Number worksheet — GCSE Higher

1.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

2.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

3.Work out (−3) × 4 + 2 × (−5)

4.Work out 35% of 180.

5.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

6.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?

7.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

8.Work out (−2)³ + (−3)² − (−4)

9.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

10.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

11.Simplify (3a²)² × (2a)³

12.Write 5/6 as a decimal, showing clearly which digit recurs.

13.Work out −(−3)⁴ + (−3)³

14.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

15.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.