Number worksheet — GCSE Higher

1.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

2.Work out ⁴√16

3.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

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

5.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

6.Write 7/12 as a decimal, showing clearly which digit is recurring.

7.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

8.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

9.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

10.Write ∛(x²) as a single power of x.

11.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

12.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

13.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

14.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

15.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