Ratio, proportion and rates of change worksheet — GCSE Higher

1.The height of a candle, in cm, is measured as it burns: t = 0 min, height = 20.0; t = 3 min, height = 18.7; t = 5 min, height = 17.5; t = 6 min, height = 16.6; t = 7 min, height = 15.4; t = 9 min, height = 13.4. Which pair of readings gives the best estimate of the instantaneous rate of change of the height at t = 6 minutes, and why?

2.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

3.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.

4.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

5.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.

6.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

7.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

8.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.

9.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

10.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.

11.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.

12.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.

13.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.

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.In a fruit drink, cranberry juice and apple juice are mixed in the ratio 3:7. Write the amount of apple juice as a fraction of the amount of cranberry juice, in its simplest form.