Bearings, Scale Drawing & Constructions (Edexcel IGCSE Maths): Exam Questions

The bearing of a ship from a lighthouse is $050^{\circ}$.

Work out the bearing of the lighthouse from the ship.

Manchester airport is on a bearing of $330^{\circ}$ from a London airport.

Find the bearing of the London airport from Manchester airport.

The London airport is 200 miles from Manchester airport.

A plane leaves Manchester airport at 10 am to fly to the London airport. The plane flies at an average speed of 120 mph.

What time does the plane arrive at the London airport?

Martin and Janet are in an orienteering race.

Martin runs from checkpoint $A$ to checkpoint $B$, on a bearing of $065^{\circ}$.

Janet is going to run from checkpoint $B$ to checkpoint $A$.

Work out the bearing of $A$ from $B$.

The bearing of Paris from London is 149°.

Work out the bearing of London from Paris.

The scale diagram shows the position on a map of a house, $A$

House $C$ is on a bearing of 110° from $A$. The distance from $A$ to $C$is 700 m.

Mark the position of $C$ on the diagram with a cross (×). Label your cross $C$.

Write the scale of the map in the form $1:n$

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

Here is a triangle.

Give a reason why the length of side $AB$ cannot be 35 m

The bearing of $A$ from $B$ is 310°

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

Work out the bearing of $C$ from $A$.

Circle your answer.

An equilateral triangle has side length 16 metres.

Using ruler and compasses only, construct a scale drawing of the triangle. Use the scale 1 centimetre represents 2 metres.

Scale: 1 cm represents 2 m

This map shows part of a village.

Neil knows that Packer Street is 180m long in real life.

i) Neil measures the map. He says

Packer Street is 3.5cm long. High Street is 11.2cm long. Therefore, I calculate that High Street is 576m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct.

ii) Jodie measures the same map.

She says

I think Packer Street is longer than Neil’s measurement of 3.5cm. Therefore, High Street must be longer than 576m in real life.

Is Jodie’s reasoning correct? Show how you decide.

On another map, Packer Street is 2.4cm long.

Express the scale of this map in the form 1 : $n$.

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

A model railway is built using the scale 1 : 87.

On the model railway, the distance between the rails is 16.5 mm.

Calculate, in metres, the distance between the rails for a full-size train.

.................... metres

The scale of a map is 1 cm represents 25 m.

i) The length of a path is 240 m.

Work out the length, in centimetres, of the path on the map.

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

ii) The scale 1 cm represents 25 m can be written in the form 1: k.

Find the value of k.

k = ..................................................... [1]

The diagram shows the position of a lighthouse $L$ and a harbour $H$.

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

Work out the real distance between $L$ and $H$.

Measure the bearing of $H$ from $L$.

A boat $B$ is 20km from $H$ on a bearing of $040^{\circ}$.

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

The diagram shows the positions of a lighthouse $L$, a yacht $Y$ and a tanker $T$ on a map.

Scale 1 cm represents 10 km

Measure the bearing of $L$ from $Y$.

The tanker, $T$, sails 80km on a bearing of $320^{\circ}$.

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, $A$ and $B$.

Church $C$ is on a bearing of $130^{\circ}$ from church $A$. Church $C$ is on a bearing of $245^{\circ}$ from church $B$.

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

Mark the position of church $C$ with a cross ($\times$). Label it $C$.

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 $BAC$. You must show all your construction lines.

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

Using ruler and compasses only, construct the bisector of angle $ABC$. 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 $140\mathrm{metres}$ from the library on a bearing of $220^{\circ}$

Show the position of the post box on the scale drawing. Mark the position with a cross $(\times)$ and label it $P.$

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.

Use ruler and compasses to construct the perpendicular bisector of the line $DE$. 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 ($A$), 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.

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

$J$ and $K$ are ships.

$P$ is a port.

$J$ is due South of $P$. Angle $JPK=56^{\circ}$ $JP=KP$

Work out the bearing of $J$ from $K$.

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 $R$.

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.

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 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.

ii) A is due east of B.

Calculate the bearing of *D *from A.