Number worksheet — GCSE Foundation

1.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

2.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

3.Write 200 as a product of its prime factors, using index notation.

4.Which one of these statements is true?

5.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.Using only 20p coins and 10p coins, and at least one of each, work out how many different ways there are to make exactly 60p. List the possibilities systematically.

8.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

9.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

10.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

11.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

12.Write down the value of 7⁰

13.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

14.Write these numbers in order, starting with the smallest: 3, −1, 0, −5

15.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.