CENTRAL ALABAMA COMMUNITY COLLEGE

COURSE SYLLABUS Spring 2007

Math 112 - Precalculus

Instructor : K.W. Nicholson

Phone: 256 215 4336 email: nnicholson@cacc.cc.al.us

Webpage: http://caccphysics.cacc.cc.al.us

COURSE TITLE AND CREDIT:

Math 112 Pre - Calculus Algebra without trig

3 hours Lecture per week for 15 weeks: 3 Semester Hours credit

COURSE PREREQUISITES: Two years of high school algebra and appropriate mathematics placement score or survival of MTH 100

I. COURSE DESCRIPTION

This course emphasizes algebra of functions and includes polynomial, rational, exponential, and logarithmic functions. Additional topics include linear and quadratic equations, systems of equations, matrices, and the binomial theorem,.

II. AIMS AND OBJECTIVES

As a result of successfully completing this course, the student should be able to:

1. Graph linear, quadratic, exponential and logarithmic functions, inverses of functions, rational functions, and conic sections.

2. Find the equations of lines from given information

3. Find inverse functions algebraically and graphically.

4. Graph exponential and logarithmic functions, and solve logarithmic and exponential equations.

5. Do synthetic division and use it to find zeros of polynomial functions.

6. Find real zeros of polynomial functions.

III. CONTENT AND ORGANIZATION

1: Basic Algebra Review

Radical Expressions

• Simplifying Radicals

• Simplifying Radical Expressions, Part 2

• Rationalizing a Binomial Denominator or Numerator of a Radical

2: Equations and Inequalities

Inequalities

• An Introduction to Solving Inequalities

• Solving Compound Inequalities

• More on Solving Compound Inequalities

• Solving Word Problems Involving Inequalities

Inequalities - Quadratics

• Solving Quadratic Inequalities

• Solving Quadratic Inequalities: Another Example

Inequalities - Rationals

• Solving Rational Inequalities

• Solving Rational Inequalities: Another Example

• Determining the Domains of Expressions with Radicals

Inequalities - Absolute Value

• Matching Number Line Graphs with Absolute Values and Inequalities

• Solving Absolute Value Equations

• Solving Equations with Two Absolute Value Expressions

• Solving Absolute Value Inequalities

• Solving Absolute Value Inequalities: More Examples

3: Relations and Functions

Graphing Circles

• Finding the Center-Radius Form of the Equation of a Circle

• Finding the Center and Radius of a Circle

• Decoding the Circle Formula

• Solving Word Problems Involving Circles

Graphing Lines

• An Introduction to Linear Functions: Slope

• Finding the Slope of a Line Given Two Points

• Interpreting Slope From a Graph

• Graphing a Line Using Point and Slope

Equations of Lines

• Writing the Equation of Line in Slope Intercept Form

• Writing the Equation of a Line Given Two Points

• Writing the Equation of a Line in Point-Slope Form

• Matching Equations in Slope-Intercept Form with Their Graphs

• Writing an Equation for a Line in Standard Form

An Introduction to Functions

• An Introduction to Relations and Functions

• Introduction to Functions and the Vertical Line Test

• Identifying Functions

• Function Notation and Finding Function Values

Domain and Range

• Finding the Domain and Range of a Function

• Domain and Range: One Explicit Example

• Satisfying the Domain of a Function

Graphing Functions

• Graphing Some Important Functions

• Graphing Piecewise Defined Functions

• Matching Equations with Their Graphs

Greatest Integer Function

• Graphing the Greatest Integer Function

• The Greatest Integer Function

Manipulating Graphs: Shifting and Stretching

• Shifting Curves Along Axes

• Shifting or Translating Curves Along Axes

• Transforming with Translation and Shifts

• Stretching a Graph

Composite Functions

• Using Operations on Functions

• Composite Functions

• Components of Composite Functions

• Finding Functions That Form a Given Composite

Composite Functions - Applications

• Finding the Difference Quotient of a Function

• Word Problems Involving Composite Functions

4: Polynomial and Rational Functions

Quadratic Functions - Basics

• Deconstructing the Graph of a Quadratic Function

• Nice Looking Parabolas

• Graphs of Parabolas

• Word Problems Involving Quadratic Equations

Polynomials - Long Division

• Using Long Division to Divide Polynomials

• Long Division: Another Example

Polynomials - Synthetic Division

• Using Synthetic Division to Divide Polynomials

• More Synthetic Division

5: Exponential and Logarithmic Functions

Function Inverses

• Understanding Inverse Functions

• Deciding Whether a Function is One-to-One: The Horizontal Line Test

• Deciding whether Two Functions are Inverses of Each Other

• Graphing the Inverse of a Function

Finding Function Inverses

• Finding the Inverse of a Function

Exponential Functions

• An Introduction to Exponential Functions

• Graphing Exponential Functions: Useful Patterns

• Graphing Exponential Functions: More Examples

Applying Exponential Functions

• Using Properties of Exponents to Solve an Equation

• Finding Present Value and Future Value

• Finding an Interest Rate to Match Given Goals

The Number e

• e

• Applying Exponential Functions

Logarithmic Functions

• Introduction to Logarithmic Functions

• Converting Between Exponential and Logarithmic Functions

Solving Logarithmic Functions

• Finding the Value of a Logarithmic Function

• Solving Log Equations

• Graphing Logarithmic Functions

• Matching Logarithmic Functions with Their Graphs

Properties of Logarithms

• Properties of Logarithms

• Expanding a Logarithmic Expression Using Properties

• Combining Logarithmic Expressions

Evaluating Logarithmic Functions

• Evaluating Logarithmic Functions Using a Calculator

• Using the Logarithmic Change of Base Formula

Solving Exponential and Logarithmic Equations

• Solving Exponential Equations

• Solving Logarithmic Equations

• Solving Equations with Logarithmic Exponents

IV. References: Anything you can get your hands on.

V. Required Assignments:Daily quizzes, four mid-term tests, and a comprehensive final.

VI. Evaluation Procedures: Four 100 point exams, (taken in class), a 200 point comprehensive final examination (taken in class).

VII Textbook: PreCalculus, Fourth Edition, by Dugopolski

VIII. Other Important Information:

1. Grading System: A: 90 - 100 Accumulative percent, B: 80 - 89 Accumulative percent, C: 70 - 79 Accumulative percent, D: 60 - 69 Accumulative percent, F: 0 - 59 Accumulative percent.

2. If you decide to drop this course, you must do so formally before mid-term by going to student services in the Administration Building and filling out a drop form. If simply stop coming to class, you will receive an F in this course!

3. if you have a disability that may prevent you from meeting the course requirements, contact the instructor before the end of the first week of classes to file a student disability request and to discuss a reasonable plan. Course requirements will not be waived but accommodations may be made to assist you in meeting the requirements, provided you are timely in working with the instructor to develop a reasonable accommodation plan.