Level 6

Welcome to Cheenta Level 6, advanced mathematics program. This is suitable for 

• IOQM
• AMC 10 and 12
• ISI-CMI Entrances

This is the Induction module of this program. Students usually attend it at the beginning of the course.

This program is useful for AMC 10, 12, IOQM, ISI- CMI Entrances University of Waterloo Contests, UKMT, SMO.

This program is useful for AMC 10, 12, IOQM, ISI - CMI Entrances University of Waterloo Contests, UKMT, SMO.

This program is useful for AMC 10, 12, IOQM, ISI- CMI Entrances University of Waterloo Contests, UKMT, SMO.

• Basic Principles in Number Theory -
  Well ordering Principle, Mathematical
  Induction, Divisibility - Division Algorithm
  
• GCD, LCM, Bezout's Lemma, Euclidean Algorithm
  
• Prime Numbers - FTA and Number Bases
  
• Congruences - Day 1 - Basic properties
• Congruences - Day 2 - Linear Congruences and CRT
  
• Diophantine Equations
  
• Review and Evaluation
  

• 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
  
• Basic Functional Equations
  
• Review and Evaluation

• Linear and Circular Permutations
  
• Combinations and Bijection Principle
  
• Arrangements and Selections with
  Repetition - Stars and Bars
  
• Binomial Theorem and its Coefficients,
  Pascal Triangle
  
• Hockey Stick Identity,
  Multinomial Theorem and its Coefficients
  
• Pigeon - Hole Principle and
  Constructive Counting
  
• Review and Evaluation

• Linear and Circular Permutations
  
• Combinations and Bijection Principle
  
• Arrangements and Selections with
  Repetition - Stars and Bars
  
• Binomial Theorem and its Coefficients,
  Pascal Triangle
  
• Hockey Stick Identity,
  Multinomial Theorem and its Coefficients
  
• Pigeon - Hole Principle and
  Constructive Counting
  
• Review and Evaluation
  

• Triangular Inequality
  
• Congruences and Parallel Lines
  
• Properties of Triangles
  
• Similar Triangles
  
• Ceva's and Menelaus theorem
  
• Mathematical Games
  
• Review and Evaluation

• Triangular Inequality
  
• Congruences and Parallel Lines
  
• Properties of Triangles
  
• Similar Triangles
  
• Ceva's and Menelaus theorem
  
• Mathematical Games
  
• Review and Evaluation
  

This module is suitable for Mathematical Olympiads (IOQM, AMC 10-12) and ISI-CMI Entrance. Spend 15 minutes per day to achieve byte size learning. 

• Number Theory
  
• Algebra
• Geometry
• Combinatorics