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### Estimated Completion Time

2 segments / 32-36 weeks

### Overview

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 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
Polynomial Functions of Higher Degree
Real Zeros of Polynomial Functions
Complex Numbers
The Fundamental Theorem of Algebra
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
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
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

### Competencies

• Analytical Geometry
Student will demonstrate a conceptual understanding of conic sections, polar coordinates and parametric equations by recognizing, writing, and graphing equations of each type and applying parametric equations through problem solving.
• Analytical Trigonometry
Student will apply concepts of trigonometry and demonstrate understanding of trigonometry by identifying, solving and proving trigonometric equations using identities and formulas including Pythagorean identities, sum and difference identities, reciprocal identities, quotient identities, double and half angle formulas, and power reducing formulas
• Exponential and Logarithmic Functions
Student will demonstrate a conceptual understanding of exponential and logarithmic functions by simplifying and solving equations using properties of logarithms and rules of exponents, graphing logarithmic and exponential functions, and developing mathematical models that use exponential and logarithmic functions to simulate real world applications.
• Functions and Their Graphs
Student will demonstrate a conceptual understanding of functions by identifying and graphing functions and analyzing their graphs.
• Limits and Continuity
Student will demonstrate an understanding of limits by calculating first derivatives of functions using limits and rules for derivatives, using the analytic method to calculate limits of functions and identify continuous functions and types of discontinuity (point, jump or infinite).
• Polynomial and Rational Functions
Student will apply concepts and demonstrate conceptual understanding of polynomial and rational functions by graphing and solving problems using a variety of methodologies including Descartes's Rule of Signs, Fundamental Theorem of Algebra, and Rational Root Theorem.
• Series, Sequences and Proof by Mathematical Induction
Student will demonstrate a conceptual understanding of sequences and series by applying formulas to find the nth term of geometric and arithmetic sequences, sums of geometric and arithmetic series, and will complete proofs by induction.
• Triangle Trigonometry
Student will apply concepts of trigonometry by solving oblique triangles and using right triangle trigonometry (SOH-CAH-TOA), vectors, and the laws of sines and cosines to solve real-world problems.
• Trigonometric Functions
Student will apply concepts of trigonometry and make connections between the Unit Circle and trigonometric functions by analyzing and graphing trigonometric functions and applying these functions to real world applications

None

## 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.