Number worksheet — GCSE Higher

1.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

2.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

3.Work out ∛64.

4.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

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

6.Work out the value of (√5)⁴

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

8.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?

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.Round 0.006852 to 2 significant figures.

11.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.

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

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

14.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

15.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.