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Honors Precalculus

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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: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: One full year of high school credit

Course Code: PRE

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 web pages, 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 does not have any synchronous class meetings, but students may schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. Students can also contact their instructors via email with questions or concerns at any time. 

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.

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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.