Number worksheet — GCSE Higher

1.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

2.Work out (−3) × 4 + 2 × (−5)

3.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

4.Work out √3 × √12, giving your answer as an integer.

5.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

6.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.

7.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

8.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.

9.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

10.Write 0.005 in standard form.

11.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.

12.Write ∛(x²) as a single power of x.

13.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

14.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.

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