Number worksheet — GCSE Higher

1.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

2.Work out the exact value of √(2² + 3²)

3.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

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

5.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

7.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

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

9.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

10.Write 0.36 as a fraction in its simplest form.

11.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

12.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

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

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

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.