Number worksheet — GCSE Higher

1.Work out the reciprocal of (2 + 3)

2.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.

3.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

4.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

5.Work out the value of 2⁻²

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

8.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

9.Work out −4.5 + 2.8.

10.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

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

12.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.

13.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

14.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.

15.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.