Number worksheet — GCSE Higher

1.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

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

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

4.Work out 4368 ÷ 12.

5.Work out 3³ + 2⁴.

6.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

7.Round 0.006482 to 2 significant figures.

8.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

9.Work out (−2)³ + (−3)² − (−4)

10.Work out ⁴√81

11.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

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

13.Simplify √45.

14.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

15.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.