Number worksheet — GCSE Higher

1.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

2.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

3.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

4.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

5.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

6.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

7.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.

8.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

9.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

10.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

11.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

12.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

13.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.

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

15.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.