Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A concrete block exerts a force of 45 N on the ground through a base with an area of 0.05 m². Work out the pressure on the ground, in N/m².

2.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.

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

4.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

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

6.Write 3 hours 45 minutes as a decimal number of hours.

7.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.

8.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.

9.A garden centre sells two mathematically similar sacks of grass seed. The amount of lawn a sack can treat is proportional to the volume of seed inside it. The smaller sack is 20 cm tall and treats a lawn of area 30 m². The larger sack is 40 cm tall. A gardener needs to treat a lawn with an area of 500 m² using only the larger sacks. Work out the minimum number of larger sacks needed.

10.Aisha invests £3200 in Account A, which pays 5% compound interest each year. She also invests £3200 in Account B, which pays 3% simple interest each year. Work out how much more Account A is worth than Account B after 2 years.

11.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.

12.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.

13.Two scale plans of the same football pitch are drawn: Plan A has a scale of 1 : 1000 and Plan B has a scale of 1 : 200. A pitch length is 8 cm on Plan A. Work out the length of the same pitch on Plan B, in centimetres.

14.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.

15.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.