CM503 – AMC10/AMC12 and AIME Prep (High school students Only)

Description: 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. CM503 helps students improve their scores on AMC10/12 and AIME.

Who should take this course? Students who wish to enroll this class are expected to have mid AMC 10 score (100+) and/or have completed our CM401 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:

Spring CM503A (AMC10/12 Prep)

Week 1: Algebra topics (functions and graphing, polynomials, sequences, solving equations)
Week 2: Geometry topics (length and area in triangles, circles, and quadrilaterals)
Week 3: Combinatorics topics (casework, complementary, constructive counting)
Week 4: Number theory topics (factorization, GCD/LCM; primes powers; bases)

Spring CM503B (AIME Prep)

Week 1: Geometry (part 1) topics (similarity; cyclic quads and power of a point; Ptolemy)
Week 2: Geometry (part 2) topics (applications of trigonometry; laws of sines and cosines)
Week 3: Combinatorics (part 1) topics (PIE; bijections; recursion; combinatorial identities)
Week 4: Combinatorics (part 2) topics (conditional probability; events with states; graphs)
Week 5: Number theory/algebra topics (polynomials, sequences, powers of primes)

Fall Semester:
Week #            Topic
1                        Solving equations and system of equations
2                       Functions and polynomials
3                       Inequalities and optimization
4                       Sequences and series
5                       Congruence and similarity
6                       Cyclic quadrilaterals and Ptolemy theorem
7                       Computational Geometry (Laws and sines and cosines)
8                      Coordinates and solid (3D) geometry
9                      Three C’s counting techniques (Casework; complementary; constructive)
10                    Probability and geometric probability
11                     Prime factorization; lcm and gcd; Diophantine equations
12                     Modular arithmetic and divisibility

Spring Semester:
Multiple special AMC10/12 and AIME prep sessions from January to Early March

Who should skip this course: Students who scored 5+ on AIME