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MAC1105  -  College Algebra
Handouts & Worksheets


 

Overview of MAC1105 - College Algebra  -  PowerPointRule of Five

Review:  Handouts and Worksheets
PERT Study Guide for Mathematics - Link
Courtesy of AIMS Community College - Arithmetic ,  Elementary AlgebraCollege Algebra


Basic Concepts of Algebra (Review Chapter)
Our Number Systems:  Outline
Laws of Exponents: Rules:  BasicAdvanced
Defining and Classifying Polynomials:  Terminology
Factoring Polynomials:  OutlineFactor3 & Key3FactorS1 & KeyS1Factor5 Key5
Solve Linear Equations:  Worksheet3 & Key3
 

Projects:   Analyze the Graph, Graphing Grid for Picture, MyMathLab, Research Report :  Projects
     
♦♦♦♦♦   Essential Handouts, Worksheets & Homework files are noted below with
    Chapters 1 & 2  (26 pages) ,     Chapters 3, 4 & 5  (45 pages)
    Under Construction - The chapters below do not match up with the chapters in our new textbook.
Chapter 1
  Graphs, Functions, and Models
 
 
Now a
Review
Chapter
  Right Triangles
Who was Pythagoras? -  Link
The Pythagorean Theorem - Graphic
The Distance Formula (Proof) - Notes

The Midpoint Formula (Proof) - Notes

Circles:
Find an Equation of a Circle -  Theory Worksheet &  Key ,    Worksheet2
               Graph a circle given the endpoints of a diameter -  PowerPoint

Functions:
Definition, Vertical Line Test, Domain & Range 2 - Class Worksheet
                      Domain & Range:  See page 89 in the textbook for an excellent summary
Evaluate a Function Graphically - Slideshow  (10 pages, pdf)

Lines

SLOPE of a line :  Diagram
  ,  avi
Find an Equation of a Line (Slope & Y-Intercept) -  Notes ,  Class WorksheetKey
Other Forms of a Line - Notes
Linear Functions: Zero / X-Intercept / Solution - Notes
Long Distance Phone Rates 2 - WorksheetEXCEL Graph Example
Graphing Lines Using Slope and Y-Intercept 1  -  WorksheetKey

Solve Linear Equations: Worksheet3 & Key3
Solving Linear Inequalities 1  -  Worksheet  &  Key1: ( ) , [ ]  &  Key2: o , •

The TI-83/84 Graphing Calculator  -  Help Site
Getting Started: the Basics :
Notes
Problems: 
The minus key vs. negative sign, using parentheses, -   Notes (5 pages)
                  
Window Range,  Xres, and Table of Values
Graphing Calculator Computations 2 - 
Homework & Key
Scatter Diagrams and Curve Fitting on the TI-83/84  -  Notes
 
Chapter 2 More on Functions
 
 
Analyzing Functions
Describe the Graph - Notes
Analyze the Graph Class Worksheet - Homework & Key
Sign Graph - Determine the sign (+/-) of  f(x) -  Slideshow ,  Notes Notes2
Examine the Graph 1  [ f(x)>0  vs.  f(x)<0 ] -  Extra Worksheet
Increasing / Decreasing / Constant Functions - Notes ,  PowerPoint  ,  formal definition
Examine the Graph 2   [ f(x)>0 ,  f(x)<0 and increasing/decreasing ] - Class Worksheet
Relative Maximums  -  Mountains  , grf

Operations on Functions
Combinations of Functions: Sum, Difference, Product & Quotient - Notes
The Average Rate of Change of a Function - Notes
The Difference Quotient -  Notes-TheoryExample: f(x) = x3
Find the "slope" of a Parabola  -  GRAPH
avi

Symmetry
Symmetry about the x-axis, y-axis and origin - Notes ,
  Extra Worksheet & Graphs
Symmetry &  Even / Odd Functions - Notes  ,  Examples
Symmetry: about the x-axis, y-axis and origin (animations)  -  GRAPH

                 Animations (avi files) -  y-axis  ,   x-axis  ,  origin  ,  not y-axis  ,  not origin
Symmetry - 
Summary Worksheet

Transformations of Functions
Intro to Transforming Parabolas - PowerPoint
Transformation Terminology -  Notes
Vertex Form of a Parabola -  PowerPointSummary
Transforming Parabolas -  Summary
Understanding the "Slope" of a parabola.  Graphing y = ax2   -  Example
grf , Summary
Finding equations for "Intro to Transforming Parabolas" above -  WorksheetPowerPoint
Finding Equations of Parabolas -  Worksheet ,  [Large Graphs]
Finding Equations of Parabolas - Transformations Worksheet 2 -   HomeworkKey
Sketching Parabolas - WorksheetKey

The Parent Functions  - 
Summary
Transforming Parent Functions -  Class Worksheet & [Large Graphs] , Homework & Key
Transforming y = sin(x) - Notes

Piecewise-Defined Functions
Analyze Piecewise-Defined Functions 1 - Class Worksheet
Analyze Piecewise-Defined Functions 2 - Extra Worksheet
Transforming Piecewise-Defined Functions -  Worksheet 3 & Key ,   Extra Example
Transforming  y = sin(x) - Notes

 

