Advanced Algebra & Proof
Sequences, series, logarithms, binomial methods, complex numbers, proof by induction, and rigorous argument.
IB Diploma Mathematics
IB DP Mathematics: Analysis & Approaches HL
The rigorous route for students who need deep algebra, proof, calculus, vectors, and high-level mathematical argument.
AA HL
TrackAnalysis & Approaches
LevelHigher Level
FocusPaper 3 readiness
Papers & IA
Paper 1
2 hr · 110 marks · 30%
No calculator
Paper 2
2 hr · 110 marks · 30%
GDC allowed
Paper 3
1 hr · 55 marks · 20%
HL problem solving
IA
20 marks · 20%
HL exploration
Number & Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Route Navigator
Choose the right IB Math pathway
One clean page template for all IB DP mathematics routes, so students can compare without feeling lost.
Student Fit
Who should take AA HL?
Analysis & Approaches HL works best when the student's university goals, mathematical confidence, and preferred problem style match the course route.
Students applying to engineering, mathematics, physics, high-rigor computer science, quantitative economics, or any university course that asks for the strongest IB mathematics route.
Learners who can handle sustained algebra, proof-style reasoning, advanced calculus, and long multi-step questions without losing structure.
Students who want HL depth, Paper 3 confidence, and a mathematics profile that signals serious quantitative readiness.
Syllabus Map
AA HL syllabus, organized for scoring
The five IB topic families stay visible, while lessons adapt to the exact AA/AI and SL/HL demand.
Functions Depth
Polynomial and rational functions, transformations, inverse/composite functions, modulus, inequalities, and graph behaviour.
Vectors & Trigonometry
3D vectors, lines, planes, scalar/vector products, advanced identities, and exact trigonometric reasoning.
Statistics & Probability
Distributions, conditional probability, continuous random variables, and interpretation with precise notation.
Higher Calculus
Advanced differentiation, integration techniques, differential equations, Maclaurin series, and extended problem solving.
SL + HL Syllabus Map
AA HL topics: SL foundation and HL extension
HL includes the complete SL foundation. The right column shows the extra HL-only extension added on top for higher-level papers and Paper 3.
01
Number & Algebra
SL Foundation
Fully included in AA HL
Arithmetic and geometric sequences and series
Sigma notation and financial-style series contexts
Indices, surds, exponentials and logarithms
Binomial theorem foundations
Algebraic equations, inequalities and exact manipulation
Modelling with exponential and logarithmic forms
HL Extension
Extra depth beyond SL
Counting principles
Complex numbers and Argand diagrams
Proof by induction, contradiction and counterexample
Systems of equations and deeper algebra
02
Functions
SL Foundation
Fully included in AA HL
Function notation, domain and range
Composite and inverse functions
Quadratics and key graph features
Exponential and logarithmic functions
Transformations, intersections and graphical solving
Modelling and interpreting function parameters
HL Extension
Extra depth beyond SL
Rational and reciprocal functions
Polynomials, roots and factor theorems
Modulus functions and inequalities
Inverse/reciprocal trigonometric problem solving
03
Geometry & Trigonometry
SL Foundation
Fully included in AA HL
Coordinate geometry and line equations
Radians, sectors, arcs and triangle geometry
Sine rule, cosine rule, bearings and areas
Circular functions and trigonometric graphs
Trigonometric equations and identities at SL depth
Exact values and graph transformations
HL Extension
Extra depth beyond SL
Advanced trigonometric identities and equations
Vectors: lines, planes, angles and intersections
Scalar/vector products and 3D vector geometry
04
Statistics & Probability
SL Foundation
Fully included in AA HL
Sampling, bias and data presentation
Descriptive statistics and spread
Bivariate statistics and regression
Tree/Venn diagrams and conditional probability
Discrete random variables and expected value
Binomial and normal distributions
Calculator-supported probability interpretation
HL Extension
Extra depth beyond SL
Distribution depth in mixed HL questions
Advanced probability reasoning and notation
Paper 3 statistical inquiry and interpretation
05
Calculus
SL Foundation
Fully included in AA HL
Limits idea through gradient and first-principles meaning
Derivative notation and differentiation rules
Tangents, normals and optimization
Increasing/decreasing intervals and stationary points
Kinematics-style rates of change where relevant
Indefinite and definite integration
Area under curves and accumulation
HL Extension
Extra depth beyond SL
Limits and L'Hopital's rule
Implicit, parametric differentiation and related rates
Advanced integration techniques
Volumes of revolution
Differential equations
Maclaurin series
Assessment
Exam and IA preparation
1
Paper 1 and Paper 2: broad problem solving across SL and HL content.
2
Paper 3: extended-response problems requiring planning, reasoning, and communication.
3
Internal Assessment: a mathematical exploration with suitable HL depth.
How Classes Run
Teaching plan
- Build an HL map around school sequence, upcoming tests, and university target requirements.
- Separate concept classes, mixed problem sessions, and Paper 3 thinking drills.
- GDC tutorial for Paper 2 and Paper 3: graph checks, statistics workflows, numerical solving, and exam mode.
- Maintain an error bank for algebra, notation, graph interpretation, and proof structure.
- IA support focused on mathematical sophistication without making the topic artificial.
Outcome Focus
What students build in AA HL
Paper 3 readiness
Proof confidence
Calculus depth
University-grade foundation
Next Step
Start with a route check, not guesswork.
Bring the student's current syllabus, recent test, or university target. The demo class can confirm whether AA HL is the right path and where to begin.