Number worksheet — GCSE Higher

1.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.

2.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

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

4.2/3 of an amount of money is £30. Work out the amount.

5.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

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

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

8.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

9.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.

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

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.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.

13.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.

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

15.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%