Ratio, proportion and rates of change worksheet — GCSE Foundation

1.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.

2.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.

3.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.

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

5.An Ordnance Survey map has a scale of 1 : 50 000. A cycle route measures 9.4 cm on the map. Work out the real length of the route, in kilometres.

6.A straight-line graph shows the distance travelled, d kilometres, against the time taken, t hours, for a cyclist. The line passes through the origin and has a gradient of 18. Write down what the gradient of this line represents.

7.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.

8.A machine is bought for £8500. Its value depreciates by 6% each year. Work out the value of the machine after 3 years, to the nearest pound.

9.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?

10.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.

11.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.

12.An architect builds a scale model of a staircase before construction. The model is mathematically similar to the real staircase, at a scale of 1 : 10. The model covers a floor area of 0.4 m² on the plan. Work out the floor area the real staircase will cover, giving your answer in m².

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

14.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.

15.Two mathematically similar picture frames have perimeters 30 cm and 45 cm. The area of the smaller frame is 40 cm². Work out the area of the larger frame.