Number worksheet — GCSE Higher

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

2.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

3.Find the missing number: ▢ ÷ 15 = 24

4.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

5.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

6.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

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

8.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

9.A country has an area of 25,000,000 hectares. Write this area in standard form.

10.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

11.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

12.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

13.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

14.Work out (2/3)² + (1/2)². Give your answer as a fraction.

15.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.