### 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

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**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