Number worksheet — GCSE Higher

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

2.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

3.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

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

5.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

6.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

7.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

8.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

9.Work out ∛64.

10.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

11.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

12.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

13.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.