IB Math AI HL Unit 3: Geometry & Trigonometry

IB Maths AI HL Unit 3: Geometry and Trigonometry, topic by topic

Each topic in this unit has a free page with step-by-step worked examples and the key formulas, then exam-style questions with mark schemes.

• Graph Theory questions86 questions · 3 worked examples
• Scalar Products and Voronoi questions32 questions · 3 worked examples
• Vectors and Kinematics questions44 questions · 3 worked examples

Learn it first: AI HL Unit 3 notes

• Voronoi diagrams
• 3D vectors
• Vector equations of lines in 2D and 3D
• Sinusoidal modelling with seasonal data
• Graph theory

Where marks go in AI HL Unit 3

From the IB subject reports we summarise on AI HL Examiner Insights, in our own words:

• IB notation: AB as a length, vectors in columns, f⁻¹ vs f′, the variables asked for. AB (no arrow) is a length; AB with an arrow is a vector, written as a column. Displacement AB = b − a. f⁻¹ is the inverse, f′ the derivative. Answer in the question's variables.
• Graph algorithms: Prim vs nearest neighbour, no method shown, bounds mixed up. Show the algorithm: list edges in the order chosen, with weights, and say when it stops. Upper bound (nearest neighbour): best = smallest found. Lower bound (deleted vertex): MST of the rest + two shortest edges to the deleted vertex; best = largest found.
• Coupled systems and phase portraits: equilibria, eigenvectors, trajectories. Equilibrium: dx/dt = 0 and dy/dt = 0. Write the system as a matrix, find eigenvalues and eigenvectors (in the form (1, k)), and use their signs: both negative → stable node, opposite signs → saddle, complex → spiral.

The questions here are original, written in the style of IB papers with IB-style mark schemes; for real papers see the IB Maths AI HL past papers page.

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