Bearings, Constructions & Scale Drawings (CIE IGCSE Maths: Core)

A field, ABC, is in the shape of a triangle.
AC = 500m and BC = 650m.

Using a ruler and compasses only, complete the scale drawing of the field ABC.
Leave in your construction arcs.
Use a scale of 1 cm to represent 100m.
The side AB has been drawn for you.

The scale drawing shows the positions of two towns, and .
The scale is 1 centimetre represents 10 kilometres.

Work out the actual distance between town and town .

............................................ km [2]

The bearing of from is 105°.
Find the bearing of from .

Using a ruler and pair of compasses only, construct a triangle with sides 5cm, 8cm and 10 cm.
Leave in your construction arcs.

In triangle = 7cm and = 5 cm.

Using a ruler and compasses only, construct triangle .

has been drawn for you.

The scale drawing shows a rock, .

The scale is 1 centimetre represents 30 metres.

A lighthouse, , is 210m from , on a bearing of 125°.

On the diagram, mark the position of .

The scale drawing shows the positions of a lighthouse  and a ship 

The scale is 1 centimetre represents 5 kilometres.

Work out the actual distance, in kilometres, from to .

........................... km [2]

Measure the bearing of from .

[1]

Another ship, , is  from on a bearing of .

Mark and label the position of  on the scale drawing.

[2]

The bearing of a lighthouse from a coastguard station is 113°.

Work out the bearing of the coastguard station from the lighthouse.

The scale drawing shows the positions of two towns, Yatterford () and Rexley (), on a map.
The scale is 1 centimetre represents 15 kilometres.

Write the scale of the map in the form 1: .

1 : ..................................... [2]

The bearing of Bartown from Whitestoke is 073°.

Work out the bearing of Whitestoke from Bartown.

Point is 36 km from point on a bearing of 140°.

Using a scale of 1 centimetre to represent 4 kilometres, mark the position of .

Scale: 1cm to 4 km

The scale drawing shows a map of Kingswood Park.
There are two straight paths and one circular path.
The scale is 1cm represents 200m.

The scale drawing shows the positions of town and town .
The scale is 1 cm represents 12 kilometres.

Find the actual distance between town and town .

........................................... km

Town is 72 km from town and 96 km from town .
On the scale drawing, construct the position of town .

A circular garden has diameter 11.4 m.

Draw the garden accurately, using a scale of 1cm represents 1.5 m.

Scale: 1cm to 1.5m

On a map, the distance between two towns is 9.6cm.
The scale of the map is 1 : 50000.

Work out the actual distance between the two towns in kilometres.

........................................... km 

The scale drawing shows the positions of a rock, , and a statue, , on a map.
The scale is 1 centimetre represents 6 metres.

Work out the actual distance between and .

The scale drawing shows the positions of two buoys,and , in the sea.
The scale is 1 centimetre represents 20 kilometres.

Work out the actual distance between buoy and buoy .

.............................................. km [2]

The scale drawing shows the positions of town and town .

The scale is 1 centimetre represents 12 kilometres.

Measure the bearing of town from town

The bearing of town from town is 245°.

Work out the bearing of town from town .

The diagram shows three towns, and .

The bearing of town from town is 090°.

and are two sides of a regular decagon.

Work out angle .

Angle = ................................................... [3]

The scale drawing shows town , town and town on a map.
There is a straight road between town and town .
The scale of the map is 1 centimetre represents 8 kilometres.

Measure the bearing of town from town .

Work out the actual distance, in kilometres, between town and town .

............................................... km

Write the scale of the map in the form 1 : .

1 : ................................................... 

A straight road from town is on a bearing of 246°.
It meets the road from town to townat point .

On the map, draw the road from town to point .
Label the position of .

Sammy leaves town and travels to town at a constant speed of 75 km/h.

.................... h ................. min [3]

The scale drawing shows the positions of an airport () and a train station () on a map.

The scale is 1 centimetre represents 2 kilometres.

Work out the actual distance, in kilometres, of the train station from the airport.

.............................. km 

Measure the bearing of the airport from the train station.

The bus station is not shown on the map.
The bearing of the bus station from the train station is 318°.

Work out the bearing of the train station from the bus station.

The scale drawing shows the positions of three towns  and  on a map.
The scale is 1 centimetre represents 10 kilometres.

Work out the actual distance between town  and town .

.............................. km 

Measure the bearing of town from town .

[1]

Show how to use your answer to part (b)(i) to find the bearing of town  from town .

[1]

Town  is 96km from town  on a bearing of 100°.

Mark the position of town on the map.

[2]

Jez drives from town to town  in hours.

.......................... km/h [2]