Number worksheet — GCSE Higher

1.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

2.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

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

4.Find the missing number: ▢ ÷ 15 = 24

5.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

6.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

7.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

8.Work out ∛64.

9.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

10.Write down the reciprocal of 0.2

11.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

12.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

13.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

14.Simplify (3a²)² × (2a)³

15.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.