Number worksheet — GCSE Higher

1.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

2.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

3.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

4.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.

5.Write 90 as a product of its prime factors.

6.Work out the value of √(16 + 9)

7.Work out √144 − 2 × 3 + √25

8.Work out √25 + 4² − 12 ÷ 3

9.Work out 5/6 × 2/9, giving your answer in its simplest form.

10.Work out the value of 6² − 4³.

11.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

12.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

13.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

14.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

15.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.