Number worksheet — GCSE Higher

1.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

2.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

3.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

4.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

5.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.

6.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

7.Write 0.875 as a fraction in its simplest form.

8.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

9.4ˣ = 64. Work out the value of x.

10.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

11.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

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

13.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

14.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

15.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.