What is G15: Measuring and bearings?

Measure only from an accurate scale drawing, using a ruler or protractor to a precision justified by the scale. For scale 1:n, one unit on the drawing represents n of the same units in reality, so multiply drawing lengths by n and then convert units.

How many marks are G15 questions worth?

In verified past-paper appearances, G15 questions on Edexcel GCSE Maths 1MA1 have been worth 1–5 marks.

Which past exam papers has G15 appeared in?

G15 has appeared in 14 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

G15

Measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of bearings

Measuring and bearings

Worked answers, methods and verified real exam appearances for G15 on Edexcel GCSE Maths 1MA1.

Explanation

Measure only from an accurate scale drawing, using a ruler or protractor to a precision justified by the scale. For scale $1:n$ , one unit on the drawing represents $n$ of the same units in reality, so multiply drawing lengths by $n$ and then convert units.
A bearing is the clockwise angle from north at the starting point and is written with three figures, such as $052^\circ$ .
Draw a north line at the point where the journey starts.
Reverse bearings differ by $180^\circ$ .
Examiners expect the scale working, the correct direction of measurement and a three-figure bearing.

A bearing is measured clockwise from north at the starting point.

Worked example

On a map with scale $1:25\,000$ , two locations are $6.4$ cm apart. Find the real distance in kilometres.

1.Multiply by the scale factor: $6.4\times25\,000=160\,000$ cm.
2.Convert centimetres to metres: $160\,000\div100=1600$ m.
3.Convert metres to kilometres: $1600\div1000=1.6$ km.

Answer: $1.6$ km.

Common mistakes

Don't measure a bearing anticlockwise or from an east-west line.
Don't multiply by the scale factor but leave the real distance in centimetres when kilometres are requested.

Exam tip

For a bearing mark, draw the north line at the departure point and write the answer using exactly three figures.

Worked practice

Tier 1 · Easy

A ray from point

P

makes an angle of

68^\circ

clockwise from north. Write its bearing from

P

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$068^\circ$	1	A bearing is the clockwise angle from north written with three figures. Therefore $68^\circ$ is written as $068^\circ$ .

Tier 2 · Standard

On a map with north at the top, point

B

6\text{ cm}

east and

8\text{ cm}

north of point

A

. The scale is

1:20\,000

. Work out the real straight-line distance from

A

B

and the bearing of

B

from

A

. Give the bearing to the nearest degree.

(4)

(Total for Question 2 is 4 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$2\text{ km}$ $037^\circ$	4	The map distance is $\sqrt{6^2+8^2}=10\text{ cm}$ . The real distance is $10\times20\,000=200\,000\text{ cm}=2\text{ km}$ . If the bearing angle is $\theta$ , then $\tan\theta=6/8$ , so $\theta=36.9^\circ$ . Written as a three-figure bearing to the nearest degree, this is $037^\circ$ .

Tier 3 · Hard

On a scale drawing, a road of actual length

3.15\text{ km}

is represented by a line

8.4\text{ cm}

long. Find the scale in the form

1:n

. Another road is

11.2\text{ cm}

long on the same drawing. Work out its actual length in kilometres.

(4)

(Total for Question 3 is 4 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	$1:37\,500$ $4.2\text{ km}$	4	Convert $3.15\text{ km}$ to $315\,000\text{ cm}$ . The scale factor is $315\,000/8.4=37\,500$ , so the scale is $1:37\,500$ . The second road represents $11.2\times37\,500=420\,000\text{ cm}=4.2\text{ km}$ .

Tier 1 · Easy

A ship travels in a south-east direction. Write down the bearing of the ship's direction.

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$135^\circ$	1	East is bearing $090^\circ$ and south is bearing $180^\circ$ . Halfway between them is $135^\circ$ .

Tier 2 · Standard

A route on a map consists of two straight sections of lengths

4.6\text{ cm}

and

3.4\text{ cm}

. The map scale is

1:50\,000

. Work out the actual length of the route in kilometres.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$4\text{ km}$	2	The map length is $4.6+3.4=8\text{ cm}$ . The actual length is $8\times50\,000=400\,000\text{ cm}=4\text{ km}$ .

