Number worksheet — GCSE Higher

1.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

2.Simplify √8 + √18, giving your answer in the form k√2.

3.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

4.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.

5.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

6.Work out 3.7 × 24.

7.Write ∛(x²) as a single power of x.

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

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 restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

11.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

12.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

13.Estimate the value of √45, giving your answer to the nearest whole number.

14.Write 5,000,000 in standard form.

15.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.