Geometry and Trigonometry
AI SL 3.1, 3.2, 3.5
This is the topic where the exam stops asking you to 'find x' in the abstract and starts hiding real triangles inside land plots, taxi fares and animal-tracking scenarios. Three skills carry almost every mark here: reading a diagram (or building one) correctly, picking the right formula for the information you actually have, and keeping algebraic signs straight when a modulus or an obtuse angle is involved. Get comfortable switching between coordinate geometry and triangle trigonometry — questions routinely blend both in one part-question.
Overview
Geometry and Trigonometry in AI SL is applied, not abstract: every formula exists to answer 'how far, how big an angle, what's the area' in a real context — a plot of land, a triangulated location, a fare structure. The formula booklet gives you distance, midpoint, sine rule, cosine rule and area of a triangle, so the exam isn't testing recall — it's testing whether you can tell which formula fits the data you're given.
- Coordinate geometry handles anything built from points: distance, midpoint, gradient, equations of lines, and areas of polygons defined by vertices.
- Trig ratios and identities extend right-angle trigonometry to any angle between 0° and 180°, which is exactly the range the sine and cosine rules need.
- The sine and cosine rules solve triangles that aren't right-angled — the majority of triangles in real applications (land surveys, bearings, navigation) aren't.
The shape of the chapter
Command terms that decide your method
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Calculate | Produce a numerical answer, working may be brief | AO1 | Correct final value with correct units earns full marks even with minimal working shown |
| Determine | Find the value using an appropriate, possibly multi-step, method | AO2 | Method marks awarded for each correct stage even if final answer slips |
| Show that | Derive the given result algebraically — the answer is already printed, so you must produce every line that gets you there | AO2 | No marks for stating the given result without full working; examiners check every algebraic line |
| Hence | You must use the previous part's result — an independent correct method scores zero | AO2 | Markschemes explicitly penalise a fresh derivation that ignores the earlier part |
| State | Give a result with no working required | AO1 | One mark, no justification needed or expected |
Key point
Overview