Number worksheet — GCSE Higher

1.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

2.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

3.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

4.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

5.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

6.Simplify (3a²)² × (2a)³

7.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

8.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.

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

10.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

11.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

12.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

13.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

14.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

15.Round 0.006852 to 2 significant figures.