Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.

2.A candidate wants to estimate the instantaneous rate of change of a reservoir's water level, in metres, at t = 5 days after heavy rain began. The reservoir's water level is plotted against time, in days, since the rain began. The candidate uses the chord joining the points at t = 0 days and t = 20 days to estimate the rate of change at t = 5 days. Give a reason why this is likely to be a poor estimate.

3.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

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

5.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.

6.A car travels for 3 hours at an average speed of 80 km/h and then for 1 hour at an average speed of 40 km/h. Work out the average speed for the whole journey.

7.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.

8.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.

9.To make orange paint, red and yellow paint are mixed in the ratio 6:15. Write the amount of red paint as a fraction of the amount of yellow paint, in its simplest form.

10.Write 350 ml : 1.4 l as a ratio in its simplest form.

11.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

12.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.

13.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.

14.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.

15.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.