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Honors Precalculus

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Prerequisites: Qualifying math score and completion 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 webpages, and practice problems with solutions, are provided for the student. Students progress through the course at their own pace, and are expected to watch videos and review notes regularly. Each student is assigned to an 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 be scheduled as well to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final.

Instructors use virtual classroom software allowing video, voice, text, screen sharing and whiteboard interaction. Students are strongly encouraged to work on the course at least 1 hour a day, 5 days a week (for a 6 month enrollment), and email their instructors at least once per week.

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:

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.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.