Number worksheet — GCSE Higher

1.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

2.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

3.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

4.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

5.Write ∛(x²) as a single power of x.

6.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.

7.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

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

9.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

10.Write down the symbol that makes this statement true: −2/3 ___ −5/6

11.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.

12.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

13.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

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 (−36) ÷ (−6) × 2