Geometry
Apply angle, congruence, similarity, transformation, circle, mensuration, right-triangle and vector facts.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Build short justified chains from angle, congruence, similarity and circle properties.
Exam cue: Mark only stated or proved facts on the diagram.
Concept 2
Calculate lengths, areas, volumes, arcs and sectors with correct scale relationships.
Exam cue: Separate a three-dimensional problem into suitable planes or triangles.
Concept 3
Use Pythagoras, right-triangle trigonometry and vector operations in two and three dimensions.
Exam cue: Keep vector direction and component order explicit.
Risk pitfalls and guardrails
Assuming a diagram is drawn to scale.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Using the length scale factor for area or volume.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Importing the sine or cosine rules into the M5-only scope.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Diagram evidence
Use labels and stated properties rather than appearance.
Pythagoras
a²+b²=c² only with c as the hypotenuse.
SOH CAH TOA
Choose the right-triangle ratio from the named sides.
Circle tangent
A radius is perpendicular to the tangent at contact.
Similarity
Corresponding sides share one length scale factor.
Vector route
Add successive displacement vectors head to tail.
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
A regular polygon has exterior angle 24°. How many sides does it have?
An angle at the circumference standing on an arc is 38°. What angle does the same arc subtend at the centre?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”