Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.

2.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

3.A car travels 180 miles in 3 hours. A lorry travels 160 miles in 4 hours. Write the car's average speed as a fraction of the lorry's average speed, giving your answer in its simplest form.

4.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.

5.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

6.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.

7.Write the ratio 6a : 9a in its simplest form, where a is a positive number.

8.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.

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

10.A 5 kg bag of potatoes costs £4.50. Work out the cost per kilogram.

11.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?

12.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.

13.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.

14.A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.

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