Number worksheet — GCSE Higher

1.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

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

3.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

4.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

5.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

6.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

7.Work out 10% of 30% of £200.

8.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

9.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

10.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

11.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.

12.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

13.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

14.Round 0.006482 to 2 significant figures.

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