# Pre-Calculus

Logarithms and Trigonometry and Parabolas--oh my! If these mathematical buzz words strike fear into your heart, don’t worry: you’re not alone. You’ll soon master these concepts, as well as radicals, fractional exponents and other topics with Scout’s Pre-Calculus class. Lessons and skill assessments are designed to maximize your understanding and retention of key math concepts so that you have the skills to ace the test. RECOMMENDED PREREQUISITE: Successful completion of Algebra II.

Basic and On Demand are always open for registration.

Plus courses are created upon request.

## SEMESTER 1

Unit 1: Algebraic Functions

• Linear Equations and Their Graphs
• Functions Operations
• Inverse Functions
• Polynomial Division and Complex Roots
• Graphs of Polynomial Functions
• Graphing Rational Expressions
• Sketching Graphs Using Function Transformations

Unit 2: Exponential and Logarithmic Functions

• Exponential Functions and Their Graphs
• Logarithmic Functions and Their Graphs
• Properties of Logarithms
• Change of Base
• Rewriting Logarithmic Expressions
• Solving Exponential Equations
• Solving Logarithmic Equations
• Exponential Growth and Decay Models
• Logarithmic Models

Unit 3: Systems of Equations

• The Substitution Method
• Nonlinear Systems of Equations
• Solving Systems of Equations Graphically
• The Elimination Method
• Modeling and Optimization with Two-Variable Linear Systems
• Modeling with Non-Linear Systems

Unit 4: Topics of Analytic Geometry

• Introduction to Conics: Parabolas
• Finding the Standard Equation of a Parabola
• Applications of Parabolas
• Finding the Standard Equation of an Ellipse
• Graphing an Ellipse
• Applications of Ellipses
• Finding the Standard Equation of a Hyperbola
• Using Asymptotes to Sketch a Hyperbola
• Using Asymptotes to Find the Standard Equation

## SEMESTER 2

Unit 5: Trigonometry

• Trigonometric Ratios and Special Right Triangles
• Applications Involving Right Triangles
• Arc Length and the Area of a Circle
• The Unit Circle
• Evaluate Trigonometric Functions Using the Unit Circle
• Evaluate Trigonometric Functions Given a Point
• Find Reference Angles
• Use Reference Angles to Evaluate Trigonometric Functions

Unit 6: Graphs and Inverses of Trigonometric Functions

• Sine and Cosine Curves
• Amplitude and Period
• Translations of Sine and Cosine Curves
• Graph of the Tangent Function
• Graph of the Cotangent Function
• Graph of Secant
• Graph of the Cosecant Function
• Inverse Sine and Cosine Functions
• Inverse Tangent Function

Unit 7: Analytic Trigonometry

• Basic Trigonometric Identities
• Simplifying Trigonometric Expressions
• Factoring Trigonometric Expressions
• Combining Rational Trigonometric Expressions
• Finding Trigonometric Values
• Verifying Trigonometric Identities
• Using Standard Algebraic Techniques to Solve Trigonometric Identities
• Solving Trigonometric Equations Involving Multiple Angles
• Using Sum and Difference Formulas to Evaluate Trigonometric Functions
• Using Sum and Difference Formulas to verify Identities and Solve Trigonometric Equations

Unit 8: Additional Topics in Trigonometry

• Using the Law of Sines and Law of Cosines to Solve an Oblique Triangle
• Applications of the Law of Sines and Law of Cosines
• Finding the Area of an Oblique Triangle

Unit 9: A Glimpse of Calculus

• Vectors and Vector Operations
• Unit Vectors and Directional Analysis
• Application of Vectors
• Parametric Equations
• Limits of Functions