Number worksheet — GCSE Higher

1.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

2.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.

3.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

4.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

5.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

6.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

7.Write down the symbol that makes this statement true: −2/3 ___ −5/6

8.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

9.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

10.Simplify √45.

11.Simplify x⁶ ÷ x²

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

13.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

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

15.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.