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# Pre Calculus Math High School Course Outline

## 1.0 Credit

This course is designed to complete the student’s pre-calculus training. Topics from trigonometry and higher algebra are reviewed and/or extended. A study of analytic geometry is included. Basic calculus concepts including limits, derivatives, continuity and integrals will be developed. The course is designed for those capable students who have completed Algebra II. Students successfully completing this course with a grade of “C” or higher should be prepared to take Calculus.

1- Introduction

- Introduction
- Course Description
- MLA Formatting Word 2007
- MLA Documentation Updates
- MLA Citation
- MLA Incorporating Sources
- Completing Math Assessments

2- Linear & Quadratic Functions

- Lines and Points
- Three Types of Lines
- Distance and Midpoint Formulas
- Slope
- Sample Problems
- Linear Equations
- Perpendicular Bisector
- Linear Functions
- Sample Problem 1
- Sample Problem 2
- Complex Numbers
- Quadratic Equations – Factoring
- Completing the Square
- Quadratic Formula
- The Discriminant
- Quadratic Functions – Graphs
- More Examples
- Quadratic Models
- Handout: Linear & Quadratic Functions
- Assignment: Linear & Quadratic Functions

3- Polynomial Functions

- Polynomials
- Remainder Factor Theorems
- Answers To Samples
- Graphing Polynomials
- Maximums and Minimums
- Polynomial Equations
- Rational Root Theorem
- Theorems for Polynomials
- Handout: Polynomial Functions Worksheet
- Assignment: Polynomial Functions

4- Inequalities

- Linear inequalities
- Absolute Value
- Polynomial Inequalities
- Method Two
- Polynomial Inequalities in Two Variables
- Sample Problems
- Sample Problems II
- Linear Programming
- Sample problem
- Sample Problem II
- Sample III
- Handout: Inequalities Worksheet
- Assignment: Inequalities

5- Functions

- Functions
- Operations on Functions
- Sample Problems
- Example Problems
- Reflections
- Symmetry
- Graphing Problems
- Stretching and Translating
- Stretching or Shrinking
- Translating Graphs
- Inverse Functions
- Graphs of inverse functions
- Functions of Two Variables
- Handout: Functions
- Assignment: Functions

6- Exponents and Logarithms

- Integral Exponents
- Continued
- Rational Exponents
- Exponential Functions
- Rule of 72
- The number e and the function ex
- Compound Interest Formula
- Problems
- Logarithmic Functions
- Simple Log Equations
- Laws
- Single Logs
- Base Formula
- Solving Exponential Equations
- Handout: Exponents & Logarithms
- Assignment: Exponents and Logarithms

7- Analytic Geometry

- Equations of Circles
- Sample Problems
- Ellipses
- Sample Problems
- Hyperbolas
- Sample Problems
- Translations of Hyperbolas
- Parabolas
- Translations of the parabola
- Second-Degree Equations
- Essay: Hyperbolas, Asymptotes & Factoring

8- Trigonometric Functions

- Measurement of Angles
- Sine and Cosine Functions
- Quadrant points
- Evaluating and Graphing
- Reference Angles
- Four Other Trig Functions
- Graphs
- Secant graph
- Inverse Trig Functions
- Calculator problems
- Worksheet: Converting Angle Measures
- Essay: Right Triangle Trigonometry

9- Trigonometric Equations

- Trigonometric Equations
- Inclination and slope
- Sine and Cosine Curves
- Equation from the Graph
- Translations
- Graphing Examples
- More Graphing Examples
- Relationships with Functions
- Simplifying trig expressions
- Proving Identities
- Difficult Trig Equations
- Continued
- Handout: Trig Equations & Applications
- Assignment: Trig Equations and Applications

10- Triangle Trigonometry

- Solving Right Triangles
- Continued
- Area of a Triangle
- Sample Problems
- Law of Sines
- Sample Problems
- Ambiguous Case (SSA)
- Law of Cosines
- Sample Problems
- Navigation and Surveying
- Surveying
- Handout: Triangle Trigonometry
- Assignment: Triangle Trignometry

11- Trigonometry Formulas

- Formulas for Cos(a + b)
- Formulas for tan(a + b)
- Double and half-angle formulas
- Sample Problems
- Solving Trig Equations
- Continued
- Handout: Trigonometric Formulas
- Assignment: Trigonometric Formulas

12- Polar Coordinates & Complex Numbers

- Polar Coordinates
- Sketching Graphs In Polar Form
- Geometric and Trigonometric Representation Of Complex Numbers
- Powers of Complex Numbers
- Roots of Complex Numbers
- Handout: Polar Coordinates
- Assignment: Polar Coordinates

13- Sequences and Series

- Arithmetic & Geometric Sequences
- Sample Problems
- Recursive Definitions
- Arithmetic and Geometric Series
- Limits of Infinite Sequences
- Sums of Infinite Series
- Sigma Notation
- Mathematical Induction
- Essay: Sequences & Series

14- Limits and Graphs of Rational Functions

- Limits of Functions
- Quotient theorem
- Continuous vs. Discontinuous
- Graphing Rational functions
- Sample Questions
- Handout: Limits Worksheet
- Assignment: Limits

15- Introduction to Calculus

- Average Rate of Change
- Exact Rate of Change
- Problems to Try
- Derivatives in Curve Sketching
- Sample Problems
- Extreme value problems
- Velocity and Acceleration
- Sample Problem

16- Basic Calculus

- Derivatives of Products
- The Chain Rule
- Exponential and Log Derivatives
- Integration
- Areas
- ample Problems
- Handout: Basic Calculus Worksheet
- Assignment: Basic Calculus

17- Course Survey

- Handout: Course Survey
- Assignment: Course Survey

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