Math Analysis & Approaches unit guide
Geometry and Trigonometry
Trigonometric functions and identities, the unit circle, and vectors in two and three dimensions.
This unit splits into two halves that feel unrelated and are examined very differently. Trigonometry rewards memorised exact values and identity fluency; vectors reward drawing the situation before touching an equation. What they share is that both punish working in the wrong form - degrees where radians are needed, or components where a diagram would have settled it in seconds.
Topics in this unit
What gets examined
- Exact values from the unit circle, and knowing when a question requires radians.
- Solving trigonometric equations over a given interval, and finding every solution in it.
- The Pythagorean and double-angle identities, and choosing which one simplifies the problem.
- Graphs of sine, cosine and tangent under amplitude, period and phase changes.
- Scalar and vector products, and what each tells you about the angle between two vectors.
- Vector equations of lines and planes, and finding intersections, distances and angles.
How to revise it
Know the unit circle cold
The exact values at the standard angles, and the sign in each quadrant. Paper 1 assumes it, and reconstructing it under time pressure is where minutes disappear.
Count solutions against the interval
A trig equation over zero to two pi usually has more than one solution. Sketching the graph and marking where the line crosses shows how many to expect, so none go missing.
Draw the vector situation
Two lines, a plane, a point. Almost every vector question becomes obvious once drawn and opaque when attempted straight from components.
Let the products tell you the geometry
Scalar product zero means perpendicular. Vector product zero means parallel. Recognising that turns several question types into one line of work.
Where marks get lost
- Working in degrees where the question is in radians.
- Giving one solution to a trig equation when the interval contains several.
- Confusing the scalar and vector products, or their results - one is a number, one is a vector.
- Forgetting that a vector equation of a line has infinitely many valid forms.
- Using the wrong identity and making the expression more complicated rather than less.
Practise this unit
Reading about a unit only goes so far. Work through real IB-style questions on it, with mark schemes.