Mathematics Notes — Free & Complete

Argand plane, modulus and argument, De Moivre's theorem, roots of complex numbers.

Domain, range, one-to-one, onto functions. Group theory: closure, associativity, identity, inverse.

Elementary row operations, determinant by cofactor expansion, solving 3×3 systems using Cramer's rule.

Discriminant, roots formation, word problems leading to quadratic equations.

All four types of partial fraction decomposition with full worked examples.

Arithmetic and geometric progressions, sum formulas, word problems and sigma notation.

Counting principles, binomial expansion, Pascal's triangle, classical probability, conditional probability.

Step-by-step induction proofs for all standard formulas tested in boards.

Unit circle approach, all identities derived, period and amplitude, inverse function domains.

All standard identities with proofs, elimination and substitution methods.

Ambiguous case in law of sines, Heron's formula, angle of elevation/depression problems.

Limit theorems, 0/0 and ∞/∞ forms, continuity at a point and over an interval.

Product, quotient, chain rules. Differentiation of trigonometric, logarithmic, exponential functions.

First and second derivative tests, optimization word problems, Newton-Raphson method.

Standard forms, substitution method, by parts (LIATE rule), reduction formulas.

Area between curves, volume of revolution, definite integral applications.

Separation of variables, integrating factor method, applications to growth/decay problems.

Equations of conic sections, tangent and normal equations, focus-directrix properties.

Graphical method for 2-variable LPP, corner point theorem.

Work done, torque, area of parallelogram, volume of parallelepiped using vector methods.