Number worksheet — GCSE Higher

1.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.

2.Write ∛(x²) as a single power of x.

3.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

4.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

5.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

6.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

7.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.

8.Work out (−2)³ + (−3)² − (−4)

9.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

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

11.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.

12.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

13.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.

14.Work out 3 + 4 × (−2).

15.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.