Ratio, proportion and rates of change worksheet — GCSE Higher

1.A charity fun run raises money through entry fees and donations. Entry fees raise £1,260, which is 60% of the total amount raised. Work out how much money was raised through donations.

2.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.

3.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.

4.A lorry is carrying a load of mass m tonnes. Given that 1 tonne = 1000 kg, write down an expression for the mass of the load in kilograms.

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

6.The number of euros, e, received is directly proportional to the number of pounds, p, exchanged. Exchanging £40 gives 46 euros. Work out how many euros are received for £65, giving your answer to the nearest euro.

7.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.

8.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.

9.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

10.Paint costs £14.40 for every 20 m² of wall it covers. Assuming the same rate, work out the cost of the paint needed to cover 56 m² of wall.

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

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

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.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.

15.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².