Number worksheet — GCSE Higher

1.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.

2.Work out ∛(−27) + ∛8

3.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

4.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

5.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

6.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

7.Find the missing number: ▢ ÷ 15 = 24

8.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

9.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

10.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

11.Work out 100 − 4 × 5²

12.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

13.Write 60 as a product of its prime factors, using index notation.

14.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

15.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.