Number worksheet — GCSE Higher

1.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

2.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

3.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

4.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

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

6.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

7.Work out the value of 6² − 4³.

8.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

9.Write 5,000,000 in standard form.

10.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

11.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

12.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

13.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

14.Round 592.5 to the nearest 10.