Course Description
Math Challenge III and Math Challenge IV courses are for students who are qualified to participate in the AIME or USA(J)MO invitational competitions, or have an equivalent level of mathematical experience. Topics include algebra, geometry, combinatorics, and number theory, with the focus more on in-depth problem solving strategies, theorems, and techniques, including pairing, change of variables, inequalities, theorems such as Ceva and Menelaus, bijections, and more. The curricula have been proven to help students develop strong problem solving skills that make them perform well in math contests such as AIME, USA(J)MO, ARML, and ZIML Varsity.
MC III or MC IV? In most cases, it is recommended that students complete MC III before taking MC IV. MC III covers fundamentals knowledge and problem solving for students preparing for Advanced AMC 10/12 and AIME. MC IV covers topics and problem solving for students qualified for USA(J)MO and above.
Sample Topics and Problems
MC III Topics and Sample Problems (click here)
Algebra
Chapter Topics
- Review of Logarithms
- Fundamentals of Complex Numbers
- Techniques for Solving Equations
- Techniques for Solving Inequalities
Sample Questions



Geometry
Chapter Topics
- Geometry with Algebraic Techniques
- Geometric Transformations
- Transformations Continued
- Trigonometry
- Menelaus and Ceva
Sample Questions



Combinatorics
Chapter Topics
- Principles in Combinatorics
- Problem Types and Techniques
- Binomial Theorem and Combinatorial Identities
- Bijection and Review Problems
- Probability – The Classical Model
- Geometric Probability and Random Variables
Sample Questions



Number Theory
Chapter Topics
- Review of Fundamental Concepts, Methods, and Theorems
- Problem Solving Techniques in Number Theory
- The Floor Function
- Number Theory Functions
- Further Practice in Number Theory
Sample Questions



MC IV Topics and Sample Problems (click here)
Summer Sample Topics for Algebra
- Polynomials
- Inequalities
- Functional equations
- Mathematical induction
- Complex numbers
- Sequences
- One-to-one correspondence
- Algebra problems in Math Olympiads
Fall Sample Topics for Geometry
- Famous Theorems in Geometry
- Adding auxiliary lines
- Ratios in Geometry
- Straight line shapes
- Circles
- Transformations
- Concurrence and collinearity
- Analytical Geometry
- Proofs in Geometry
- Phantom points
- Area methods
- Analytical methods
- Vectors
- Solid Geometry
- Inequalities in Geometry
- Combinatorial Geometry
- Geometry problems in Math Olympiads
Winter Sample Topics for Combinatorics
- Counting
- General functions
- Graph theory
- Combinatorial identities
- Pigeonhole Principle
- Calculating twice
- Combinatorial Geometry
- Ramsey Theory
- The extremal principle
- Coloring
- Covering
- Combinatorics problems in Math Olympiads
Spring Sample Topics for Number Theory
- Integers
- The floor function
- Modular arithmetic
- Some important Number Theory Theorems
- Number base systems
- Diophantine equations
- Modular equations
- Quadratic residues
- Number Theory problems in Math Olympiads
Live Courses
Self-Paced Courses
It is recommended MC IV is taken as a live course. However, selected sessions, especially those focused on fundamental Math Olympiad topics, are available as self-paced.
Textbooks
Note: Topics for MC IV are selected for each session, so there is no textbook associated with the MC IV course.