Level 7

• System of Linear Equations in 2, 3 Variables
  
• Polynomials - Division Algorithm, Remainder and Factor Theorem, Vieta's Formula, FTA
  
• Polynomials - Rational Root Theorem, Reciprocal and Symmetric Polynomial
  
• Polynomials - Harder problems on Polynomials
  
• Complex Numbers in Algebraic Form
  
• Complex Numbers in Trigonometric Form and nth Roots unity
  
• Review and Evaluation
  

• Linear, Circular Permutations and Combinations
• Bijection Principle, Arrangements and Selections with Repetition
• Binomial, Multinomial Theorem and its coefficients; Pascal's Triangle

Cheenta Level 7 Math Olympiad Program is suitable for advanced training in mathematics.

• Congruence and Similar Triangles
  
• Cyclic Quadrilaterals and Directed Angles
  
• Incentre - Excentre Lemma and Problems on Angle Chasing
  
• Circles and Power of a Point
  
• Lengths and Ratios - Ceva's, Homothety, and Nine Point Circle
  
• Assorted Configurations
  
• Review and Evaluation
  

• Inequalities - Day 1 - AM-GM, Comparison
• Inequalities - Day 2 - Weighted AM-GM, Cauchy Schwarz Inequality
  
• Inequalities - Day 3 - Chebyshev, Rearrangement, harder problems
  
• Functional Equation on Natural Numbers
  
• Functional Equation on Real numbers
  
• Finite Series and Sequences - AP, GP, Special finite series, Trigonometric series
  
• Review and Evaluation
  

• Divisibility - Day 1 - Divisibility, Prime Numbers and Induction
  
• Divisibility - Day 2 - GCD, LCM, Parity, Number Bases
  
• Power of Integers
  
• Floor Function and Fractional Part
  
• Digits of Numbers
  
• Arithmetic Functions - Number and Sum of Divisors, Euler's Totient Function, Legendre's Formula
  
• Review and Evaluation
  

• The Pigeon Hole Principle and Erdős–Szekeres theorem
  
• Principle of Inclusion and Exclusion and GPIE
  
• Integer Solutions and Shortest Routes using GPIE; Derangements
  
• Basics of Generating Functions; Exponential Generating Function
  
• Recurrence Relations; Linear Homogeneous Recurrence Relation
  
• Introduction to Graph Theory
  
• Review and Evaluation