Ratio, proportion and rates of change worksheet — GCSE Higher

1.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

2.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

3.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

4.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.

5.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

6.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.

7.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.

8.The cost of manufacturing a spherical container is proportional to the cube of its radius. A container of radius 3 cm costs £54 to manufacture. Construct the equation connecting cost C and radius r, then work out the cost of a container of radius 5 cm.

9.A plumber charges a call-out fee plus an hourly rate. The total charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (2, 70) and (5, 130). Work out the call-out fee, in pounds.

10.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.

11.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.

12.The speed of a car is given by v = d ÷ t. A car travels 180 km in 3 hours. Work out the average speed of the car in km/h.

13.A graph shows y plotted against x. The graph is a curve that gets closer to both axes but never touches them, and y decreases as x increases. Write down whether this graph could show direct proportion, inverse proportion, or neither.

14.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

15.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.