Number worksheet — GCSE Higher

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

2.Work out √144 − 2 × 3 + √25

3.Simplify (x⁻²)³, giving your answer as a fraction.

4.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.

5.Work out −(−3)⁴ + (−3)³

6.Work out the value of (1/3)⁻²

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

8.Work out 6² − 4².

9.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

10.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

11.Work out ⁴√81

12.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

13.Work out the value of 2⁻⁴

14.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.

15.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.