Number worksheet — GCSE Foundation

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

2.Work out ⁴√16

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

4.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

5.Work out the value of 2⁻⁴

6.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

7.Simplify (y³)⁴, giving your answer as a single power of y.

8.A country has an area of 25,000,000 hectares. Write this area in standard form.

9.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

10.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

11.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

12.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

13.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

14.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.

15.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.