Bearings, Constructions & Scale Drawings (Cambridge International IGCSE Mathematics): Exam Questions

Two towns, A and B, are shown on a map. The scale of the map is 1 cm to 3 km.

Find the actual distance between A and B.

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

In triangle ABC, BC = 7.6 cm and AC = 6.2 cm.

Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The side AB has been drawn for you.

The diagram shows the positions of three cities, Geneva (G), Budapest (B) and Hamburg (H).

The bearing of Budapest from Hamburg is 133°.

Find the bearing of Hamburg from Budapest.

In triangle $PQR,QR$ = 10 cm and $PR$ = 11 cm.

Using a ruler and compasses only, construct triangle $PQR$. The line $PQ$ has been drawn for you.

Two towns, A and B, are shown on a map.

Measure the bearing of B from A.

Extract:

Two towns, A and B, are shown on a map.

Calculate the bearing of A from B. You must show all your working.

In triangle ABC, BC = 7.6 cm and AC = 6.2 cm.

Using a ruler and compasses only, construct triangle ABC. Leave in your construction arcs. The side AB has been drawn for you.

The diagram shows a triangular field, ABC, on horizontal ground.

The angle *BAC *is equal to 82.8°.

The bearing of C from A is 210°.

i) Find the bearing of B from A.

ii) Find the bearing of A from B.

The diagram shows a field, ABCD, on horizontal ground.

The angle *CAD *is 35.8° and the bearing of D from A is 070°.

Find the bearing of A from C.

In triangle $ABC$, $AB=7\mathrm{cm}$ and $BC=9\mathrm{cm}$.

Using a ruler and compass only, construct triangle $ABC$. The line $AB$ has been drawn for you.

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.

Two towns, $A$ and $B$, are shown on a map. The scale of the map is 1 cm to 5 km.

Find the actual distance between $A$ and $B$.

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

Extract:

Two towns, [A] and [B], are shown on a map.

The scale of the map is 1 cm to 5 km.

Measure the bearing of $B$ from $A$.

Extract:

Measure the bearing of [B] from [A].

109°

Calculate the bearing of $A$ from $B$.

You must show all your working.

The scale of a map is 1 : 10 000 000. On the map, the area of Slovakia is 4.9 cm².

Calculate the actual area of Slovakia. Give your answer in square kilometres.

............................................. km²

On a map with scale 1 : 25000, the area of a lake is 33.6 square centimetres.

Calculate the actual area of the lake, giving your answer in square kilometres.

........................................ km²

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

Barston is 8 km from Acton on a bearing of $037^{\circ}$. Chorlton is 9km from Barston on a bearing of $150^{\circ}$.

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

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.

Extract:

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

Calculate 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.

ii) A is due east of B.

Calculate the bearing of *D *from A.

The diagram shows the positions of three points $A$, $B$ and $C$ in a field.

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

Calculate angle $ABC$.

Angle $ABC=$ ...............................................

The bearing of $C$ from $A$ is 147°. Find the bearing of

i) $A$ from $B$,

ii) $B$ from $C$.

The diagram shows the positions of three ships, $A,B$ and $C$.

Ship $B$ is due north of ship $A$.

The bearing of ship $C$from ship $A$ is 120°

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

$A$ , $B$ and $C$ are three towns.

The bearing of $B$ from $A$ is 105° The bearing of $C$ from B is 230°

The distance of $C$ from $A$ is 180 km. The distance of $C$ from $B$ is 95 km.

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

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

A ship sails from $P$ to $Q$ and then from $Q$ to $R$.

$Q$ is 12 miles from $P$, on a bearing of 080°

$R$ is 28 miles from $Q$, on a bearing of 155°

Work out the direct distance from $P$ to $R$.