Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

2.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.

3.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

4.Jamal invests £600 in a savings account paying 3% simple interest per year. Work out the total amount in the account after 4 years.

5.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.

6.A rectangular room is drawn on a plan with a scale of 1 : 50. On the plan, the room measures 8 cm by 6 cm. Work out the real area of the room, in square metres.

7.The exchange rate is £1 = €1.15. Convert £200 to euros.

8.A savings account pays 3.5% compound interest each year. Bilal invests £1200. Work out how much interest, in total, he earns after 2 years, to the nearest penny.

9.Write 45 minutes : 2 hours as a ratio in its simplest form.

10.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.

11.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.

12.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.

13.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

14.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.

15.Write 3 hours 45 minutes as a decimal number of hours.