#### Holiday Announcement

In observance of Cesar Chavez Day, UC Scout will be closed on Friday, March 31, 2023. We will resume normal business hours on Monday, April 3, 2023.

# 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**: 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
- Graphing Quadratic Functions
- Polynomial Division and Complex Roots
- Graphs of Polynomial Functions
- Graphing Rational Expressions
- Solving Radical Equations
- 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
- Absolute Value Graphs, Equations, and Inequalities

**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
- Radian Measures
- 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 Quadratic Trigonometric Equations
- 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: Additional Topics for Advanced Mathematics**

- Vectors and Vector Operations
- Unit Vectors and Directional Analysis
- Application of Vectors
- Parametric Equations
- Limits of Functions
- The Complex Number System