### 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