Number worksheet — GCSE Higher

1.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

2.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

3.Write 0.35 as a fraction in its lowest terms.

4.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

5.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

6.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

7.Work out the value of (1/3)⁻²

8.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.

9.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

10.Work out √25 + 4² − 12 ÷ 3

11.Simplify (3a²)² × (2a)³

12.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

13.Work out how many factors 36 has.

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

15.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.