Bearings, Scale Drawing & Constructions (Edexcel IGCSE Maths A (Modular): Higher Unit 2): Exam Questions

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.

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

i) the real distance, in metres, of the hall from the post box,

ii) the bearing of the hall from the post box.

[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.

i) Work out the length of CD and AD on the scale drawing.

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

ii) Using a ruler and compasses only, complete accurately the scale drawing of the field.

[2]

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

The bearing of from is 147°. Find the bearing of 

i) from ,

[3]

ii) from .

[2]

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°.

i) The bearing of D from B is 038°.

 Find the bearing of C  from B.

[1]

ii) A is due east of B.

 Calculate the bearing of D  from A.

[5]