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.
Calculator
Ratio, proportion and rates of change worksheet — GCSE Higher
MathsUKwww.geekhero.co.uk
- 1.y is directly proportional to √x. When x = 25, y = 20. Construct the equation connecting x and y, then work out the value of x when y = 32.
- 2.A scale model of a bridge is built at a scale of 1 : 120. The real bridge is 84 m long. Work out the length of the model, in centimetres.
- 3.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.
- 4.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.
- 5.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
- 6.A factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.
- 7.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.
- 8.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
- 9.A population of penguins on an island is 2400. The population is predicted to grow by 7% each year. Work out the predicted population after 2 years, to the nearest whole number.
- 10.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?
- 11.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.
- 12.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.
- 13.A map has a scale of 1 : 25 000. Two towns are 5 km apart in real life. Work out the distance between the towns on the map, in centimetres.
- 14.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.
- 15.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.
Build your own mix at the worksheet builder.