Number worksheet — GCSE Higher

1.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.

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

3.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

4.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

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

6.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

7.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

8.Given that 2⁵ = 32, work out 2⁶.

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

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

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.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

13.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

14.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

15.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.