## 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**

1- Introduction

2- Course Description

3- MLA Formatting Word 2007

4- MLA Documentation Updates

5- MLA Citation

6- MLA Incorporating Sources

7- Completing Math Assessments

**2- Linear & Quadratic Functions**

1- Lines and Points

2- Three Types of Lines

3- Distance and Midpoint Formulas

4- Slope

5- Sample Problems

6- Linear Equations

7- Perpendicular Bisector

8- Linear Functions

9- Sample Problem 1

10- Sample Problem 2

11- Complex Numbers

12- Quadratic Equations – Factoring

13- Completing the Square

14- Quadratic Formula

15- The Discriminant

16- Quadratic Functions – Graphs

17- More Examples

18- Quadratic Models

Handout: Linear & Quadratic Functions

Assignment: Linear & Quadratic Functions

**3- Polynomial Functions 3- Polynomial Functions**

1- Polynomials

2- Remainder Factor Theorems

3- Answers To Samples

4- Graphing Polynomials

5- Maximums and Minimums

6- Polynomial Equations

7- Rational Root Theorem

8- Theorems for Polynomials

Handout: Polynomial Functions Worksheet

Assignment: Polynomial Functions

**4- Inequalities**

1- Linear inequalities

2- Absolute Value

3- Polynomial Inequalities

4- Method Two

5- Polynomial Inequalities in Two Variables

6- Sample Problems

7- Sample Problems II

8- Linear Programming

9- Sample problem

10- Sample Problem II

11- Sample III

Handout: Inequalities Worksheet

Assignment: Inequalities

**5- Functions**

1- Functions

2- Operations on Functions

3- Sample Problems

4- Example Problems

5- Reflections

6- Symmetry

7- Graphing Problems

8- Stretching and Translating

9- Stretching or Shrinking

10- Translating Graphs

11- Inverse Functions

12- Graphs of inverse functions

13- Functions of Two Variables

Handout: Functions

Assignment: Functions

**6- Exponents and Logarithms**

1- Integral Exponents

2- Continued

3- Rational Exponents

4- Exponential Functions

5- Rule of 72

6- The number e and the function ex

7- Compound Interest Formula

8- Problems

9- Logarithmic Functions

10- Simple Log Equations

11- Laws

12- Single Logs

13- Base Formula

14- Solving Exponential Equations

Handout: Exponents & Logarithms

Assignment: Exponents and Logarithms

**7- Analytic Geometry**

1- Equations of Circles

2- Sample Problems

3- Ellipses

4- Sample Problems

5- Hyperbolas

6- Sample Problems

7- Translations of Hyperbolas

8- Parabolas

9- Translations of the parabola

10- Second-Degree Equations

Essay: Hyperbolas, Asymptotes & Factoring

**8- Trigonometric Functions**

1- Measurement of Angles

2- Sine and Cosine Functions

3- Quadrant points

4- Evaluating and Graphing

5- Reference Angles

6- Four Other Trig Functions

7- Graphs

8- Secant graph

9- Inverse Trig Functions

10- Calculator problems

Worksheet: Converting Angle Measures

Essay: Right Triangle Trigonometry

**9- Trigonometric Equations**

1- Trigonometric Equations

2- Inclination and slope

3- Sine and Cosine Curves

4- Equation from the Graph

5- Translations

6- Graphing Examples

7- More Graphing Examples

8- Relationships with Functions

9- Simplifying trig expressions

10- Proving Identities

11- Difficult Trig Equations

12- Continued

Handout: Trig Equations & Applications

Assignment: Trig Equations and Applications

**10- Triangle Trigonometry**

1- Solving Right Triangles

2- Continued

3- Area of a Triangle

4- Sample Problems

5- Law of Sines

6- Sample Problems

7- Ambiguous Case (SSA)

8- Law of Cosines

9- Sample Problems

10- Navigation and Surveying

11- Surveying

Handout: Triangle Trigonometry

Assignment: Triangle Trignometry

**11- Trigonometry Formulas**

1- Formulas for Cos(a + b)

2- Formulas for tan(a + b)

3- Double and half-angle formulas

4- Sample Problems

5- Solving Trig Equations

6- Continued

Handout: Trigonometric Formulas

Assignment: Trigonometric Formulas

**12- Polar Coordinates & Complex Numbers**

1- Polar Coordinates

2- Sketching Graphs In Polar Form

3- Geometric and Trigonometric Representation Of Complex Numbers

4- Powers of Complex Numbers

5- Roots of Complex Numbers

Handout: Polar Coordinates

Assignment: Polar Coordinates

**13- Sequences and Series**

1- Arithmetic & Geometric Sequences

2- Sample Problems

3- Recursive Definitions

4- Arithmetic and Geometric Series

5- Limits of Infinite Sequences

6- Sums of Infinite Series

7- Sigma Notation

8- Mathematical Induction

Essay: Sequences & Series

**14- Limits and Graphs of Rational Functions**

1- Limits of Functions

2- Quotient theorem

3- Continuous vs. Discontinuous

4- Graphing Rational functions

5- Sample Questions

Handout: Limits Worksheet

Assignment: Limits

**15- Introduction to Calculus**

1- Average Rate of Change

2- Exact Rate of Change

3- Problems to Try

4- Derivatives in Curve Sketching

5- Sample Problems

6- Extreme value problems

7- Velocity and Acceleration

8- Sample Problems

**16- Basic Calculus**

1- Derivatives of Products

2- The Chain Rule

3- Exponential and Log Derivatives

4- Integration

5- Areas

6- Sample Problems

Handout: Basic Calculus Worksheet

Assignment: Basic Calculus

**17- Course Survey**

Handout: Course Survey

Assignment: Course Survey

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