Number worksheet — GCSE Higher

1.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

2.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

3.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

4.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

5.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.

6.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.

7.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

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

9.Work out the value of √(16 + 9)

10.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

11.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

12.Work out 10% of 30% of £200.

13.4ˣ = 64. Work out the value of x.

14.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

15.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.