Pearson EdexcelGCSE MathsGeometry and measuresFoundation and Higher
Visual model
Bearings are measured clockwise from north
NB65∘bearings use three digits
Gold-standard guide
20 mins
What you will learn
Measure and solve three-figure bearing problems.
Use a clear step-by-step method for bearings.
Check your answer and avoid the most common exam mistake.
Useful before you start
Core number skillsEarlier geometry and measures skillsShowing clear working
Core knowledge
Know the rule, then use it
These are the short notes. Read each one, then check you can use it in the worked example below.
Method
Method
Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°)
Step 1
Draw a diagram and find angle PQR
North at Q points up
Step 2
Apply Pythagoras since the angle is 90°
PR2 = PQ2 + QR2 = 122 + 82 = 144 + 64 = 208
Step 3
Find the bearing from R back to P
Find angle at R using trigonometry, then work out the three-figure bearing
Watch out
Watch out
Students forget the three-digit rule, writing 40° instead of 040°
f
Bearing rule
Bearings are measured clockwise from north.
f
Format
Always write bearings using three digits.
Worked example
A ship sails from port P on a bearing of 040° for 12 km to point Q. It then sails on a bearing of 130° for 8 km to point R. Find the distance PR and the bearing from R back to P.
1
Draw a diagram and find angle PQR: North at Q points up. PQ is on bearing 040° from P. QR is on bearing 130° from Q.The angle between PQ (looking back from Q, bearing 220°) and QR (bearing 130°) is 220° − 130° = 90°.
2
Apply Pythagoras since the angle is 90°: PR2 = PQ2 + QR2 = 122 + 82 = 144 + 64 = 208. PR = 208 ≈ 14.4 km.
3
Find the bearing from R back to P: Find angle at R using trigonometry, then work out the three-figure bearing. 3°.Bearing from R to P ≈ 040° + 180° + adjustment (full working needed with diagram).
Final answer
PR ≈ 14.4 km
Question ladder
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
Workedreasoning
A ship sails from port P on a bearing of 040° for 12 km to point Q. It then sails on a bearing of 130° for 8 km to point R. Find the distance PR and the bearing from R back to P.
3 marks4 minsbearings-worked
Show solution
Worked solution
1.Draw a diagram and find angle PQR: North at Q points up. PQ is on bearing 040° from P. QR is on bearing 130° from Q.The angle between PQ (looking back from Q, bearing 220°) and QR (bearing 130°) is 220° − 130° = 90°.
2.Apply Pythagoras since the angle is 90°: PR2 = PQ2 + QR2 = 122 + 82 = 144 + 64 = 208. PR = 208 ≈ 14.4 km.
3.Find the bearing from R back to P: Find angle at R using trigonometry, then work out the three-figure bearing. 3°.Bearing from R to P ≈ 040° + 180° + adjustment (full working needed with diagram).
Final answer
PR ≈ 14.4 km
Mark points
M1: draw a diagram and find angle pqr
M1: apply pythagoras since the angle is 90°
M1: find the bearing from r back to p
A1: PR ≈ 14.4 km
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Diagnosticrecall
A bearing from A to B is 070°. What is the back-bearing from B to A?
1 mark2 minsbearings-q1
Show solution
Worked solution
1.Spot the skill: Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°).
2.Use the draw a diagram and find angle pqr stage first, then apply pythagoras since the angle is 90°.
3.Keep the final answer visible: 250°.
Final answer
250°
Mark points
g. 040°, not 40°).the back-bearing from b to a = bearing from a to b ± 180° (add or subtract to keep within 000°–360°).
A1: 250°
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Easyprocedure
A bearing of 295°. Draw the direction.
2 marks3 minsbearings-q2
Show solution
Worked solution
1.Spot the skill: Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°).
2.Use the apply pythagoras since the angle is 90° stage first, then find the bearing from r back to p.
3.Keep the final answer visible: 295° is in the NW quadrant (315° is NW, so 295° is slightly west of NW).
Final answer
295° is in the NW quadrant (315° is NW, so 295° is slightly west of NW)
Mark points
g. 040°, not 40°).the back-bearing from b to a = bearing from a to b ± 180° (add or subtract to keep within 000°–360°).
A1: 295° is in the NW quadrant (315° is NW, so 295° is slightly west of NW)
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Mediumreasoning
Point B is 5 km due east of A. Point C is 5 km due north of B. Find the bearing from A to C.
3 marks4 minsbearings-q3
Show solution
Worked solution
1.Spot the skill: Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°).
2.Use the find the bearing from r back to p stage first, then draw a diagram and find angle pqr.
3.Keep the final answer visible: 045°.
Final answer
045°
Mark points
g. 040°, not 40°).the back-bearing from b to a = bearing from a to b ± 180° (add or subtract to keep within 000°–360°).
A1: 045°
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Hardproblem solving
Convert bearing 225° to a compass direction.
3 marks5 minsbearings-q4
Show solution
Worked solution
1.Spot the skill: Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°).
2.Use the draw a diagram and find angle pqr stage first, then apply pythagoras since the angle is 90°.
3.Keep the final answer visible: SW.
Final answer
SW
Mark points
g. 040°, not 40°).the back-bearing from b to a = bearing from a to b ± 180° (add or subtract to keep within 000°–360°).
A1: SW
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Exam-stylemulti-step
A plane flies on bearing 140° for 200 km, then 230° for 150 km. How far from start?
4 marks6 minsbearings-q5
Show solution
Worked solution
1.Spot the skill: Bearings: always measured clockwise from north, always written as three digits (for example 040°, not 40°).
2.Use the apply pythagoras since the angle is 90° stage first, then find the bearing from r back to p.
3.Keep the final answer visible: Requires cosine rule: ≈ 312 km.
Final answer
Requires cosine rule: ≈ 312 km
Mark points
g. 040°, not 40°).the back-bearing from b to a = bearing from a to b ± 180° (add or subtract to keep within 000°–360°).
A1: Requires cosine rule: ≈ 312 km
Watch out
Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
Grade 9 stretchproblem solving
The bearing of B from A is 065 degrees. Find the bearing of A from B.
AB65∘+180∘
4 marks7 minsbearing-g9
Show solution
Worked solution
1.Reverse the direction by adding 180 degrees.
2.Write the answer using three digits.
Final answer
245 degrees
Mark points
M1: use 65 + 180
A1: 245 degrees
Watch out
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Timed checkpoint
12 mins - 9 marks
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Bearings - 2 marksA bearing from A to B is 070°. What is the back-bearing from B to A?Mark answer
Answer
250°
2Angles, lines and polygons - 2 marksThe exterior angle of a regular polygon is 24°. How many sides?Mark answer
Answer
15
3Properties of shapes - 2 marksName all 2D shapes with equal diagonals that bisect each other.Mark answer
Answer
Rectangle, square
4Perimeter, area and volume - 3 marksFind the perimeter of a rectangle with length 13 cm and width 8 cm.Mark answer
Answer
42 cm
Mastery check
I can explain the method for bearings.
I can show clear working without skipping key steps.
I can avoid this mistake: Students forget the three-digit rule, writing 40° instead of 040°.Also, back-bearings require adding or subtracting 180° — not simply reversing the digits.Always add 180° if the forward bearing is less than 180°, subtract 180° if it is greater.
This guide follows the Pearson Edexcel GCSE Mathematics 1MA1 specification. Practice questions are original Learnova questions shaped around official content and exam skills.