Number worksheet — GCSE Higher

1.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

2.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

3.2/3 of an amount of money is £30. Work out the amount.

4.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

5.Simplify (y³)⁴, giving your answer as a single power of y.

6.Simplify (3a²)² × (2a)³

7.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

8.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.

9.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

10.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

11.Given that 2⁵ = 32, work out 2⁶.

12.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.

13.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

14.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

15.Work out the value of 6² − 4³.