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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: 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

• 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.

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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.