Number worksheet — GCSE Higher

1.Work out 6² − 4².

2.Work out the value of √49 + ∛27

3.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?

4.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

5.Work out 36 ÷ (2 × 3)

6.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

7.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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

9.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

10.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

11.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

12.Write 0.005 in standard form.

13.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

14.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

15.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.