Number worksheet — GCSE Higher

1.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

2.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

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

5.Work out 5⁰ + 5¹ + 5²

6.Work out the value of (√5)⁴

7.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

8.Work out the value of √(16 + 9)

9.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

10.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

11.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

12.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

13.Simplify (3a²)² × (2a)³

14.Work out ⁴√81

15.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.