Syllabus breakdown

AI SL Geometry and Trigonometry syllabus points

The official syllabus elements assessed across Paper 1 and Paper 2 in Topic 3.

  1. 3.13D spatial geometry: volume and surface area of cylinders, cones, spheres, pyramids, and angle between lines and planes
  2. 3.2Trigonometry in non-right-angled triangles: Sine rule $\frac{a}{\sin A} = \frac{b}{\sin B}$, Cosine rule $c^2 = a^2 + b^2 - 2ab\cos C$, area of a triangle $\frac{1}{2}ab\sin C$, navigation bearings
  3. 3.3Voronoi diagrams: sites, perpendicular bisector boundaries, cell regions, vertices, nearest neighbor interpolation
  4. 3.4The toxic waste problem: circumcenters, finding the largest empty circle, optimal facility siting equidistant from neighboring settlements

Interactive guides

Topic 3 Interactive Study Guides

Each guide features full notes, 10 progressive practice exercises with complete markschemes, formula sheets with common pitfalls, and an exam mini test.

Lesson 3.3 (Core AI Focus)

Voronoi Diagrams & Nearest Neighbor

Constructing perpendicular bisectors, boundary equations, vertices as circumcenters, and nearest neighbor cell assignment.

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Lesson 3.4

Toxic Waste & Largest Empty Circle

Finding optimal facility locations that maximize clearance distance from surrounding towns using Voronoi vertices.

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Lesson 3.1

3D Geometry & Right-Angled Solids

Volume and surface area of cylinders, cones, pyramids, spheres, slant heights, and 3D angle projections.

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Lesson 3.2

Non-Right-Angled Trig & Bearings

Sine rule, cosine rule, triangle area, 3-figure navigation bearings, and real-world surveying triangulation.

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Exam insights

Key ideas & Voronoi Construction Method

  • Midpoint and Negative Reciprocal Gradient: Every Voronoi edge separating two sites $A(x_1, y_1)$ and $B(x_2, y_2)$ is the perpendicular bisector. It passes through midpoint $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ with gradient $m_{\perp} = -\frac{1}{m_{AB}}$.
  • Voronoi Vertices are Circumcenters: A vertex where three cells meet is equidistant to all three sites. It forms the center of the unique circumcircle passing through the three points.
  • Largest Empty Circle: The center of the largest empty circle that contains no sites in its interior must lie either at a Voronoi vertex or on the boundary of the region.

Course navigation

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