Mathematics

Angles, circular functions, identities, and equations

Extending the number system to ℂ = {a + ib : a,b ∈ ℝ}

Nature of roots, Vieta's formulas, and graphical interpretation

Solving and graphing inequalities in one and two variables

Counting arrangements and selections systematically

Expanding (a+b)ⁿ and the coefficients that govern it

Arithmetic, geometric, and special series

Circles, parabolas, ellipses, and hyperbolas

Coordinates, distance, section formula in three dimensions

Classical and empirical probability, addition and multiplication theorems

Types of relations, composition of functions, and invertibility

Principal values, domain/range, and important identities

Rectangular arrays, operations, and special types

Scalar value from a square matrix — area, volume, and solving linear systems

Tangents, normals, rates of change, monotonicity, and optimisation

Indefinite and definite integration techniques

Area under and between curves

Order, degree, and methods of solution

Scalars, vectors, dot and cross products

Lines and planes in 3D space using vectors

Optimising linear objectives subject to linear constraints

Conditional probability, Bayes' theorem, random variables, and probability distributions