**Session ** | **Topics** | **Subtopics** |

1a | Patterns and Sequences | *Sigma notation and series, arithmetic/geometric series, mathematical induction* |

| Exponents and logarithms | *Law of exponents/logarithms, change of base* |

| Counting principles | *Permutations and combinations, binomial theorem* |

1b | Complex numbers | *Operations with complex numbers, cartesian/polar form, complex plane, powers of complex numbers, complex roots, solving systems of equations* |

| Functions | *Function notation, odd/even functions, inverse/composite functions, one-to-one/many-to-one functions, graphs of functions, transformations of graphs, rational/exponential/logarithmic functions, polynomial functions and their graphs, factor and remainder theorems, fundamental theorem of algebra, solving quadratic equations, solving inequalities of functions* |

2 | Statistics | *Population, sample, random sample, frequency distribution of discrete/continuous data, grouped data, mean, variance, standard deviation* |

| Probability | *Venn diagrams, combined/mutually-exclusive events, conditional probability, independent events, Bayes’ theorem, probability distributions, probability density functions, mean/mode/median/variance/standard deviation, binomial/poisson/normal distributions* |

3 | Trigonometry | *Radian, arc length, sector area, the unit circle and trigonometric identities, special angles, Pythagorean identities, compound angle identities, double angle identities, cosine rule* |

| Trigonometric functions | *Trigonometric composite/inverse functions, solving trigonometric equations* |

| Vectors | *Vector addition/subtraction, scalar/vector product, vector equation of a line/plane, intersections of lines and planes* |

4 | Limits and derivatives | *Limits, continuity and convergence, derivative of a function, tangents and normals, higher order derivatives, derivatives of different functions, product/quotient rules, chain rules for composite functions, related rates of change, implicit differentiation, maxima and minima, optimisation, relationship between derivatives* |

| Integration | *Antiderivatives, indefinite and definite integrals, area of regions enclosed by curves, volume of revolution, kinematics, integration by substitution/parts* |