Number worksheet — GCSE Higher

1.Simplify (x⁻²)³, giving your answer as a fraction.

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

3.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.

4.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

5.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

6.Work out 36 ÷ (2 × 3)

7.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

8.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

9.Simplify (y³)⁴, giving your answer as a single power of y.

10.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.

11.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?

12.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

13.Simplify √45.

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

15.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.