Printable · GCSE Higher · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Higher
Fifteen questions across the ratio, proportion and rates of change statements at Higher 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 Higher
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- 1.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
- 2.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?
- 3.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 4.A shop's takings were £4500 in May. In June the takings fell by £900. Write the June takings as a fraction of the May takings, in its simplest form.
- 5.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.
- 6.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.
- 7.A textbook is reduced from £60 to £45. Work out the percentage reduction.
- 8.Write 400 g : 1.5 kg as a ratio in its simplest form.
- 9.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.
- 10.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
- 11.A cyclist's speed, in metres per second, is plotted against time, in seconds, since she sets off. Which statement correctly pairs the gradient of a tangent to this graph, and the area between the graph and the time-axis, with what each one represents?
- 12.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.
- 13.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.
- 14.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
- 15.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.
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