Ratio, proportion and rates of change worksheet — GCSE Higher

1.40% of a number is 12 more than 25% of the same number. Work out the number.

2.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

3.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.

4.A gardener mixes 300 ml of plant feed concentrate with 1.2 litres of water to make a spray. Write the ratio of concentrate to water in its simplest form.

5.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.

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

7.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?

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

9.Order these three values from smallest to largest: 3/8, 0.43, 41%.

10.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

11.A kettle uses 2.1 kWh of energy. A toaster uses 0.9 kWh of energy. Write the energy used by the kettle as a fraction of the energy used by the toaster, giving your answer in its simplest form.

12.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.

13.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

14.Write 400 g : 1.5 kg as a ratio in its simplest form.

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