Number worksheet — GCSE Higher

1.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

2.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

3.Given that 2⁵ = 32, work out 2⁶.

4.Work out (−2)² − 3

5.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

6.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.

7.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

8.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

9.Work out √25 + 4² − 12 ÷ 3

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.Work out 3³ + 2⁴.

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

13.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

14.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

15.Simplify 2³ × 2⁴, giving your answer as a single power of 2.