Geometry
Locus
Inequality
Area problems
- Carpet Strategy
- Maximising area
- $ \textrm{Inradius} \times \textrm{semi peri meter} = \textrm{Area} $ : application
Lines, Angles and Triangle
- Angle opposite to largest side: Application
- Vectors
- Angle Bisector Theorem – application
- Extended Pythagoras Theorem
- Ceva’s Theorem
- Menelaus Theorem:
Geometry of Circles
- Opposite angles of a cyclic quadrilateral adds up to $180^o$: Application in RMO 2008 Problem 1
- Cyclic Quadrilaterals, Napoleon Triangles: Part 1, Part 2, Part 3
- Inradius, Exradius
- Incenter and con-cyclic points: Application in RMO
- Orthocenter and Circles:
- Power of a Point
- Sine rule and Incenter
- Nine Point Circle:
- Euler formula: $ d^2 = R^2 – 2R\times r$
- Circles in Circle
Geometric Transformation
- Translation – Concept and Application
- Reflection – Concept and Application
- Rotation – Application in Fermat Point Problem
- Inversion – Application, Concept, Part 1, Part 2
Complex Numbers in Geometry
Mass Point Geometry
Combinatorics
Basic Combinatorics
Bijection Principle
Invariance Principle
Extremal Principle
Combinatorial Argument
Partitions
- Partition of $n$ distinct objects into $2$ classes
- Partition of $n$ distinct objects into $3$ classes
- Partition and Recurrence Relation
- Partitions and Generating Functions
Number Theory
Modular Arithmetic
- Arithmetic of Remainders – the experiment
- Arithmetic of Remainders – the proof
- Theory of congruence – introduction
- Congruence relation is an equivalence relation
- Properties of Congruence Relation
- Euclid Algorithm and Modular Inverse
- GCD and Modular Inverse
- Application Problem: Part 1, Part 2, Part 3
- Application Problem: $ 7 $ divides $ 3^{2n+1} + 2^{n+2} $
Divisibility
- Pairing of Divisors
- Solving Equations with primes
- Number Theoretic Function
- Bezout’s Theorem
- Multiplicative Function: Application
Advanced Topics
- Chinese Remainder Theorem
- Geometric Excursion in Number Theory: Part 1, Part 2, Part 3
Algebra
Inequality
- AM-GM Inequality
- Cauchy Schwarz
- Quadratic Mean
- Jensen Inequality – Concept