Number worksheet — GCSE Higher

1.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

2.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

3.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

4.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

5.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

6.Work out ∛(−27) + ∛8

7.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

8.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

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

10.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

11.Work out 3 × (−2)² − 5

12.Work out √25 + 4² − 12 ÷ 3

13.Work out 36 ÷ (2 × 3)

14.Work out √225 ÷ 3.

15.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.