Ratio, proportion and rates of change worksheet — GCSE Higher

1.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

2.Two mathematically similar cylinders have volumes 64 cm³ and 216 cm³. Work out the ratio of the height of the smaller cylinder to the height of the larger cylinder, in simplest form.

3.Two mathematically similar garden ponds have surface areas of 12 m² and 27 m². The fencing needed to go around the smaller pond costs £96. Assuming the cost of fencing is proportional to the perimeter of the pond, work out the cost of fencing the larger pond.

4.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.

5.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?

6.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.

7.A printer's ink cartridge level, I millilitres, is plotted against the number of pages printed, p, and the points lie on a straight line. The line passes through (0, 24) and (300, 9). The printer has now printed 300 pages. Work out how many more pages it can print before the cartridge is empty.

8.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.

9.A car uses fuel at a constant rate. It uses 24 litres of fuel to travel 300 km. Assuming the same rate, work out how many litres of fuel are needed for a journey of 175 km.

10.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.

11.A gym charges members a joining fee plus a fixed amount per month. The total amount paid, C pounds, is shown on a straight-line graph against the number of months, m. The line passes through the points (3, 130) and (7, 210). Work out the total amount a member will have paid after 12 months.

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

13.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.

14.A smoothie recipe combines 350 cm³ of mango juice with 650 cm³ of orange juice. Work out the total volume of the smoothie in litres.

15.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.