Ratio, proportion and rates of change worksheet — GCSE Higher

1.A map has a scale of 1 : 25 000. Two towns are 5 km apart in real life. Work out the distance between the towns on the map, in centimetres.

2.y is directly proportional to √x. When x = 25, y = 20. Construct the equation connecting x and y, then work out the value of x when y = 32.

3.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.

4.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.

5.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.

6.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.

7.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.

8.The cost, in pounds, of hiring a minibus is modelled against the number of passengers booked. A tangent to the cost graph at 20 passengers passes through the points (16, 184) and (24, 216). Work out the instantaneous rate at which the cost increases with each extra passenger, at 20 passengers.

9.Two quantities, P and Q, are in inverse proportion. A graph is drawn with P on the vertical axis and Q on the horizontal axis. Write down which description fits the shape of this graph.

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

11.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.

12.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.

13.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.

14.An Ordnance Survey map has a scale of 1 : 50 000. A cycle route measures 9.4 cm on the map. Work out the real length of the route, in kilometres.

15.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?