Number worksheet — GCSE Higher

1.Work out the value of 6² − 4³.

2.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

3.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

4.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

5.Work out 6² − 4².

6.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.

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

8.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

9.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

10.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

11.Write 0.005 in standard form.

12.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

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

14.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

15.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.