Ratio, proportion and rates of change worksheet — GCSE Higher

1.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

2.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.

3.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

4.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.

5.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

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

7.Write 250 g : 2 kg as a ratio in its simplest form.

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

9.The value of a delivery van, in £, is plotted against its age, in years, since it was bought. At age 2 years, the gradient of the tangent to the graph is −950. What does this tell you about the van at age 2 years?

10.The number of subscribers to a streaming app, in thousands, is plotted against time, in months since launch. A tangent to the graph at t = 6 months has gradient 4.8. A tangent at t = 18 months has gradient 1.1. A manager claims the app is growing faster at 18 months than it was at 6 months. Work out how the growth rate has changed, and decide whether the manager is correct.

11.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.

12.A taxi journey of m miles costs C pounds, where C = 2.5m + 3. A driver says the ratio C : m is the same for every journey. Is the driver correct? Give a reason for your answer.

13.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.

14.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.

15.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.