Number worksheet — GCSE Higher

1.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

2.Write 0.005 in standard form.

3.Work out (−2)³ + (−3)² − (−4)

4.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

5.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

6.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

7.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

8.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

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

10.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

11.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

12.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

13.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.

14.Work out the value of √(16 + 9)

15.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.