Number worksheet — GCSE Higher

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

2.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

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

4.Work out ∛64.

5.Write 12 as a product of its prime factors.

6.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

8.Work out 3³ + 2⁴.

9.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

10.Work out 3.7 × 24.

11.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

13.Simplify x⁶ ÷ x²

14.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

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.