Ratio, proportion and rates of change worksheet — GCSE Higher

1.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.

2.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.

3.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.

4.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.

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

6.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.

7.Two mathematically similar cubes have edge lengths 2 cm and 6 cm. Write the ratio of the volume of the smaller cube to the volume of the larger cube in its simplest form.

8.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.

9.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.

10.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.

11.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.

12.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.

13.A shop's number of online orders is proportional to its number of in-store orders. Last month there were 45 in-store orders and 180 online orders. Write the ratio of online orders to in-store orders, in its simplest form.

14.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?

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