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 watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.
- 2.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?
- 3.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.
- 4.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.
- 5.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.
- 6.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
- 7.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.
- 8.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.
- 9.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 10.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
- 11.A window cleaner charges a call-out fee plus an amount per window. The total charge, C pounds, is shown on a straight-line graph against the number of windows cleaned, w. The line passes through the points (2, 14) and (6, 26). Work out the gradient of the line.
- 12.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
- 13.y is directly proportional to x, and y = 7x. Work out the value of x when y = 35.y = 7x
- 14.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.
- 15.Two scale plans of the same football pitch are drawn: Plan A has a scale of 1 : 1000 and Plan B has a scale of 1 : 200. A pitch length is 8 cm on Plan A. Work out the length of the same pitch on Plan B, in centimetres.
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