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Numbers and Algebra
AASL and AAHL
- Arithmetic and Geometric Sequences & Series
..Exponents and Logarithms - Radicals and Rational Exponents
- Binomial Expansions
. Proof by Mathematical Induction (AAHL only)
- Complex Numbers (AAHL only)
- Solving Equations (Real and Complex)
Functions
Domain , Range and Sketching
- Concept of a Function ,Domain and Range
- Composite Functions ,Inverse Functions
- Function Transformations,Polynomial Functions
- Rational Functions
- Exponential and Logarithmic Functions
- Piece-wise Functions,Absolute Value Functions
- Even and Odd Functions,Asymptotic Behaviour and Limits (Introductory)
Trigonometry and Geometry
- Radian Measure,Trigonometric Functions
- Graphs of Trigonometric Functions
- Trigonometric Identities and Equations
- Inverse Trigonometric Functions
- The Sine Rule, Cosine Rule, and Area of a Triangle
- 3D Geometry
- Vectors in Two and Three Dimensions
- Vector Applications (including angles, projections, and geometric proofs)
Statistics and Probability
- Representation of Data
- Statistical Measures (mean, median, variance, standard deviation)
- Probability Concepts
- Probability Distributions,Binomial Distribution
- Normal Distribution
- The Central Limit Theorem (AAHL only)
- Hypothesis Testing (AAHL only)
Calculus
- Concept of a Limit and Derivative,Rules of Differentiation
- Derivatives of Trigonometric, Exponential, and Logarithmic Functions
- Applications of Derivatives,
- Implicit Differentiation and Related Rates (AAHL only)
- L’Hôpital’s Rule and Optimization Problems (AAHL only)
- Antiderivatives and Indefinite Integrals
- Definite Integrals and Area Under Curves
- Integration by Substitution and by Parts (AAHL only)
- Differential Equations and Modelling (AAHL only)
