Ratio, proportion and rates of change worksheet — GCSE Higher

1.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

2.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

3.A hiker's distance from the start of the trail, in kilometres, is plotted against time, in minutes, since she set off. At t = 45 minutes she stops to rest, so her distance from the start is neither increasing nor decreasing at that instant. Which statement about the tangent to the distance–time graph at t = 45 minutes is correct?

4.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.

5.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.

6.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.

7.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.

8.A mobile phone tariff is shown on a straight-line graph with the monthly cost, C pounds, on the vertical axis and the amount of data used, g gigabytes, on the horizontal axis. The line passes through (0, 10) and (8, 26). Work out the gradient and say what it represents.

9.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.

10.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

11.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.

12.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

13.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.

14.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

15.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.