Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.

2.1 litre = 100 centilitres. Work out how many centilitres there are in 6 litres.

3.Square P has sides of length 3 cm. Square Q has sides of length 12 cm. Write the ratio of the area of square P to the area of square Q in its simplest form.

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

5.Write 3/4 as a percentage.

6.A population of penguins on an island is 2400. The population is predicted to grow by 7% each year. Work out the predicted population after 2 years, to the nearest whole number.

7.A cookery class lasts 45 minutes. A double lesson at school lasts 2 hours. Write the length of the cookery class as a fraction of the length of the double lesson. Give your answer in its simplest form.

8.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?

9.A water butt is being filled from a hosepipe at a constant rate while a small leak drains water out at a constant rate, giving a constant net rate of change. The volume of water in the butt, V litres, is shown on a straight-line graph against time, t minutes. The line passes through the points (5, 20) and (15, 60). The butt is empty at t = 0. Work out how many minutes it takes to reach a volume of 100 litres.

10.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.

11.Two mathematically similar oil drums have a length scale factor of 3 from the smaller drum to the larger drum. Work out the volume scale factor from the smaller drum to the larger drum.

12.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.

13.y is directly proportional to x, and y = 7x. Work out the value of x when y = 35.

14.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.

15.Two straight-line graphs represent y = 2x and y = 5x. For the same value of x, where x ≠ 0, write down the ratio of the y-value on the first graph to the y-value on the second graph, in its simplest form.