AMC Competition Prep Courses
Systematic Training · Top Scores

AMC 8 Express Program — 60 Hours

This course is designed for students with a solid school math foundation who want to compete in AMC 8 and aim for a score of 20+. The 60-hour program includes complimentary printed course materials, covering everything from systematic knowledge building to advanced problem-solving reinforcement.

Phase 1: Systematic Knowledge Building

1. Number Theory

2. Algebra

3. Mid-Term Review

Mid-term test + comprehensive review to consolidate first-half learning.

4. Geometry

5. Probability & Statistics

Phase 2: Advanced Problem-Solving Reinforcement

• Number Theory — comprehensive training
• Speed & Ratio — combined exercises
• Equations & Inequalities — advanced training
• Systems of Equations — advanced training
• Pythagorean Theorem — advanced training
• Plane Geometry — comprehensive training
• Volume — comprehensive training
• Permutations & Combinations — advanced training
• Probability — advanced training
• Mock exam paper analysis

Note: ① Course hours may be adjusted based on student progress; ② Students are expected to complete homework and do preview/review for each lesson.

AMC 10 Full Competition Prep Program

Designed for students with some competition experience and a good school math foundation, but who have not yet systematically organized their competition knowledge and have gaps across topic areas. Students scoring 9–14 correct answers on the AMC 10 diagnostic test are placed in the full program.

The course goal is to help students build a complete and systematic competition math knowledge system, gradually mastering problem-solving techniques and strategies through topic-specific training. After the course, students can further participate in pre-exam sprint sessions and one-on-one tutoring based on their progress.

Course Syllabus

1. Number Theory

• Prime Factorization; Number of divisors, Sum/Product of divisors; LCM and GCD; *Euclidean Algorithm and Bézout's Theorem
• Congruence Theory; *Euler's Theorem and Fermat's Little Theorem
• Divisibility Rules; Sets and Venn Diagrams; Principle of Inclusion and Exclusion
• Digit Representation and Base Conversion; Infinite Repeating Decimals

2. Algebra

• Arithmetic, Geometric, and Periodic Sequences; General Recursive Sequences
• Algebraic Operations; Binomial Theorem, Pascal's Triangle, *Hockey-stick Theorem; Polynomials and Division Algorithm, Simple Remainder Theorem
• Functions and Graphs; Coordinate System; Linear and Quadratic Functions; *Gaussian Function
• Linear and Quadratic Equations; Vieta's Theorem; *Higher-Degree Polynomial Equations and Their Vieta's Theorem
• Linear Inequalities and Systems; AM-GM Inequality; *Cauchy's Inequality; Absolute Value Inequality

3. Geometry

• Basics: Angles, Lines; Parallel and Similar
• Triangles: Perimeter and Area; Pythagorean Theorem; Heron's Formula; Angle Bisector Theorem; Median and Centroid
• Quadrilaterals: Rectangle, Square, Parallelogram; Rhombus; Trapezoids
• Circles: Perimeter and Area, Arc Length and Sector; Chords, Circumscribed Angles, Tangents; Cyclic Quadrilaterals; Power of a Point; *Ptolemy's Theorem
• Solid Geometry: 3D Space and Planes; Rectangular Box, Cube; Prism; Pyramid; Surface Area and Volume; *Frustums; Cylinder and Sphere

4. Combinatorics

• Basic Counting Principles: Sum and Product Rules; Geometric Counting Problems
• Permutations and Combinations; Circular Permutation; Grouping Theorem; Balls into Boxes
• Elementary Probability and Simple Statistics

AMC 12 Full Competition Prep Program

Designed for students with some competition experience and a good school math foundation, but who have not yet systematically organized their competition knowledge and have gaps across topic areas. Students scoring 8–13 correct answers on the AMC 12 diagnostic test are placed in the full program.

The course goal is to help students build a complete and systematic competition math knowledge system, gradually mastering problem-solving techniques and strategies through topic-specific training. After the course, students can further participate in pre-exam sprint sessions and one-on-one tutoring based on their progress.

Course Syllabus

1. Number Theory

• Prime Factorization: Number of Divisors, Sum/Product of Divisors; Factorization Method for LCM and GCD; Euclidean Algorithm and *Bézout's Theorem
• Congruence Theory and Divisibility: Modulus and Residue, Properties of Congruence, *Modular Inverse; Divisibility Rules; Inclusion-Exclusion Principle; *Euler's Theorem / Fermat's Little Theorem; *Chinese Remainder Theorem (CRT); *Wilson's Theorem
• Digit Representation and Base Conversion, Short Division Algorithm; Infinite Repeating Decimals

2. Algebra

• Arithmetic, Geometric, and Periodic Sequences; Recursive Sequences and *Characteristic Equation Method
• Algebraic Manipulation; Pascal's Triangle and Binomial Theorem, Hockey-stick Theorem; Polynomials and Division Algorithm, Fundamental Theorem of Algebra, Generalized Remainder Theorem, Rational Root Theorem, Vieta's Theorem for Higher-Degree Polynomials
• Polynomial Inequalities; Fundamental Inequality, Cauchy's Inequality and Extreme Value Problems
• Trigonometric Functions and Trigonometric Identities; *Product-Sum and Sum-Product Identities
• Logarithm and Its Calculation
• Complex Numbers; Properties of Conjugates and Modulus; Vector Representation; Polar Form; De Moivre's Theorem, Roots of Unity

3. Geometry

• Basics; Law of Sines and Law of Cosines; Heron's Formula, Area and Area Method
• Triangles: Similar Triangles; Angle Bisector and Angle Bisector Theorem, *Angle Bisector Length Formula; Median and Centroid, Median Length Formula; Centers of a Triangle; Menelaus' and Ceva's Theorem, Stewart's Theorem
• Circles: Basic Geometric Properties; Cyclic Quadrilaterals; Power of a Point Theorem; *Ptolemy's Theorem
• Solid Geometry: Box, Cube, Prism; Pyramids; Surface Area and Volume; *Frustums; Cylinder and Sphere; *Three Perpendiculars Theorem; *Euler's Polyhedron Formula

4. Combinatorics

• Basic Counting Principles: Sum and Product Rules; Geometric Counting Problems
• Permutations and Combinations; Circular Permutation; Grouping Theorem; Balls into Boxes; *Advanced Combinatorics Identities; *Recursive Methods in Combinatorics
• Elementary Probability and Simple Statistics