Number worksheet — GCSE Higher

1.Expand and simplify √3(2 + √12).

2.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

3.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

4.Round 592.5 to the nearest 10.

5.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

6.Work out the reciprocal of (2 + 3)

7.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

8.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

9.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.

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

11.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

12.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

13.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

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

15.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.