IB DP · Mathematics AA/AI

Mathematics AA/AI Syllabus

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Block A

Algebra, Number Theory and Sequences

1. Number Sets and Operations on Sets

2. Mathematical Logic and Proofs

3. Proof by Mathematical Induction

4. Arithmetic Sequences - Properties and Applications

5. Geometric Sequences - Finite and Infinite Sums

6. Percentages, Compound Interest and Amortization

7. Powers and Roots - Advanced Operations

8. Logarithms - Definitions and Properties

9. Exponential Equations and Inequalities

10. Logarithmic Equations and Inequalities

11. Factorials, Permutations and Combinations

12. The Binomial Theorem - Expansions and Specific Terms

13. Complex Numbers - Introduction and Algebraic Form

14. The Argand Plane and Trigonometric Form

15. De Moivre's Theorem and Roots of Complex Numbers

Block B

Functions, Equations and Trigonometry

1. The Concept of a Function, Domain and Range

2. Composite Functions and Inverse Functions

3. Linear Functions and Systems of Equations

4. Quadratic Functions - General, Vertex and Factored Form

5. Quadratic Inequalities and Nonlinear Systems

6. Polynomials - The Remainder and Factor Theorems

7. Rational Functions and Their Asymptotes

8. Transformations of Function Graphs (Translations, Reflections, Scaling)

9. Radian Measure, Sectors and Arcs of a Circle

10. Definitions of Trigonometric Functions in a Right Triangle

11. Trigonometric Functions of a Directed Angle and Their Graphs

12. Trigonometric Identities (Sum and Difference Formulas)

13. Trigonometric Equations

14. The Sine Rule and Cosine Rule

15. Inverse Trigonometric Functions

Block C

Geometry, Vectors and Statistics

1. Fundamentals of Analytic Geometry in the Plane

2. Vectors in 2D - Addition, Subtraction, Scalar Multiplication

3. Vectors in 3D - Coordinates in Space

4. The Scalar (Dot) Product and the Angle Between Vectors

5. The Vector (Cross) Product and the Area of a Parallelogram

6. The Vector and Parametric Equations of a Line

7. Relative Positions of Lines in Space

8. The Equation of a Plane

9. Angles Between Lines and Planes, and Distances

10. Descriptive Statistics - Measures of Central Tendency and Spread

11. Data Presentation - Histograms and Box Plots

12. Fundamentals of Probability - Dependent and Independent Events

13. Conditional Probability and Bayes' Theorem

14. Discrete Random Variables and the Binomial Distribution

15. Continuous Random Variables and the Normal Distribution

Block D

Introduction to Calculus

1. Limits of Sequences and Functions

2. Vertical and Horizontal Asymptotes from the Perspective of Limits

3. Continuity of Functions

4. An Intuitive Introduction to the Derivative (Difference Quotient)

5. Derivatives of Basic Power Functions

6. Differentiation Rules: Sum, Product, Quotient

7. The Chain Rule (Derivative of a Composite Function)

8. Derivatives of Trigonometric, Exponential and Logarithmic Functions

9. Higher-Order Derivatives and Points of Inflection

10. Applications of Derivatives: Optimization and Local Extrema

11. Applications of Derivatives in Kinematics (Displacement, Velocity, Acceleration)

12. The Concept of the Indefinite Integral and Basic Formulas

13. Integration by Substitution and by Parts

14. The Definite Integral and the Fundamental Theorem of Calculus

15. Applications of Integrals: Areas and Volumes of Solids of Revolution