Higher Level Extensions
AI HL Syllabus & AHL Topics
Combines all standard AI SL topics with 90 hours of high-level applied mathematical concepts.
Topic 1 (AHL)
Matrices & Complex Numbers
- Matrix Multiplication, Determinants & Inverses
- Eigenvalues & Eigenvectors (\( \det(A - \lambda I) = 0 \))
- Diagonalization & Matrix Powers \( A^n \)
- Complex Numbers in Cartesian & Polar Form
- Geometric Transformations via Matrices
Explore Topic 1 AHL Guide
Topic 2 (AHL)
Advanced Modelling Functions
- Logistic Differential Growth Models \( f(t) = \frac{L}{1 + Ce^{-kt}} \)
- Piecewise Functions & Spline Interpolation
- Sinusoidal Modelling & Phase Shifts
- Linear Transformations of Functions
Explore Topic 2 AHL Guide
Topic 3 (AHL)
Graph Theory & 3D Vectors
- Graphs, Digraphs, Adjacency Matrices & Walks
- Eulerian Trails & Chinese Postman Problem
- Hamiltonian Cycles & Travelling Salesperson (TSP)
- Minimum Spanning Trees (Kruskal's & Prim's)
- 3D Vector Kinematics & Line Intersections
Explore Topic 3 AHL Guide
Topic 4 (AHL)
Markov Chains & Inferences
- Transition Matrices & Regular Markov Chains
- Steady-State Distributions & Absorbing States
- Continuous Random Variables & PDFs
- Poisson Distribution Models & Mean Rates
- Hypothesis Tests: One-Sample, Two-Sample, & Paired \(t\)-Tests
Explore Topic 4 AHL Guide
Topic 5 (AHL)
Coupled Differential Equations
- First-Order Differential Equations via Integration
- Euler's Numerical Step Method for ODEs
- Coupled Linear Systems: \( \frac{dx}{dt} = ax + by, \frac{dy}{dt} = cx + dy \)
- Phase Portraits, Equilibrium Points & Stability
- Predator-Prey & Epidemic Dynamic Simulations
Explore Topic 5 AHL Guide
AI HL Assessment Format
Paper 1
30% · 120 Mins · 110 Marks
Compulsory short-response questions spanning both SL core and AHL topics. GDC required.
Paper 2
30% · 120 Mins · 110 Marks
Extended problem-solving questions focusing on in-depth real-world applications. GDC required.
Paper 3
20% · 60 Mins · 55 Marks
Two extended mathematical investigation tasks assessing sustained exploration and generalization.
Internal Assessment
20% · Mathematical Exploration
Independent 12–20 page exploration evaluated against criteria A–E. Read the IA guide →