Use geometry vocabulary, angle measures and bearings
Name common shapes and circle parts, measure angles, and read or calculate three-figure bearings clockwise from north.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
From which direction are bearings measured?
What you will learn
- Use geometric terms for shapes, angles and solids
- Measure and draw angles in degrees
- Interpret and reverse three-figure bearings
Use precise names
Use point, vertex, line, plane, parallel, perpendicular, perpendicular bisector, bearing, right angle, acute/obtuse/reflex angle, interior/exterior angle, similar, congruent and scale factor. Classify equilateral, isosceles, scalene and right-angled triangles; square, rectangle, kite, rhombus, parallelogram and trapezium; and regular/irregular polygons such as pentagons, hexagons, octagons and decagons.
Name simple solids such as cube, cuboid, prism, cylinder, pyramid, cone and sphere, and distinguish their faces, surfaces and edges. Circle terms include centre, radius, diameter, circumference, semicircle, chord, tangent, arc, sector and segment. Core does not require the term hemisphere or proof of congruence; Extended adds tetrahedron, hemisphere, frustum and major/minor arcs.
Measure from a stated reference
A three-figure bearing is measured clockwise from north: due east is 090° and due south is 180°. Use leading zeros and label the north reference.
The reverse bearing points back along the same route and differs by 180°, reduced to 000°–359°. Use a ruler for straight edges and a protractor for angle measurements.
Pause and explain
What is the reverse bearing of 070°?
Worked example
The bearing of B from A is 025°. Find the bearing of A from B.
Show the worked solution
- A reverse direction differs by 180°.
- 025° + 180° = 205°.
- Write three digits and keep the clockwise-from-north convention.
Answer Bearing of A from B: 205°.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A ship travels from A to B on a bearing of 064°. Find the bearing from B back to A.
Give me a hint
Add 180° to reverse the bearing.
Compare my reasoning
- 064° + 180° = 244°.
- The result is below 360°.
- Write it as a three-figure bearing.
244°.
Look for these in your work
- Clockwise reference used
- Half-turn added
- Three figures written
Name the segment from a circle's centre to its circumference, a line through the centre joining two circumference points, and the region enclosed by two radii and an arc.
Give me a hint
Recall radius, diameter and sector.
Compare my reasoning
- The centre-to-circumference segment is a radius.
- The full chord through the centre is a diameter.
- The enclosed region is a sector.
Radius; diameter; sector.
Look for these in your work
- Each description matched
- Diameter identified as a special chord
- Sector distinguished from segment
A rescue boat travels on a bearing of 135° from a harbour. Find its return bearing and explain how a compass rose prevents a direction error.
Give me a hint
Use the reverse-bearing rule and identify north as the reference.
Compare my reasoning
- 135° + 180° = 315°.
- The return direction is 315°.
- A compass rose fixes north as zero and bearings increase clockwise.
315°; use north as zero and turn clockwise.
Look for these in your work
- Reverse direction found
- Three-figure result given
- Reference convention explained
Common mistakes
- Measuring a bearing anticlockwise
- Omitting leading zeros
- Confusing a chord with an arc
- Treating a sector and segment as the same region
What can you explain now?
What is the bearing due west?
Compare with the explanation
270°
Bearings start at north and turn clockwise.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do geometry vocabulary and the north-clockwise convention describe a diagram precisely?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.