Number worksheet — GCSE Higher

1.Write 7/12 as a decimal, showing clearly which digit is recurring.

2.Work out 4368 ÷ 12.

3.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

4.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.

5.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

6.Write down the symbol that makes this statement true: −2/3 ___ −5/6

7.Work out ∛64.

8.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

9.Work out the value of 6² − 4³.

10.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

11.Write 60 as a product of its prime factors, using index notation.

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

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

14.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

15.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.