has an area of 45,000 cm². Work out the area of this section in m².
- 15.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
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