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Competitive Mathematics I

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Open to: Grades 9-12

Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Algebra I, Geometry, and Competitive Mathematics Prep or equivalent; completion of Algebra II and prior participation in AMC 10 recommended

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: CM1

Course Description


This course is designed to extend skills in problem solving taught in Competitive Mathematics Prep, to foster mathematical creativity, and to prepare students for competitions similar to the American Mathematics Competition (AMC 10, 12). Students learn to think at an advanced level as they tackle challenging problems. Students explore a variety of math topics and problem-solving strategies in-depth, and practice problem-solving contest-style problems. Topics addressed in this course will include advanced concepts from algebra, geometry, and precalculus. Videos from Art of Problem Solving review both the material and problem-solving skills as students progress through the required textbook. There are timed practice AMC 10 and 12 exams that students complete as well to help them prepare for the real exams. 

For a detailed list of topics, click the List of Topics tab.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructor via email with questions or concerns at any time. Live one-on-one online review sessions can also be scheduled to prepare for the graded assessments, which include homework, unit exams, and a cumulative midterm and final.

This course has synchronous virtual class meetings, but participation is optional. Students may also schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. View the Strategy Session schedule on this webpage for class meeting times. Meetings will be recorded for students who are unable to attend due to scheduling conflicts.

Terms and Conditions

Virtual classrooms, and student activities in the classroom, may be recorded and added to the course as an ongoing asset for all class students to review. Students may be invited to interact in CTY community spaces that include students and instructors and potentially specially invited guests that are not enrolled in their course. Videos from YouTube or other web providers may be present in the course. Video recommendations or links provided at end of videos are generated by the video host provider and are not CTY recommendations.  Student contributions (e.g., projects, forum posts, etc.) may remain in the course after the student completes the course. These artifacts may be preserved to showcase student work or to continue important conversations.

Competitive Math 1


Materials Needed

The Art of Problem Solving, Vol. 1: The Basics, by Sandor Lehoczky, Richard Rusczyk, 7th Edition
  • ISBN-13: 978-0977304561
  • ISBN-10: 0977304566

Competitive Math textbook


List of Topics

The following topics will be covered in the course:

  • Exponents and Logarithms
  • Complex Numbers
  • Linear Equations
  • Proportions
  • Number Theory
  • Quadratic Equations
  • Special Factorizations and Manipulations
  • Reasoning with Definitions
  • An Introduction to Circles
  • Angles
  • Triangles
  • Quadrilaterals
  • Polygons
  • Areas
  • Coordinate Geometry
  • Power of a Point
  • Three Dimensional Geometry
  • Geometric Transformations
  • Functions
  • Inequalities
  • Operations and Relations
  • Sequences and Series
  • Combinatorics
  • Statistics and Probability
  • Sets
  • Proofs

Strategy Session

A weekly strategy session will be held online every Tuesday evening from 8 - 9 p.m. ET. Attendance is optional and all sessions are recorded so students can watch them at a later time. Instructions and details are posted on the course website for enrolled students.

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

Zoom online virtual classroom
This course uses an online virtual classroom which can be used for instructor-student communication if the student has any questions about the course or curriculum. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students will need a computer with the Zoom desktop client installed to watch any recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.