IBDP · Maths AI HL
Geometry and Trigonometry
AI 3.1, 3.2, 3.3, 3.5
27 min readAdvanced~23% of AI HL papers (Topic 3 core content, examined in both Paper 1 and Paper 2)
This is the topic where a decimal-place slip or a calculator in the wrong angle mode quietly destroys three marks in a row. Every question here — a survey plot, a sprinkler radius, a flight path — is really one of three engines running underneath: the distance/midpoint machinery that turns points into shapes, SOHCAHTOA and the unit circle that turn any angle into a ratio, and the sine/cosine rules that solve any triangle at all. Get the engine choice right and the arithmetic is routine; get it wrong and no amount of careful calculation saves you.
Overview
What this topic actually tests
- Everything here reduces to two skills: turning a real scene (survey plot, flight path, sprinkler, logo) into coordinates and triangles, then grinding through a formula without a sign error.
- Three formula families do all the work: distance & midpoint (points → lengths), SOHCAHTOA & the unit circle (right triangles and any angle → ratios), sine/cosine rule (any triangle → lengths and angles).
- The command term decides how much working is expected — 'write down' wants none, 'show that' wants every line since the target answer is already given to you.
The shape of the chapter
Command terms that decide your working
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Write down | State the result with no working required | AO1 | Marks awarded for the correct answer alone — but a wrong answer here recovers zero method marks, so double-check on your calculator before moving on. |
| Calculate | Obtain a numerical answer, showing the method used | AO2 | Working must still be shown even though 'calculate' sounds like 'just use your calculator' — a bald wrong answer with no substitution loses the method mark too. |
| Find | Same as Calculate — an answer is expected, method shown | AO2 | Treat identically to Calculate; show the substitution into the formula before the final value. |
| Show that | Prove a given result using algebra or exact values | AO2/AO3 | Must reach the EXACT stated value (e.g. √13), not a decimal approximation — rounding early loses the mark even if the rounded decimal matches. |
| Hence | Use a previous result or answer to reach the next one | AO3 | You must visibly reuse the earlier part; re-deriving the result by a completely different method can be marked as not satisfying 'hence'. |
| Determine | Find an answer using a suitable, possibly multi-step, method | AO2 | Similar to 'Find', but often signals that more than one formula must be chained together in sequence. |
Key point
Distance, midpoint, sine rule, cosine rule and the area formula ½ab sinC are all printed in the IB formula booklet — gradient, the perpendicular bisector construction, the equation of a circle and the shoelace area formula are not. Those four you must be able to build from memory.
Overview