Number worksheet — GCSE Higher

1.Write down the symbol that makes this statement true: −2/3 ___ −5/6

2.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

3.A country has an area of 25,000,000 hectares. Write this area in standard form.

4.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

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

6.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.

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

8.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

9.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

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

11.Work out 5/6 × 2/9, giving your answer in its simplest form.

12.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

13.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

14.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.