Math Challenge III & IV

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)

Math Challenge III has four terms, each with an associated textbook. Learn more about the topics in each term below.

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)

Math Challenge IV has four terms, each with an associated textbook. Note: This is a multi-year class. Students may continue to enroll in MC-IV for up to 3 years and all the major math Olympiad sub-topics shall be covered. Since the size of this class is small, the topics are customized according to the knowledge level of the enrolled students. Learn more about sample topics in each term below.

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

Please visit our “Live Math Courses” page by clicking here for registration for upcoming 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.