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Honors Precalculus (NCAA Approved)

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

Prerequisites: Successful completion of at least one semester of Algebra II or the equivalent

Course Format: Session Based. See calendar for session dates and application deadlines.

Course Length: 30 weeks

Recommended School Credit: One full year of high school credit

Student Expectations: Students are strongly encouraged to work at least 1 hour a day, 5 days a week.

Course Code: PREY

Course Description


This is a full-length online Honors Precalculus course for accelerated students. In this course, students will extend topics introduced in Algebra II and learn to manipulate and apply more advanced functions and algorithms. This course provides a mathematically sound foundation for students who intend to study Calculus.

Online course materials, such as videos, notes, interactive webpages, and practice problems with solutions, are provided for the student. Students are expected to watch videos and review notes regularly. Each student is assigned to a CTY instructor to help them during their course. Videos in the course are provided by Thinkwell.

In this course, participation in forums and synchronous online virtual sessions are required as part of the final grade. Discussion forums are located within the course where students will be required to respond to a given prompt and then comment on responses by other students. Online sessions, led by a CTY instructor, are held in Adobe Connect, which allows for video, voice, text, screen sharing, and whiteboard interaction. 

Students can contact their instructors via email with questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well, to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final.

Topics include:

  • Relations and functions
  • Polynomial and rational functions
  • Exponential and logarithmic functions
  • Special topics
  • Systems of equations and matrices
  • The trigonometric functions
  • Trigonometric identities
  • Applications of trigonometry
  • Topics in analytic geometry
  • Limits

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

Honors Precalculus course banner

Proctor Requirements

Proctor Requirements

A proctor is required for this course if the student’s goal is to obtain a grade. Please review Proctor Requirements for more details.

Materials Needed

Graphing calculator recommended, such as:

  • TI-83 PLUS
  • TI-84 PLUS
  • TI-85
  • TI-86

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Relations and Functions

  • Function Basics
  • Working with Functions
  • Function Domain and Range
  • Equations of a Line
  • Graphing Functions
  • Quadratic Functions: The Vertex
  • Manipulating Graphs: Shifts and Stretches
  • Manipulating Graphs: Symmetry and Reflections
  • Composite Functions
  • Circles

Polynomial and Rational Functions

  • Polynomials:  Long Division
  • Polynomials:  Synthetic Division
  • The Remainder Theorem
  • The Factor Theorem
  • The Rational Zero Theorem
  • Zeros of Polynomials
  • Graphing Simple Polynomial Functions
  • Rational Functions
  • Graphing Rational Functions
  • Inequalities: Rationals and Radicals

Exponential and Logarithmic Functions

  • Function Inverses
  • Finding Function Inverses
  • Exponential Functions
  • Applying Exponential Functions
  • Logarithmic Functions
  • Properties and Graphs of Logarithms
  • Evaluating and Applying Logarithms
  • Solving Exponential and Logarithmic Equations
  • Applying Exponents and Logarithms

Special Topics

  • Conic Sections: Parabolas
  • Conic Sections: Ellipses
  • Conic Sections: Hyperbolas
  • Identifying Conic Sections
  • Binomial Coefficients and the Binomial Theorem
  • Arithmetic and Geometric Sequences
  • Induction
  • Combinations, Permutations and Probability

Systems of Equations and Matrices

  • Solving Linear Systems by Substitution and Elimination
  • Linear Systems of Equations in Three Variables
  • Using Linear Systems: Investments and Partial Fractions
  • Solving Nonlinear Systems
  • Operations with Matrices
  • The Gauss-Jordan Method
  • Evaluating and Applying Determinants
  • Using Inverses of Matrices to Solve Linear Systems
  • Systems of Inequalities
  • Linear Programming

The Trigonometric Functions

  • Angles, Radian Measure, and Arc Length
  • Right Angle Trigonometry
  • The Trigonometric Functions
  • Graphing Sine and Cosine
  • Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts
  • Graphing Other Trigonometric Functions
  • Inverse Trigonometric Functions

Trigonometric Identities

  • Basic Trigonometric Identities
  • Simplifying Trigonometric Expressions
  • Determining Whether a Trigonometric Function Is Odd, Even, or Neither
  • Proving Trigonometric Identities
  • Solving Trigonometric Equations
  • The Sum and Difference Identities
  • Double-Angle Identities
  • Other Advanced Identities

Applications of Trigonometry

  • The Law of Sines
  • The Law of Cosines
  • Heron's Formula
  • Vectors: Operations and Applications
  • Components of Vectors and Unit Vectors
  • Complex Numbers in Trigonometric Form
  • Using DeMoivre's Theorem to find Powers and Roots of Complex Numbers
  • Functions in Polar Coordinates and their Graphs

Topics in Analytic Geometry

  • Rotation of Conics
  • Parametric Equations
  • Graphs of Polar Equations
  • Polar Equations of Conics


  • The Concept of a Limit and Finding Limits Graphically
  • The Limit Laws
  • Evaluating Limits
  • Continuity and Discontinuity

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Sample Video

Precalculus video demo with Professor Edward Burger

System 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 for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.