Number worksheet — GCSE Higher

1.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.

2.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

3.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

4.Simplify √45.

5.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

6.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

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

8.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

9.Work out −(−3)⁴ + (−3)³

10.Write 90 as a product of its prime factors.

11.Round 0.006482 to 2 significant figures.

12.Work out ⁴√16

13.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

14.Simplify √8 + √18, giving your answer in the form k√2.

15.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.