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.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

3.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

4.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

5.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

6.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

7.Bella's electricity supplier charges 28.5p per unit (kWh). Last month she used 340 units. Work out the total cost, giving your answer in pounds.

8.Work out 10% of 30% of £200.

9.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

10.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

11.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.

12.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

13.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

14.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

15.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.