Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.

2.6 identical taps fill a paddling pool in 20 minutes. Each tap fills at the same steady rate. Work out how long 3 of these taps would take to fill the same pool.

3.Given that a is 40% of b, write the ratio a : b in its simplest form.

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

5.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?

6.A bag of potatoes has a mass of 3 kg. A bag of carrots has a mass of 5 kg. Write the mass of the potatoes as a fraction of the mass of the carrots.

7.Write the ratio 20 : 30 in its simplest form.

8.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.

9.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.

10.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.

11.Which of these ratios is equivalent to 2:3?

12.The ratio of two lengths is 0.6 : 1.5. Write this ratio in its simplest whole-number form.

13.x is 2/3 of y. Write the ratio x : y in its simplest form.

14.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.

15.A statue exerts a downward force of 68.4 N on its base, which has an area of 2.85 m². Work out the pressure that the statue exerts on its base, in N/m².