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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. This course has synchronous virtual class meetings and students may also schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. The instructor will schedule meeting dates/times at the start of the course. Meetings will be recorded for students who are unable to attend due to scheduling conflicts.

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 Zoom, 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.

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. 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.

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

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:

Functions and Their Graphs

  • Rectangular Coordinates
  • Graphs of Equations
  • Linear Equations in Two Variables
  • Functions
  • Analyzing Graphs of Functions
  • A Library of Parent Functions
  • Transformations of Functions
  • Combinations of Functions: Composite Functions
  • Inverse Functions
  • Mathematical Modeling and Variation

Polynomial and Rational Functions

  • Quadratic Functions and Models
  • Polynomial Functions of Higher Degree
  • Polynomial and Synthetic Division
  • Complex Numbers
  • Zeros of Polynomial Functions
  • Rational Functions
  • Non-linear Inequalities

Exponential and Logarithmic Functions

  • Exponential Functions and their Graphs
  • Logarithmic Functions and their Graphs
  • Properties of Logarithms
  • Exponential and Logarithmic Equations
  • Exponential and Logarithmic Models


  • Trigonometric Functions of Any Angle
  • Graphs of Sine and Cosine Functions
  • Graphs of Other Trigonometric Functions
  • Inverse Trigonometric Functions
  • Applications and Models

Analytic Trigonometry

  • Using Fundamental Identities
  • Verifying Trigonometric Identities
  • Solving Trigonometric Equations
  • Sum and Difference Formulas
  • Multiple-Angle and Product-to-Sum Formulas

The Trigonometric Functions

  • Law of Sines
  • Law of Cosines
  • Vectors in the Plane
  • Vectors and Dot Products
  • The Complex Plane

Systems of Equations and Inequalities

  • Linear and Non-Linear Systems of Equations
  • Two-Variable Linear Systems
  • Multivariable Linear Systems
  • Partial Fractions
  • Systems of Inequalities
  • Linear Programming

Matrices and Determinants

  • Matrices and Systems of Equations
  • Operations with Matrices
  • The Inverse of a Square Matrix
  • The Determinant of a Square Matrix
  • Applications of Matrices and Determinants

Sequences, Series, and Probability

  • Sequences and Series
  • Arithmetic Sequences and Partial Sums
  • Geometric Sequences and Series
  • Mathematical Induction
  • The Binomial Theorem
  • Counting Principles
  • Probability

Topics in Analytic Geometry

  • Lines
  • Introduction to Conics: Parabolas
  • Ellipses
  • Hyperbolas
  • Rotation of Conics
  • Parametric Equations
  • Polar Coordinates
  • Graphs of Polar Equations
  • Polar Equations of Conics

Limits and Introduction to Calculus

  • Introduction to Limits
  • Techniques for Evaluating Limits
  • The Tangent Line Problem
  • Limits at Infinity and Limits of Sequences
  • The Area Problem

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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.

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.

Electronic Texbook (eBook) and WebAssign Online Homework System: This course requires the use of WebAssign for online homework and access to the electronic textbook. Visit the WebAssign website for system requirements.