Number worksheet — GCSE Higher

1.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.

2.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

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

4.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

5.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.

6.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

7.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

8.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

9.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

10.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

11.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.

12.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

13.Work out 10% of 30% of £200.

14.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

15.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³