Mathiit Online

Algebra

• Algebraic Identities, Algebraic Manipulations, and an attempt to understand
• Symmetric functions. Introduction to Sequences and Progression (AP,GP,HP,AGP). Summation Operator and Summation techniques. 
• Inequality method to Solve Problems and Diophantine Equations. Polynomial and Theorem (Factor,Remainder, Rational Root, Intermediate Value theorem, Vieta’s relation, Newton Girard Formula, Identity Theorem and applications, Interpolation techniques).
• Solution of Quadratic Equations. Nature of roots and its applications. Formation of Quadratic Equations and transformation of roots. Common roots in polynomials. Application of nth roots of unity.

Number theory

• Introduction to Number system, Divisibility theorem and related corollaries, Divisibility tests for integers. GCD and its properties, LCM and its Properties. Prime numbers and its Properties. Modular Arithmetic. Arithmetic Functions.
• Fermat, Wilson and Eular theorem. Diophantine equations. Surds. Perfect Square and Perfect cube. Greatest integer function and its Properties.

Combinatorics

• Fundamental Counting Principles. Factorial notation. 
• Combination and associated theorems. 
• Permutations and associated theorems. 
• Circular Permutation. Inclusion exclusion Principle. Derangement and associated identities. 
• Bijection Principle Generating function method. Counting via recursion. Board based Problems.

Geometry

• Basic Nomenclature. Angle chasing techniques (complementary and supplementary angles, Vertically Opposite Angles (VOA), parallel lines and angles Corresponding angles and Alternate angles, Angle Sum theorem Congruent triangles, Similar triangles). 
• Theorems in a triangle (Triangle Inequality, Pythagoras theorem, Acute and obtuse angled theorem, Area Lemma – Area ratio theorem of Similar triangles, Mid-Point theorem, Basic Proportionality theorem, Apollonius theorem, Stewarts theorem). 
• Quadrilaterals (Rectangle, Square, parallelogram, rhombus, trapezium, Ceva’s theorem, Menelaus theorem) Circles and associated theorem.
•  Cyclic Quadrilaterals). Trigonometry (Sine rule, Cosine rule, m-n theorem, centers and radii)