Bearings, Scale Drawing & Constructions (Edexcel IGCSE Maths)

The diagram shows the position of a lighthouse  and a harbour .

The scale of the diagram is 1 cm represents 5 km.

Work out the real distance between and .

Measure the bearing of from .

A boat  is 20km from  on a bearing of .

On the diagram, mark the position of boat with a cross (x).
Label it .

The diagram shows the positions of a lighthouse , a yacht  and a tanker  on a map.

Scale 1 cm represents 10 km

Measure the bearing of from .

The tanker, , sails 80km on a bearing of .

Find the distance, in km, between the tanker and the lighthouse when the tanker is closest to the lighthouse.

The diagram shows the position of two churches,  and .

Church  is on a bearing of  from church .
Church  is on a bearing of  from church .

In the space above, draw an accurate diagram to show the position of church .

Mark the position of church  with a cross ().
Label it .

Use ruler and compasses to construct the perpendicular bisector of the line segment  AB.
You must show all your construction lines.

The diagram shows the positions of three points, A, B and C, on a map.

The bearing of B from A is 070°

Angle ABC is 50°
AB = CB

Work out the bearing of C from A.

Use ruler and compasses to construct the bisector of angle .
You must show all your construction lines.

Use ruler and compasses only to construct the perpendicular bisector of the line .
You must show all your construction lines.

Using ruler and compasses only, construct the bisector of angle .
You must show all your construction lines.

The scale drawing shows the position of a hall and the position of a library.

Scale:  represents

A post box is  from the library on a bearing of 

Show the position of the post box on the scale drawing.
Mark the position with a cross  and label it 

Use your scale drawing to find

[2]

Use ruler and compasses to construct the perpendicular bisector of the line .
You must show all your construction lines.

The scale diagram below shows two cities, P and Q.

A plane departs from P at 09 47 and arrives at Q at 12 07.

Work out the average speed, in kilometres per hour, of the plane.

...................... km/h

Give one reason why your answer may be inaccurate.

The diagram shows the positions of three towns, Acton (), Barston () and Chorlton ().

Barston is 8 km from Acton on a bearing of .
Chorlton is 9km from Barston on a bearing of .

Find the bearing of Chorlton from Acton.
Give your answer correct to 1 decimal place.
You must show all your working.

The diagram shows the positions of three ships, and .

Ship is due north of ship .

The bearing of ship from ship is 120°

Calculate the bearing of ship from ship .
Give your answer correct to the nearest degree.

,  and  are three towns.

The bearing of  from  is 105°
The bearing of from B is 230°

The distance of  from  is 180 km.
The distance of  from  is 95 km.

Calculate the distance of  from .
Give your answer correct to 3 significant figures.

........................km 

and are ships.

is a port.

is due South of .
Angle

Work out the bearing of from .

A ship sails from to and then from to .

is 12 miles from , on a bearing of 080°

is 28 miles from , on a bearing of 155°

Work out the direct distance from to .

The diagram shows the positions of two towns, Amton and Bisham.

The bearing of Bisham from Amton is b°.
The bearing of Amton from Bisham is 6b°.

Calculate the 3-figure bearing of Amton from Bisham.

A, B, C and D are four towns.

B is 25 kilometres due East of A.
C is 25 kilometres due North of A.
D is 45 kilometres due South of A.

Work out the bearing of B from C.

Calculate the bearing of D from B.

The scale drawing shows two boundaries, AB and BC, of a field ABCD.
The scale of the drawing is 1 cm represents 8 m.

The boundaries CD and AD of the field are each 72 m long.

.......................................... cm [1]

The diagram shows the positions of three points , and in a field.

Show that is 118.1 m, correct to 1 decimal place.

Calculate angle .

Angle ................................................ 

The bearing of from is 147°.

Find the bearing of 

The diagram shows a field ABCD.
The bearing of B from A is 140°. 
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.

Find the bearing of D from B.

The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m, BD = 168 m and AD = 205.8 m.

Angle CBD = 106°.