Number worksheet — GCSE Higher

1.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

2.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

3.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

4.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

5.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

6.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

7.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

8.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

9.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

10.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

11.Work out 35% of 180.

12.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

13.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

14.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

15.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.