Number worksheet — GCSE Higher

1.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

2.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

3.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

4.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

5.Write 0.06 as a fraction in its simplest form.

6.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?

7.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

8.Work out 3 × (−2)² − 5

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

10.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

11.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

12.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

13.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

14.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

15.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%