Number worksheet — GCSE Higher

1.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

2.4ˣ = 64. Work out the value of x.

3.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

4.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

5.Work out 5/6 × 2/9, giving your answer in its simplest form.

6.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

7.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

8.Round 0.006852 to 2 significant figures.

9.Work out the value of √49 + ∛27

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

11.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

12.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

13.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

14.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

15.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.