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.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.
- 2.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.
- 3.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.
- 4.The density of a type of wood is 0.8 g/cm³. Work out the mass of a piece of this wood with a volume of 150 cm³.
- 5.A graph shows y plotted against x. The graph is a curve that gets closer to both axes but never touches them, and y decreases as x increases. Write down whether this graph could show direct proportion, inverse proportion, or neither.
- 6.A blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.
- 7.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
- 8.A ratio is 3 : 5. Write the first part of the ratio as a fraction of the whole.
- 9.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.
- 10.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.
- 11.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?
- 12.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.
- 13.£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.
- 14.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.
- 15.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.
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