Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Triangle ABC is mathematically similar to triangle PQR, with angle B corresponding to angle Q. Work out the value of tan(angle Q).

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

3.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

4.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.

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

6.Two mathematically similar logos are printed on a poster. They have areas 20 cm² and 45 cm². Nadia says that the length scale factor from the smaller logo to the larger logo is 45 ÷ 20 = 2.25. Give a reason why Nadia is incorrect, and work out the correct length scale factor.

7.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.

8.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.

9.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.

10.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.

11.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.

12.Two mathematically similar tins have heights 8 cm and 12 cm. Jayden says that the volume of the larger tin is 1.5 times the volume of the smaller tin. Give a reason why Jayden is incorrect, and work out the correct volume scale factor.

13.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

14.A straight-line graph shows the cost, C pounds, of buying n litres of paint. The line passes through the origin and through the point (5, 40). Work out the gradient of the line.

15.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.