Number worksheet — GCSE Higher

1.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

2.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

3.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

4.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

5.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

6.Expand and simplify √3(2 + √12).

7.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

8.Work out 3 × (−2)² − 5

9.Work out the exact value of √(2² + 3²)

10.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.

11.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

12.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

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

14.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.

15.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.