Number worksheet — GCSE Higher

1.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

2.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.

3.Work out 36 ÷ (2 × 3)

4.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

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

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

7.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

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

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

10.Expand and simplify √3(2 + √12).

11.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

12.Work out the value of (√5)⁴

13.Work out 100 − 4 × 5²

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

15.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?