Number worksheet — GCSE Higher

1.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

2.Work out the exact value of √(2² + 3²)

3.Work out the value of 2⁻²

4.Which statement about the number 91 is correct?

5.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

6.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

7.Work out 3³ + 2⁴.

8.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

9.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

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

11.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

12.Write 60 as a product of its prime factors, using index notation.

13.Write 7/12 as a decimal, showing clearly which digit is recurring.

14.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

15.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.