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Competitive Mathematics Prep

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Open to: Grades 7-12

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

Prerequisites: Successful completion of Algebra I or Geometry; prior participation in mathematics competitions recommended

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: CPM

Course Description


This course is designed to extend skills in problem solving taught in MathCounts, to foster mathematical creativity, and to prepare students for competitions similar to the American Mathematics Competition (AMC 8, 10). Students learn to think at an advanced level as they tackle challenging problems. Students explore a variety of math topics including advanced concepts from number theory, probability, algebra, and geometry. Students learn to apply various problem-solving strategies while completing contest-style problems. The course provides notes, practice problems, and videos from Art of Problem Solving to allow students to learn and review both the material and problem-solving skills. As students progress through the course, they will complete timed practice AMC 8 and 10 exams to help them prepare for real competitions.

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 any 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, quizzes, and a cumulative final exam.

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 schedule on the Strategy Session tab for class meeting times. Meetings will be recorded for students who are unable to attend due to scheduling conflicts.

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.

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Materials Needed

There are no required materials for this course.

List of Topics

The following topics will be covered in the course:

  1. Sets
  2. Number Theory
  3. Modular Arithmetic \& Diophantine Equations
  4. Exponents, Sequences, and Series
  5. Equations
  6. Ratios, Rates, and Proportions
  7. Probability
  8. Combinatorics
  9. Triangles and Circles
  10. Areas
  11. Coordinate Geometry
  12. 3D Geometry

Strategy Session

A weekly strategy session will be held online every Thursday 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.