Number worksheet — GCSE Higher

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

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

3.Write 5/6 as a decimal, showing clearly which digit recurs.

4.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

5.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

6.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

7.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

8.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

9.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

10.Work out −(−3)⁴ + (−3)³

11.Work out 6² − 4².

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

13.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

14.Write 0.875 as a fraction in its simplest form.

15.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.