Number worksheet — GCSE Higher

1.Write 0.36 as a fraction in its simplest form.

2.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

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

4.Work out 5/6 × 2/9, giving your answer in its simplest form.

5.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.

6.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

7.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

8.Write 90 as a product of its prime factors.

9.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

10.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

11.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

12.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

13.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

14.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

15.Simplify 2³ × 2⁴, giving your answer as a single power of 2.