Number worksheet — GCSE Higher

1.Simplify √8 + √18, giving your answer in the form k√2.

2.Simplify ⁴√(16a⁸b¹²)

3.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.

4.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

5.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

6.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

7.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

8.Work out the value of (1/3)⁻²

9.Simplify (x⁻²)³, giving your answer as a fraction.

10.Work out (−6) + (−4) × 3

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

12.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

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.Work out √225 ÷ 3.

15.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.