Number worksheet — GCSE Higher

1.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

2.Work out the value of √49 + ∛27

3.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

4.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

5.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

6.Work out ∛(−27) + ∛8

7.Work out √3 × √12, giving your answer as an integer.

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.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.

10.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.

11.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.

12.Work out (−3) × 4 + 2 × (−5)

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

14.Which of these statements about −0.7 and −0.25 is true?

15.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.