Course image Level 7A - General

Level 7

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

Course image Algebra AIME δ - 7A - 130323

Level 7

- 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

Course image Number Theory A8 θ - 7A - 010523

Level 7

- 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

Course image Combinatorics A8 δ - 7A

Level 7

- 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