Number worksheet — GCSE Higher

1.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.

2.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

3.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

4.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

5.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

6.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

7.Work out the value of √(16 + 9)

8.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

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

10.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

11.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

12.Simplify x⁶ ÷ x²

13.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

14.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

15.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.