Number worksheet — GCSE Higher

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

2.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

3.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

4.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

5.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

6.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?

7.Find the missing number: 17 × ▢ = 391

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

9.Simplify x⁷ × x⁴, giving your answer as a single power of x.

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

11.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

12.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

13.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

14.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

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