Number worksheet — GCSE Higher

1.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

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

3.Find the missing number: 17 × ▢ = 391

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

5.Work out the value of (1/3)⁻²

6.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

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

8.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

9.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

10.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.

11.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

12.√700 lies between which two consecutive integers?

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

14.Simplify (y³)⁴, giving your answer as a single power of y.

15.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.