CM601 – Contest Math Level 6 (Advanced)

This class is intended for students who have been active in math competitions for a few years and are willing to improve their scores by learning more in depths topics and techniques. CM 601 helps students improve their scores on AMC 10/12 and AIME.

Who should take this course? Students who wish to enroll this class are expected to have mid AIME score (6-10) and/or have completed our CM501 course for both fall and spring semesters.

Homework: A 10-15 question problem set will be assigned by the end of each class. Students are expected to spend about 2 hours per week outside the class to finish the homework.

What will be covered:

2019 Spring

Week 1 – 8: Geometry
Week 9 – 10: Number Theory

Week 1: Angles; Similarity; Pythagorean theorem; Special triangles; Area formulas in a triangle
Week 2: Length; Angle bisector theorem; Ratio lemma; Ceva and Menelaus theorems
Week 3: Law of Cosines; Law of Sines; applications of trigonometric identities
Week 4: Circles; Power of a point; Radical axes; Cyclic quads; Ptolemy theorem
Week 5: Coordinates (distance formula; etc.); Geometric transformations (reflection and rotation)
Week 6: Solid (3D) geometry (dihedral angle, etc.)
Week 7: Geometric inequalities and optimization; Constructibility
Week 8: Advanced topics: Homothety; Projective Geo; Incenter Excenter Lemma; Spiral similarity
Week 9: Powers of primes; Fermat’s Little theorem (FLT); Euler’s theorem
Week 10: Congruences; Chinese remainder theorem; Algebraic methods in solving NT problems

2018 Fall (Combinatorics)
Week 1. Review: Casework; Complementary Counting; Constructive Counting
Week 2. Principle of Inclusion and Exclusion (PIE)
Week 3. Counting by bijections
Week 4. Counting in Two Ways
Week 5. Distribution problems
Week 6. Proof techniques: Pigeonhole Principle; Induction; Invariants
Week 7. Fibonacci/Catalan Numbers
Week 8. Recursion
Week 9. Linearity of Expectation
Week 10. Generating Functions
Week 11. Graphs
Week 12. Combinatorial Identities
Summer (Online Only): Algebra
Week 1: Solving system of equations
Week 2: Functions review and special functions
No class on June 19.
Week 3: Exponents and logarithms
Week 4: Quadratic Equations and graphing parabola
Week 5: Polynomials I Division and Factor Theorem
Week 6: Polynomials II Vieta Formulas
Week 7: Complex Numbers and Roots of Unity
Week 8: Inequalities and Cauchy Schwarz Inequality
Week 9: Optimization: Maxima and minima
Week 10: Arithmetic and Geometric Sequences and Series

Who should skip this course: Students who scored 12+ on AIME