Number worksheet — GCSE Higher

1.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

2.Simplify ⁴√(16a⁸b¹²)

3.Work out (5 + 2) × 3²

4.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

5.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.

6.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

7.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.

8.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

9.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

10.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

11.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

12.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

13.Work out (−6) + (−4) × 3

14.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

15.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.