Number worksheet — GCSE Higher

1.Write 12 as a product of its prime factors.

2.Work out the value of 2⁻⁴

3.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

4.A country has an area of 25,000,000 hectares. Write this area in standard form.

5.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

6.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.

7.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

8.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

9.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

10.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

11.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

12.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

13.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

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

15.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.