Number worksheet — GCSE Higher

1.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?

2.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

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

4.Write 0.325 as a fraction in its simplest form.

5.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

7.Work out 5/6 × 2/9, giving your answer in its simplest form.

8.Given that 2⁵ = 32, work out 2⁶.

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

10.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

11.Work out the value of 2⁻⁴

12.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

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

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

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