Number worksheet — GCSE Higher

1.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

2.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

3.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

4.Write 0.06 as a fraction in its simplest form.

5.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

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

7.Simplify x⁶ ÷ x²

8.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

9.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

10.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

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

12.Work out ∛64.

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

15.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?