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Competitive Mathematics II

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Open to: Grades 9-12

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

Prerequisites: Successful completion of Precalculus and Competitive Mathematics I or the equivalent, and prior participation in AMC 10 or 12 or similar.

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: CM2

Course Description


This course is designed to extend skills in problem solving taught in Competitive Mathematics I, to foster mathematical creativity, and to prepare students for competitions similar to the American Mathematics Competition (AMC 12) and the American Invitational Mathematics Examination (AIME).

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 the ‘Art of Problem Solving’ review both the material and problem-solving skills as students progress through the required textbook. There are timed practice AMC 12 and AIME exams that students complete as well to help them prepare for the real exams.

As with every CTY Online Programs course, the student is assigned an instructor to provide feedback, monitor the progress of the student, and grade assessments. 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, tests, 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 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.

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. 

Welcome to Competitive Mathematics II

Materials Needed

There is a textbook purchase required for this course:

The Art of Problem Solving, Volume 2: and Beyond, by Rusczyk and Lehoczky, 7th Ed.

The Art of Problem Solving, Volume 2 and Beyond

A graphing calculator is recommended, such as:

  • TI-83 PLUS
  • TI-84 PLUS

List of Topics

There are five units and twenty-five chapters covering the following topics:

  • Logarithms
  • Triangles
  • Cyclic Quadrilaterals
  • Conics and Polar Coordinates
  • Polynomials
  • Functions
  • Limits
  • Complex Numbers
  • Vectors and Matrices
  • Cross Products and Determinants
  • Analytic Geometry
  • Equations and Expressions
  • Inequalities
  • Combinatorics
  • Sequences and Series
  • Counting
  • Continued Fractions
  • Probability
  • Geometric Constructions
  • Collinearity and Concurrency
  • Advanced Geometric Properties
  • Number Theory
  • Diophantine Equations
  • Graph Theory

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.