Number worksheet — GCSE Higher

1.Write 60 as a product of its prime factors, using index notation.

2.Work out √144 − 2 × 3 + √25

3.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.

4.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

5.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?

6.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

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

8.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

9.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.

10.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

11.Work out the value of √(16 + 9)

12.Work out (−3) × 4 + 2 × (−5)

13.Work out 36 ÷ (2 × 3)

14.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

15.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.