Number worksheet — GCSE Higher

1.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

2.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

3.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

4.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.

5.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.

6.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

7.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

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

9.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

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

11.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

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

13.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

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

15.Given that 2⁵ = 32, work out 2⁶.