Number worksheet — GCSE Higher

1.Simplify x⁶ ÷ x²

2.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

3.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

4.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

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

6.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

7.Simplify x⁷ × x⁴, giving your answer as a single power of x.

8.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

9.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

10.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

11.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

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

13.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

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

15.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.