Number worksheet — GCSE Higher

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

2.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

3.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.

4.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

5.Work out −4.5 + 2.8.

6.Simplify (3a²)² × (2a)³

7.Work out (−6) + (−4) × 3

8.Work out how many factors 100 has.

9.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.

10.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.

11.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

12.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

13.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

14.Which of these is written correctly in standard form?

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