Number worksheet — GCSE Higher

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

2.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

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

4.4ˣ = 64. Work out the value of x.

5.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

6.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

7.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

8.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

9.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.

10.Work out the value of √49 + ∛27

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

12.Work out (−6) + (−4) × 3

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

14.Work out 3 × (−2)² − 5

15.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.