Number worksheet — GCSE Higher

1.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.

2.Last year a company made a profit of £5,200,000. Write this amount in standard form.

3.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

4.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

5.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

6.Simplify ⁴√(16a⁸b¹²)

7.Write 5/6 as a decimal, showing clearly which digit recurs.

8.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

10.2/3 of an amount of money is £30. Work out the amount.

11.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

12.Work out 35% of 180.

13.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

14.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

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