Constructions, loci, bearings, plans and elevations – Year 11 GCSE maths test to download as PDF

The bearing of \(B\) from \(A\) is \(072^\circ\). \(C\) is 8 km due south of \(B\).

1. Work out the bearing of \(A\) from \(B\). (1 mark)
2. Work out the bearing of \(B\) from \(C\). (1 mark)
3. Explain how you know that angle \(ABC=108^\circ\). (2 marks)

A map has scale \(1:20\,000\).

1. A path is 6.5 cm long on the map. How long is it in kilometres? (2 marks)
2. A real distance of 2.4 km is shown on the map. How many centimetres is this? (2 marks)

A path \(AB\) is 5 m long. A flowerbed is the set of points within 3 m of the path.

1. Sketch the boundary of the flowerbed. (2 marks)
2. Work out the perimeter of the flowerbed to 1 decimal place. (2 marks)

Construct the perpendicular bisector of a line \(PQ\) of length 9 cm and describe it.

1. Describe the steps. (3 marks)
2. State a property of every point on the bisector. (1 mark)

A ship sails 15 km on a bearing of \(030^\circ\) and then 20 km on a bearing of \(120^\circ\).

1. Work out the distance of the ship from its starting point. (2 marks)
2. Work out the bearing of the ship from its starting point, to the nearest degree. (2 marks)