Ratio, proportion and rates of change worksheet — GCSE Higher

1.Write 350 ml : 1.4 l as a ratio in its simplest form.

2.An ice-cream van's daily takings, in £, are modelled by a curve plotted against the average temperature that day, in °C. At a temperature of 22°C, the gradient of the tangent to this curve is 14. What does this gradient tell you about the takings at 22°C?

3.The population of a town, P thousand, is plotted against time, t years, since 2020. A tangent to the graph at t = 6 has gradient 2.5. What does this gradient represent?

4.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

5.A cleaning solution is made by mixing disinfectant and water in the ratio 1 : 9. Priti wants to make 6 litres of the solution in total. Work out how much disinfectant she needs.

6.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².

7.Write the ratio 5 : 8 in the form 1 : n.

8.An online shop's total number of orders received is recorded at the end of each day for five consecutive days: Day 1, 1,284 orders; Day 2, 1,509 orders; Day 3, 1,830 orders; Day 4, 2,296 orders; Day 5, 2,510 orders. Work out between which two consecutive days the average rate of increase in orders was greatest.

9.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.

10.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.

11.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.

12.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.

13.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

14.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.

15.A firework rocket's height above the ground, in metres, t seconds after launch, is modelled by h = 30t − 5t². Use a chord between t = 1 second and t = 3 seconds to estimate the instantaneous rate of change of the height at t = 2 seconds, in m/s.