Number worksheet — GCSE Higher

1.√700 lies between which two consecutive integers?

2.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

3.Work out (5 + 2) × 3²

4.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

5.Round 592.5 to the nearest 10.

6.Simplify √45.

7.Work out (−2)² − 3

8.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

9.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.

10.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

11.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

12.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.

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

14.Write 5,000,000 in standard form.

15.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.