IB Mathematics AA HL Syllabus
The IB Mathematics: Analysis and Approaches HL course is built on five core topics, which are assessed across three exam papers. Paper 1 is non-calculator, Paper 2 requires a graphic display calculator, and Paper 3 is a problem-solving paper also requiring a calculator.
Topic 1: Number and Algebra
- Sequences and Series Arithmetic and geometric progressions, including sums of infinite series.
- Exponents and Logarithms Laws of exponents and logarithms, including change of base.
- The Binomial Theorem Expansion of (a + b)ⁿ for positive integer n, and for rational n.
- Proof Methods of proof including induction, contradiction, and counter-examples.
- Complex Numbers Operations with complex numbers in Cartesian and polar form, including De Moivre's theorem.
Topic 2: Functions
- Function Basics Concepts of domain, range, inverse, and composite functions.
- Graph Features Asymptotes, intercepts, and transformations of graphs.
- Types of Functions Properties of linear, quadratic, exponential, logarithmic, and rational functions.
- Polynomials Factor and remainder theorems, and finding roots of polynomial equations.
Topic 3: Geometry and Trigonometry
- Trigonometric Identities Compound angle, double angle, and Pythagorean identities.
- Trigonometric Functions Graphs and properties of sin, cos, and tan, and their inverses.
- Solving Equations Solving trigonometric equations in a finite interval.
- Vectors Vector algebra, scalar and vector products, and their geometric interpretations.
- Lines and Planes Vector equations of lines and planes, intersections, and angles between them.
Topic 4: Statistics and Probability
- Descriptive Statistics Measures of central tendency and dispersion; regression and correlation.
- Probability Laws of probability, conditional probability, and Bayes' theorem.
- Probability Distributions Binomial, Poisson, and normal distributions and their properties.
- Hypothesis Testing Formulating hypotheses and conducting tests for means and correlation.
Topic 5: Calculus
- Differential Calculus Limits, first principles, and rules for differentiation (product, quotient, chain).
- Applications of Differentiation Kinematics, rates of change, and optimization problems.
- Integral Calculus Indefinite and definite integrals, including integration by substitution and parts.
- Applications of Integration Finding areas between curves and volumes of revolution.
- Differential Equations Solving first-order differential equations by separating variables or using an integrating factor.