Pre-Calculus Honors

As a mathematical analyst, you will investigate how advanced math concepts can solve problems encountered in operating national parks. This course includes analytical geometry and trigonometry.

Major Concepts:

Functions and Their Graphs

• Functions and Their Properties
• Graphs of Functions
• Building Functions from Functions
• Inverse Functions
• Graphing Transformations

Polynomial and Rational Functions

• Quadratic Functions
• Polynomial Functions of Higher Degree
• Real Zero of Polynomial Functions
• Complex Zeros
• Fundamental Theorem of Algebra
• Rational Functions and Asymptotes
• Graphs of Rational Functions

Exponential and Logarithmic Functions

• Exponential and Logistic Modeling
• Logarithmic Functions and Their Graphs
• Properties of Logarithms
• Equation Solving

Trigonometric Functions

• Angles and Their Measures
• Trigonometric Functions of Acute Angles
• Trigonomteric Functions: The Unit Circle
• Trigonometric Functions of Any Angle
• Sine and Cosine Functions
• Inverse Trigonometric Functions

Analytic Trigonometry

• Using Fundamental Identities
• Solving Trigonometric Equations
• Proving Trigonometric Equations
• Sum and Difference Formulas
• Multiple-Angle Formulas

Additional Topics in Trigonometry

• Law of Sines and Cosines
• Vectors in the Plane
• Dot Products of Vectors
• DeMoivre’s Theorem and nth Roots

Sequences, Series, and Proof by Induction

• Arithmetic Sequences
• Geometric Sequences
• Series and Summation
• Mathematical Induction

Analytic Geometry

• Introduction to Conics: Parabolas
• Ellipses
• Hyperbolas
• Conics Collage
• Parametric Equations
• Polar Coordinates
• Graphs of Polar Equations

Limits and Introduction to Calculus

• Introduction to Limits and the Derivative
• Techniques for Evaluating  Limits
• Evaluating One-Sided Limits
• Continuity at a Point