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Estimated Completion Time

2 segments / 36 weeks


Students, as mathematic analysts, investigate how advanced mathematics concepts are used to solve problems encountered in operating national parks. As students venture from algebra to trigonometry, they analyze and articulate the real-world application of these concepts. The purpose of this course is to study functions and develop skills necessary for the study of calculus. This course includes algebra, analytical geometry, and trigonometry.

Note: Pre-Calculus is an honors-only course.


Note: content varies depending on the course version. For currently enrolled students, please refer to the syllabus located in the course information area for curriculum specifics.

Major Topics and Concepts

Segment 1

  • Functions and Their Graphs
  • Introduction to Function
  • Graphs of Function
  • Shifting, Reflecting and Stretching Graphs
  • Combinations of Functions
  • Inverse Functions
  • Polynomial and Rational Functions
  • Quadratic Functions
  • Polynomial Functions of Higher Degree
  • Real Zeros of Polynomial Functions
  • Complex Numbers
  • The Fundamental Theorem of Algebra
  • Writing about Polynomials
  • Rational Functions and Asymptotes
  • Graphs of Rational Functions
  • Exponential and Logarithmic Functions
  • Exponential Functions and Their Graphs
  • Logarithmic Functions and Their Graphs
  • Properties of Logarithms
  • Solving Exponential and Logarithmic Equations and their Models
  • Trigonometric Functions
  • Radian and Degree Measure
  • Trigonometric Functions: The Unit Circle, Any Angle
  • Right Triangle Trigonometry
  • Trigonometric Function of Any Angle
  • Graphs and Analysis 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: Linear, Factored or Quadratic
  • Sum and Difference Formulas
  • Multiple Angle Formulas


Segment 2

  • Additional Topics in Trigonometry
  • Laws of Sines and Cosines and Applications
  • Vectors in the Plane and 3 Dimensions
  • Vectors and Dot Products
  • Cross Product of To Vectors
  • Complex Numbers in Trigonometric Form and DeMoivre’s Theorem for Roots
  • Sequences, Series, and Poof by Induction
  • Sequences and Summation Notation
  • Arithmetic and Geometric Sequences
  • Mathematical Induction
  • Topics in Analytic Geometry
  • Conic Sections: Parabolas, Ellipses, Hyperbolas
  • Conics Collage
  • Parametric Equations
  • Polar Coordinates and their Graphs
  • Limits and Introduction to Calculus
  • Introduction to Limits
  • Evaluating Limits and One-Sided Limits
  • Continuity at a Point



Credits 1

Competency Group Overview

Meets mathematics graduation requirement.


  • Functions
    Students will demonstrate an understanding of functions by analyzing key features of their graphs, solving and graphing problems modeled by polynomial, rational, radical, exponential, logarithmic, and piecewise functions, and creating constraints of functions.
  • Applications of Functions
    Students will demonstrate an understanding of applications of functions by solving systems of equations, solving mathematical problems involving combined and composite functions, graphing inverse functions, and solving the numerical value of a difference quotient.
  • Conic Sections
    Students will demonstrate an understanding of conic sections by creating equations of conics, graphing the equations of conics, analyzing key features, and solving real-world problems modeled with conics.
  • Sequences and Series
    Students will demonstrate an understanding of sequences and series by solving problems involving arithmetic and geometric sequences and series in mathematical and real-world contexts.
  • Trigonometry
    Students will demonstrate an understanding of trigonometry by evaluating trigonometric functions and their angles, solving mathematical problems using the Laws of Sines and Cosines, explaining the Unit Circle, and graphing trigonometric functions.
  • Trigonometric Identities and Formulas
    Students will demonstrate an understanding of trigonometric identities and formulas by solving problems using the Pythagorean Trigonometric Identities, proving angle formulas, and solving trigonometric equations.
  • Vectors
    Students will demonstrate an understanding of vectors by composing vectors in component, linear, and trigonometric form, solving problems involving vectors, and evaluating vector scalars and magnitude.
  • The Coordinate Plane
    Students will demonstrate an understanding of the coordinate plane by graphing equations in the polar coordinate plane, solving problems involving complex numbers represented on the coordinate plane, and graphing parametric equations.


Algebra I, Geometry, and Algebra II.


Course: To complete the honors version of this offering, you must discuss this with your instructor during your welcome call.

Project/Experience: Honors is awarded by earning "Exceeds" on all rubric assessments.

Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.