Ratio, proportion and rates of change worksheet — GCSE Higher

1.Simplify the ratio 45 : 30 : 75 to its simplest form.

2.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.

3.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.

4.A sequence is defined by the iterative rule x_{n+1} = 0.5x_n + 20, with x_0 = 0. By working out x_1, x_2 and x_3, find the value that the sequence is approaching.

5.A car travels for 3 hours at an average speed of 80 km/h and then for 1 hour at an average speed of 40 km/h. Work out the average speed for the whole journey.

6.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.

7.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

8.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.

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

11.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.

12.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.

13.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.

14.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.

15.A metal cylinder has a mass of 356.5 g and a volume of 47 cm³. Work out the density of the cylinder, in g/cm³, to 1 decimal place.