Number worksheet — GCSE Higher

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

2.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.

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

4.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

5.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

6.Which of these statements about −0.7 and −0.25 is true?

7.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

8.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

9.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

10.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

11.Work out 35% of 180.

12.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.

13.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

14.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

15.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.