AA HL Mathematics

Arithmetic sequences and series, Geometric sequences and series, Sum to infinity and convergence, Sigma notation, Laws of logarithms and change of base, Exponential and logarithmic equations, Equations reducible to quadratic form, Partial fractions, Telescoping series, Compound interest annuities and loan repayments, Exponential growth and decay models

Complex numbers in Cartesian polar and Euler form, Modulus and argument, De Moivre's theorem and roots of unity, Polynomial equations with complex roots, Geometry on the Argand diagram, Binomial theorem with positive integer index, Binomial expansion with fractional and negative indices, Permutations and combinations, Arrangements with repeated and restricted elements, Proof by mathematical induction, Proof by contradiction and counter-example

Domain and range, Composite and inverse functions, Polynomial functions factor and remainder theorem, Sum and product of roots, Rational functions and asymptotes, Graph transformations, Modulus equations and inequalities, Exponential and logarithmic functions, Odd and even functions, Modelling with functions including logistic growth, Solving equations graphically with a GDC

Radian measure arc length and sector area, Non-right-angled triangle trigonometry, Sine rule including the ambiguous case, Cosine rule and area of a triangle, Trigonometric identities and compound angle formulae, Double and triple angle formulae, The form R sin of x plus alpha, Solving trigonometric equations, Inverse trigonometric functions, Graphs and modelling with sinusoidal functions, Three dimensional geometry and angles in solids, Bearings and angles of elevation

Systems of linear equations, Complex numbers and polynomial roots, Sequences series and sigma notation, Logarithms and exponential equations, Function composition and inverses, Modulus and inequalities, Trigonometric identities and equations, Counting principles, Proof by induction contradiction and counter-example, Modelling across topics