Number worksheet — GCSE Higher

1.Which of these is written correctly in standard form?

2.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

3.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.

4.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

5.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

6.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

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

8.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.

9.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

10.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

11.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

12.Find the missing number: 17 × ▢ = 391

13.Work out √225 ÷ 3.

14.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

15.Work out 3 × (−2)² − 5