Tier 3 · Hard

A lighthouse is on a bearing of

046^\circ

from a harbour. A boat leaves the lighthouse on a bearing of

166^\circ

. Work out the smaller angle between the direction from the lighthouse to the harbour and the boat's direction.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	$60^\circ$	3	The bearing of the harbour from the lighthouse is the reverse bearing, $046^\circ+180^\circ=226^\circ$ . The smaller angle between bearings $226^\circ$ and $166^\circ$ is $226^\circ-166^\circ=60^\circ$ .

Tier 2 · Standard

A rectangular playground measures

72\text{ m}

45\text{ m}

. A plan of the playground uses the scale

1 : 2500

. Work out the dimensions of the playground on the plan. Give your answers in centimetres.

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$2.88\text{ cm}$ by $1.8\text{ cm}$	3	$72\text{ m}=7200\text{ cm}$ and $45\text{ m}=4500\text{ cm}$ . Divide each real length by $2500$ : $7200\div2500=2.88$ and $4500\div2500=1.8$ . The plan dimensions are $2.88\text{ cm}$ by $1.8\text{ cm}$ .

Tier 3 · Hard

A rescue boat travels from

P

Q

on a bearing of

038^\circ

. At

Q

it turns

126^\circ

clockwise and travels to

R

. It then returns directly from

R

Q

. At

Q

it turns

101^\circ

anticlockwise from its return direction and begins a new course. Work out the bearing of

R

from

Q

, the bearing of

Q

from

R

and the bearing of the new course.

(4)

(Total for Question 8 is 4 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	$164^\circ$ $344^\circ$ $243^\circ$	4	The bearing from $Q$ to $R$ is $038^\circ+126^\circ=164^\circ$ . The reverse bearing from $R$ to $Q$ is $164^\circ+180^\circ=344^\circ$ . Turning $101^\circ$ anticlockwise from this return direction gives $344^\circ-101^\circ=243^\circ$ .

Tier 3 · Hard

A map has scale

1 : 40\,000

. The map is enlarged to

125\%

of its original size. On the enlarged copy, a path is

13.5\text{ cm}

long. Work out the real length of the path in kilometres.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$4.32\text{ km}$	4	Before the enlargement, the path was $13.5\div1.25=10.8\text{ cm}$ long on the map. Its real length is $10.8\times40\,000=432\,000\text{ cm}$ . Since $100\,000\text{ cm}=1\text{ km}$ , the real length is $4.32\text{ km}$ .

Q10

Tier 3 · Hard

Point

Q

is due north of point

P

. Point

R

is on a bearing of

122^\circ

from

P

, and

\angle PRQ=37^\circ

. Work out

\angle PQR

and the bearing of

Q

from

R

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	$\angle PQR=21^\circ$ Bearing $=339^\circ$	4	The bearing of $Q$ from $P$ is $000^\circ$ , so $\angle QPR=122^\circ$ . The angle sum of triangle $PQR$ gives $\angle PQR=180^\circ-122^\circ-37^\circ=21^\circ$ . The bearing of $P$ from $R$ is $122^\circ+180^\circ=302^\circ$ . From $R$ , the ray to $Q$ is $37^\circ$ clockwise from the ray to $P$ , so its bearing is $302^\circ+37^\circ=339^\circ$ .

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2021-11	3F	Q5	1	Allowed	Foundation	QP MS
2023-11	2H	Q6	2	Allowed	Higher	QP MS
2019-06	3H	Q23	5	Allowed	Higher	QP MS
2021-11	2F	Q5	2	Allowed	Foundation	QP MS
2024-11	1F	Q7	3	Non-calculator	Foundation	QP MS
2019-11	1F	Q27	5	Non-calculator	Foundation	QP MS
2024-06	2F	Q7	3	Allowed	Foundation	QP MS
2019-11	1H	Q8	5	Non-calculator	Higher	QP MS
2022-11	2F	Q6	2	Allowed	Foundation	QP MS
2023-06	2F	Q7	3	Allowed	Foundation	QP MS
2023-11	1F	Q4	1	Non-calculator	Foundation	QP MS
2023-11	2F	Q27	2	Allowed	Foundation	QP MS
2022-06	3F	Q13	4	Allowed	Foundation	QP MS
2023-06	3F	Q17	2	Allowed	Foundation	QP MS

Other points in G Geometry and measures

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