Number worksheet — GCSE Higher

1.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

2.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

3.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

4.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

5.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

6.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

7.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

8.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.

9.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

10.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

11.Simplify x⁶ ÷ x²

12.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

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

14.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.

15.Simplify (3a²)² × (2a)³