Constructions, Loci and Bearings
Construct accurate geometric objects, describe loci and solve bearing problems.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Compass-and-straightedge constructions
Exam cue: Preserve construction arcs, translate each distance condition into a locus and measure bearings clockwise from north.
Concept 2
Loci and regions
Exam cue: Confirm scale, angle direction, feasible-region overlap and the three-digit bearing format.
Concept 3
Three-figure bearings
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar multi-step contexts.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Measuring a bearing anticlockwise or from a line other than north.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Bearing format
Three figures, measured clockwise from north.
Equidistant from two points
The perpendicular bisector.
Fixed distance from a point
A circle centred on that point.
Constructions, Loci and Bearings: method
Preserve construction arcs, translate each distance condition into a locus and measure bearings clockwise from north.
Constructions, Loci and Bearings: check
Confirm scale, angle direction, feasible-region overlap and the three-digit bearing format.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — A bearing is measured clockwise from north. What is east's three-figure bearing?
Shared F/H · AO1 technique · Non-calculator — The bearing of B from A is 065°. What is the bearing of A from B?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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