Number worksheet — GCSE Higher

1.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

2.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

3.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

4.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

5.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

6.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

7.Which one of these statements is true?

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

9.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.

10.Write 5/6 as a decimal, showing clearly which digit recurs.

11.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.

12.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

13.3/5 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.

14.Find the missing number: 17 × ▢ = 391

15.Work out the value of √49 + ∛27