What are bearings in the context of Edexcel IGCSE Mathematics?

In Edexcel IGCSE Mathematics, bearings are a way of expressing direction. They are measured in degrees, clockwise from the north direction. Bearings are typically used in navigation and map reading to describe the direction from one point to another.

How do you calculate a bearing between two points?

To calculate a bearing from one point to another, you first draw a north line at the starting point. Then, measure the angle clockwise from the north line to the line connecting the two points. This angle, measured in degrees, is the bearing. It is always expressed as a three-digit number, for example, 045° or 230°.

Why are bearings always given as three-digit numbers?

Bearings are expressed as three-digit numbers to ensure clarity and avoid confusion. This format ensures that all bearings are consistently represented, with leading zeros added if necessary. For example, a bearing of 5 degrees is written as 005°.

What is the difference between true bearings and compass bearings?

True bearings are measured in degrees from the true north, which is a fixed point on the Earth's surface. Compass bearings, on the other hand, are measured using a magnetic compass and can vary slightly due to magnetic declination. In Edexcel IGCSE Mathematics, bearings are typically assumed to be true bearings unless otherwise specified.

How are bearings used in solving geometry and trigonometry problems?

Bearings are used in geometry and trigonometry to solve problems involving direction and distance. They are often used in conjunction with trigonometric ratios to calculate unknown distances or angles in navigation and surveying problems. Understanding bearings is essential for solving real-world problems that involve directional movement.

Why is "Writing $47°$ instead of $047°$" a common mistake in Bearings?

Why it happens: Forgetting the leading zero. How to avoid it: Bearings ALWAYS three digits. Add leading zeros if needed. Source: 4MA1/1H — examiner reports 2022-2024

Why is "Measuring anticlockwise from North" a common mistake in Bearings?

Why it happens: Confusion with standard maths conventions. How to avoid it: ALWAYS clockwise from NORTH. Standard maths convention is anticlockwise from East — different!

Why is "Adding $180°$ to a bearing already $> 180°$" a common mistake in Bearings?

Why it happens: Mechanical application. How to avoid it: If original > 180°: SUBTRACT 180°. Result must be in [0°, 360°].

Geometry and TrigonometryEdexcel IGCSE Mathematics (4MA1)

Bearings

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Bearings Study Notes — Edexcel IGCSE 4MA1 Higher Tier (2026 onwards)

Three-digit bearings measured CLOCKWISE from NORTH. Standard for navigation; combined with trigonometry.

What you’ll learn

Mapped to the Cambridge IGCSE 4MA1 syllabus (2026 onwards).

4.9 — Read and use bearings.
4.9 — Find back bearings.
4.9 — Combine bearings with trigonometry for navigation problems.

Reading bearings

$3$ digits. Clockwise from North.

Bearing = angle measured CLOCKWISE from NORTH.

Always 3 digits. $047°$ , $123°$ , $310°$ . (Not $47°$ , $123°$ , $310°$ .)

Compass directions:

Direction	Bearing
North	$000°$ or $360°$
North-East	$045°$
East	$090°$
South-East	$135°$
South	$180°$
South-West	$225°$
West	$270°$
North-West	$315°$

Back bearing. The bearing in the OPPOSITE direction.

If original < $180°$ : ADD $180°$ . If original > $180°$ : SUBTRACT $180°$ .

(So back bearing always in $[0°, 360°]$ .)

Examples:

$060°$ → back $240°$ .
$250°$ → back $070°$ .
$090°$ → back $270°$ .

Worked qualitative. Why is North = $000°$ ?

Bearings start at North and rotate clockwise.
North is the starting point: $0°$ rotation.
Convention from compass orientation.

Edexcel tip. ALWAYS three digits. Mark schemes deduct for missing leading zeros.

Three digits.
Clockwise from North.
N = $000°$ , E = $090°$ , S = $180°$ , W = $270°$ .
Back bearing: $\pm 180°$ .

Bearings with trigonometry

Combine with right-angle trig for navigation problems.

Common scenario: A ship/aeroplane travels on a bearing for a distance. Find positions or new bearings.

Method:

Sketch the diagram.
Identify right triangle with the bearing as one angle.
Hypotenuse = distance travelled.
North/South = adjacent or opposite (depending on bearing).
East/West = opposite or adjacent.

Worked example. Ship sails $20$ km on bearing $050°$ .

Right triangle setup:

Hypotenuse: $20$ km.
Angle from North: $50°$ .
North component (adjacent to bearing): $20 \cos 50° \approx 12.86$ km.
East component (opposite to bearing): $20 \sin 50° \approx 15.32$ km.

So the ship has moved $12.86$ km north and $15.32$ km east.

Multi-leg journeys. Add the components leg by leg.

Example: Leg 1 north $5$ + east $3$ . Leg 2 north $-2$ + east $7$ . Net: north $3$ , east $10$ .

Final position can be converted back to bearing via $\tan^{-1}$ .

