Number worksheet — GCSE Foundation

1.Simplify x⁷ × x⁴, giving your answer as a single power of x.

2.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.

3.Which of these units would be most appropriate to use when stating the mass of a small car?

4.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.

5.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

6.A tin of beans has a mass of 650 g. A bag of rice has a mass of 1.35 kg. Work out the total mass, in kilograms.

7.Work out −7 − (−3).

8.Put these three numbers in order of size, starting with the smallest: 3/8, 0.4, 0.35

9.Round 592.5 to the nearest 10.

10.Work out an estimate for 312 × 19, by rounding each number to 1 significant figure.

11.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

12.Write 260,000 in standard form.

13.A piece of ribbon is 2.4 metres long. Kim cuts 40 cm from it. Work out the length of ribbon left, in millimetres.

14.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.

15.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.