Extended investigative and problem-solving paper (HL only)
—
1 hour
HL: 20%
Mathematical Exploration (IA)
Internal Assessment involving investigation and exploration
30 hours
30 hours
20%
Topics
1 Number & Algebra
SL Topics
HL Topics
SL 1.1 Standard Form
HL 1.10 Permutations & Combinations
SL 1.2 Arithmetic Sequences
HL 1.11 Advanced Binomial Expansion
SL 1.3 Geometric Sequences
HL 1.12 Partial Fractions
SL 1.4 Financial Mathematics
HL 1.13 Complex Numbers Basics
SL 1.5 Intro to Logarithms
HL 1.14 Polar & Euler Form
SL 1.6 Simple Proofs
HL 1.15 De Moivre’s Theorem
SL 1.7 Laws of Exponents & Logs
HL 1.16 Complex Roots
SL 1.8 Infinite Geometric Series
HL 1.17 Proof by Induction
SL 1.9 Binomial Theorem
HL 1.18 Systems of Linear Equations
2 Functions
SL Topics
HL Topics
SL 2.1 Equations of Lines
HL 2.12 Factor & Remainder Theorems
SL 2.2 Functions & Inverses
HL 2.13 Rational Functions
SL 2.3 Graphing Functions
HL 2.14 Odd & Even Functions
SL 2.4 Features of Graphs
HL 2.15 Self-Inverse Functions
SL 2.5 Composite Functions
HL 2.16 Domain Restrictions
SL 2.6 Quadratic Functions
HL 2.17 Inequalities
SL 2.7 Quadratic Equations
HL 2.18 Modulus Graphs
SL 2.8 Rational Functions
HL 2.19 Advanced Polynomial Functions
SL 2.9 Exponential Functions
HL 2.20 Advanced Transformations
SL 2.10 Logarithmic Functions
HL 2.21 Analytical Graphing
SL 2.11 Transformations of Functions
HL 2.22 Advanced Function Modelling
3 Geometry & Trigonometry
SL Topics
HL Topics
SL 3.1 3D Geometry & Distance
HL 3.9 Reciprocal Trig Functions
SL 3.2 Sine Rule & Cosine Rule
HL 3.10 Inverse Circular Functions
SL 3.3 Bearings & Elevation
HL 3.11 Compound Angle Identities
SL 3.4 Circles & Radians
HL 3.12 Vector Basics
SL 3.5 Unit Circle
HL 3.13 Scalar (Dot) Product
SL 3.6 Exact Trig Values
HL 3.14 Vector Equations of Lines
SL 3.7 Circular Functions
HL 3.15 Vector Classification
SL 3.8 Trig Equations
HL 3.16 Vector Product
HL 3.17 Vector Planes
HL 3.18 Intersections of Lines & Planes
4 Statistics & Probability
SL Topics
HL Topics
SL 4.1 Sampling Techniques
HL 4.13 Bayes’ Theorem
SL 4.2 Histograms & Box Plots
HL 4.14 Random Variables
SL 4.3 Mean, Median & Mode
HL 4.15 Advanced Probability
SL 4.4 Correlation & Regression
HL 4.16 Statistical Modelling
SL 4.5 Probability Basics
SL 4.6 Conditional Probability
SL 4.7 Discrete Random Variables
SL 4.8 Binomial Distribution
SL 4.9 Normal Distribution
SL 4.10 Regression Lines
SL 4.11 Statistical Testing
SL 4.12 Z-values & Inverse Normal
5 Calculus
SL Topics
HL Topics
SL 5.1 Introduction to Calculus
HL 5.12 First Principles
SL 5.2 Increasing & Decreasing Functions
HL 5.13 Limits & L’Hôpital’s Rule
SL 5.3 Differentiation Basics
HL 5.14 Implicit Differentiation
SL 5.4 Tangents & Normals
HL 5.15 Related Rates
SL 5.5 Introduction to Integration
HL 5.16 Advanced Integration
SL 5.6 Chain, Product & Quotient Rules
HL 5.17 Integration by Parts
SL 5.7 Second Derivative
HL 5.18 Volumes of Revolution
SL 5.8 Maxima & Minima
HL 5.19 Differential Equations
SL 5.9 Kinematics
HL 5.20 Euler’s Method
SL 5.10 Indefinite Integration
HL 5.21 Homogeneous Differential Equations
SL 5.11 Definite Integration & Areas
HL 5.22 Maclaurin Series
AA SL vs AA HL
AA SL
AA HL
Focuses on strong algebraic skills, functions, calculus, and mathematical reasoning.
Covers all SL content in much greater depth with advanced calculus, proofs, vectors, complex numbers, and differential equations.
Suitable for students interested in subjects like economics, business, natural sciences, and some engineering pathways.
Ideal for students planning to study mathematics, physics, computer science, engineering, or highly quantitative university courses.
At Maths Republic Academy, we make IB Mathematics AA simple, engaging, and exam-focused — helping students build strong concepts, improve confidence, and achieve top scores.