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.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

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.Work out (−2)³ + (−3)² − (−4)

5.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

6.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

7.Work out √25 + 4² − 12 ÷ 3

8.Work out ∛(−27) + ∛8

9.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

10.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

11.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

12.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

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

14.Simplify √45.

15.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.