IBDP · Maths AA SL
Geometry and Trigonometry
AA SL Topic 3: Geometry and Trigonometry (3.1-3.6)
34 min readStandard~15-20% of AA SL teaching time; appears on both Paper 1 (no GDC) and Paper 2 (GDC), often combined with coordinate algebra questions
This is the topic where algebra, shape and angle collide. Coordinate geometry gives you an algebraic handle on points and circles; trig ratios extend that to angles; the sine and cosine rules let you drop the '90°' requirement altogether. IB loves stitching all three into one question — find a length from coordinates, feed it into a cosine rule, then decide if a triangle even exists. Get the booklet formulas substituted correctly and this becomes mechanical, not mysterious.
Overview
Why this topic bites
- Coordinate geometry is the 'grammar' — distance, midpoint, gradient — that gets reused inside sine/cosine rule questions once a triangle is given as three points instead of three side lengths.
- Right-angle trig (SOHCAHTOA) only works when there's a 90° angle in the triangle you're solving; the moment it's not right-angled, you must switch to the sine or cosine rule — spotting that switch is the single most examined skill here.
- Almost every formula you need is in the data booklet; the exceptions you must memorise are the distance/midpoint/gradient formulas, the exact trig values at 0°, 30°, 45°, 60°, 90°, and the decision rule for which of sine/cosine rule fits which given information.
The shape of the chapter
Command terms this topic tests hardest
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Show that | Prove a stated result using algebra/geometry, arriving EXACTLY at the given answer | AO2 | Every line of working must appear — since the answer is given, no marks exist for the final number, only for method; skipping the completing-the-square step loses the marks even if the centre 'looks right'. |
| Hence | Use the immediately preceding result to reach the next answer | AO2 | A correct final answer reached by an independent method (not built on the given result) is not credited when 'hence' is used. |
| Determine | Obtain the answer with relevant working shown (less rigid than 'show that') | AO2 | Working must still appear for method marks even though the answer isn't pre-stated. |
| Justify | Give a calculation or reason that supports a conclusion | AO3 | A bare 'yes/no' scores 0 — the actual comparison (e.g. distance vs radius, or angle sum check) must be written explicitly. |
| Calculate | Produce a numerical answer via formula substitution | AO2 | Correct substitution earns method marks even if the final rounding/arithmetic slips. |
| Sketch | Draw an approximate but correctly shaped diagram with key features labelled | AO1 | Missing labelled values (angle, side, axis) costs marks even when the shape is right. |
Key point
Radians vs degrees mode is the single most common lost mark in this whole topic — check your calculator mode before every trig calculation, and re-check the moment appears in an arc-length or sector-area question.
Overview