Number worksheet — GCSE Higher

1.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

2.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

3.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

4.Work out 35% of 180.

5.Round 0.006482 to 2 significant figures.

6.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

7.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

8.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.

9.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

10.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.

11.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

12.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

13.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

14.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

15.Given that 2⁵ = 32, work out 2⁶.