Worked qualitative. A ship sails $5$ km north then $12$ km east. What's its straight-line distance and bearing from start?

Distance: Pythagoras. $\sqrt{25 + 144} = 13$ km.
Bearing: angle from North. $\tan \theta = 12/5 = 2.4$ , so $\theta \approx 67.4°$ .
Bearing: $067°$ .

Edexcel tip. Sketch the diagram. Identify the right triangle. Use SOH CAH TOA. Mark schemes credit each step.

Sketch first.
Right triangle with bearing as one angle.
N/S and E/W components.
Use Pythagoras for distances.

How it’s examined

Bearings on Higher Tier (3-6 marks). Often combined with trigonometry. Examiner reports flag (1) missing leading zeros, (2) measuring anticlockwise, (3) wrong back-bearing direction.

Sources: Pearson Edexcel International GCSE Mathematics A 4MA1 specification (2026 onwards); 4MA1 Examiner Reports — Jan and May/Jun 2022-2024 series; Past Papers — 4MA1/1H May/Jun 2024. Last reviewed 2026-05-07.

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Step-by-step worked examples — Bearings

Step-by-step solutions to past-paper-style questions on bearings, written exactly the way a tutor would explain them at the board.

1Read a bearing
Foundation• bearing
Question
$B$ is due East of $A$ . What is the bearing of $B$ from $A$ ?
Step-by-step solution
1. Step 1
  Bearings are measured CLOCKWISE from NORTH.
2. Step 2
  East is $90°$ clockwise from North.
3. Step 3
  Bearing: $090°$ (always 3 digits).
Answer
$090°$
Examiner tip
Bearings are ALWAYS three digits: $090°$ , not $90°$ . Mark schemes deduct.
2Back bearing
Higher• Adapted from 4MA1/1H May/Jun 2024 Q14• back bearing
Question
Bearing of $B$ from $A$ is $060°$ . Find the bearing of $A$ from $B$ .
Step-by-step solution
1. Step 1
  Back bearing: add $180°$ if original $< 180°$ , subtract $180°$ if original $> 180°$ .
2. Step 2
  $060° + 180° = 240°$ .
Answer
$240°$
Examiner tip
Back bearing: $\pm 180°$ . Choose the one that gives a 3-digit angle in $[0°, 360°]$ .
3Bearing combined with trigonometry
Higher• bearing, trigonometry
Question
A ship sails on a bearing of $050°$ for $20$ km. How far north and east has it travelled?
Step-by-step solution
1. Step 1
  Bearing $050°$ = $50°$ clockwise from North.
2. Step 2
  Right triangle: hypotenuse $20$ , angle $50°$ from North-South line.
3. Step 3
  North component (adjacent): $20 \cos 50° \approx 12.86$ km.
4. Step 4
  East component (opposite): $20 \sin 50° \approx 15.32$ km.
Answer
North $\approx 12.86$ km. East $\approx 15.32$ km.
Examiner tip
Choose right triangle with the bearing as one of its angles. The hypotenuse is the distance travelled.

Key Definitions and Keywords — Bearings

Definitions to memorise and the exact keywords mark schemes credit for bearings answers — sharpened from recent examiner reports for the 2026 Pearson Edexcel IGCSE 4MA1 sitting.

Bearing
Examiner keyword
An angle measured CLOCKWISE from NORTH. Always written as 3 digits (e.g. $047°$ , not $47°$ ).
Example
North = $000°$ or $360°$ . East = $090°$ . South = $180°$ . West = $270°$ .
Back bearing
The bearing in the OPPOSITE direction. Add or subtract $180°$ .
Example
$060°$ → back bearing $240°$ .

Common Mistakes and Misconceptions — Bearings

The traps other students keep falling into on bearings questions — taken from recent Pearson Edexcel IGCSE 4MA1 examiner reports and mark schemes — and how to avoid them.

✕Writing $47°$ instead of $047°$
4MA1/1H — examiner reports 2022-2024
Why it happens
Forgetting the leading zero.
How to avoid it
Bearings ALWAYS three digits. Add leading zeros if needed.
✕Measuring anticlockwise from North
Why it happens
Confusion with standard maths conventions.
How to avoid it
ALWAYS clockwise from NORTH. Standard maths convention is anticlockwise from East — different!
✕Adding $180°$ to a bearing already $> 180°$
Why it happens
Mechanical application.
How to avoid it
If original $> 180°$ : SUBTRACT $180°$ . Result must be in $[0°, 360°]$ .

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Video lesson

Short walkthrough of the concepts students most often get stuck on.

Bearings — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Bearings

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Read a bearing

2Back bearing

3Bearing combined with trigonometry

Bearing

Back bearing

✕Writing 47°47°47° instead of 047°047°047°

✕Measuring anticlockwise from North

✕Adding 180°180°180° to a bearing already >180°> 180°>180°

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Bearings — frequently asked questions

✕Writing $47°$ instead of $047°$

✕Adding $180°$ to a bearing already $> 180°$