Chapter 3
  Quadratic Functions and Equations; Inequalities
   
The Complex Number System

The Number Systems: Flowchart
Visualizing Complex Numbers (uses Trigonometry)
   Equality  ,     Addition - parallelogram vs. vectors  ,     Subtraction  ,     Multiplication
   Graph & Modulus  ,     Argument  ,     Trig Form ,
Using Complex Numbers - The Mandelbrot Set

Algebraic Techniques of Solving Quadratic Equations
Solving Quadratic Equations Outline
Complete the Square Method  ,  Class Notes [Large Print]  ,  PowerPoint
Quadratic Formula:  Proof  ,   Discriminant  ,  Homework & Key

Using the Graphing Calculator to Solve Equations
Functions: Zeros / X-Intercepts / Solutions / Factors - Class Notes
TI-83/84 Plus Graphing Calculator :  Solving Equations (3 pages) - Summary
Solving Equations with your Graphing Calculator 2 - Homework Key   (MoreKey)

Applications of Parabolas

Flying parabolic arcs in the Vomit Comet to film Apollo 13 -  Notes
Spinning in Zero Gravity  ,  Zero G Flight  ,  Space Lab Winners (2:00-2:45)

Anvil Launching Competition:  -  The right way  ,  Something goes wrong

Maximizing an "Enclosed" Area of a Rectangle -  Homework
   GRAPH:      ex) 1  ,  ex) 2  ,  ex) 3  ,  ex) 4
   Videos:        ex) 1  ,  ex) 2  ,  ex) 3  ,  ex) 4
(Video animations work best in QuickTime to make them interactive)

Finding the Maximum Volume of a Box - Box: PDF , Word ; Table: PDF , Excel

Solving Equations and Inequalities
Absolute Value Inequalities - 
NotesLarger
Solving Equations & Inequalities Review Homework
     
Chapter 4
  Polynomial and Rational Functions
 

 


Power Functions:   f(x) = xn
   Graphs with tables ,  Graphs only ,
   End Behavior

Polynomials

Forms of a Parabola -  Notes
Polynomials: Definitions, Classify & Properties - Terminology  ,
Studying End Behavior - 
End Behavior
Repeated Zeros of a Polynomial (multiplicity), 3 Cases - Notes
Factoring Polynomials: using Zeros and Multiplicity Summary - Notes
Factoring a Polynomial Using Its Graph - Class Worksheet Key ,   Homework & Key
SUMMARY: Factoring Polynomials / Find Zeros of Polynomials 1 - Homework
Functions: Zeros / X-Intercepts / Solutions / Factors - Notes
Intermediate Value Theorem - Notes
The Rational Zeros Theorem - Notes

Rational Functions
Rational Functions and Asymptotes Summary  -  Notes: BasicNotes: Advanced

Find an Equation of the Rational Function given its Table of Values -  Notes
Graphs of Rational Functions:
   with a Hole ,
   with a Slant Asymptote ,
   Special Cases

Solving Rational Inequalities using a Table - Notes

     
Chapter 5
  Exponential and Logarithmic Functions

 

 


Summary of Exponential and Logarithmic Functions - Summary1
  ,  Summary2

Exponential Functions
Magic Penny Problem - Class Worksheet  ,  PowerPoint
Exponential Functions
   Graph  f(x) = 2x    -  Notes1 ,
   Analyze the Graph of  f(x) = 2x  -  Class Worksheet  
   Graphs of other exponential functions -  Notes2
   Graphs of decreasing exponential functions -  Notes3

What is  e ? -  Notes  ,  PowerPoint
Translating Exponential Functions - Notes
Estimating Exponential Functions - Extra Notes
Doubling Rice Grains - Grains of rice on a checkerboard - Notes , supporting calculations
Visualize the graph of  y = 10x  -  Notes (8 pages)
Visualize Powers of 10 - Web Link
Power Functions vs. Exponential Functions - Notes

Finding the Inverse Function:  f -1(x)
Mapping  f(x)  and  f -1(x)  -  Notes
One-to-one Functions:  Definition  , 
Testing if relations are one-to-one
     Relations 1

     More Relations 2
     Parent Functions
Steps to Find the Inverse Function Example
     Outline
     Example1  ,  Example2

Functions and Inverses  -  Homework
Graph of  f(x), f -1(x) and y = x  -  Notes

Logarithmic Functions
What is a Logarithm? History & Applications  -  Notes
Laws of Exponents 2 -  Notes
Evaluating Logarithms - Class Worksheet  ,  Worksheet 2
What is the Common Logarithm of a Number?  -  Notes
Change-of-Base Formula -  Proof
Analyze the Graph of  f(x) = log2(x)  -  Class Worksheet (3 pages)
Graphs of Logarithmic Functions -  Notes
Exponential and Logarithmic Functions - Symmetry
   y = 2x  and  log2x  -  Notes
   More functions  -  Notes

History of Logarithms - Summary  ,  Complete
How were logarithms used in the past?  -  MultiplicationRoots
Table of Logarithms - Table
Estimating Logarithmic Functions - Extra Notes

Applications of Exponential Functions
Drug Medication - Homework
Compound Interest  -  Proof  ,   Class Worksheet Key
Healing of Wounds - Class Worksheet
Monthly Payment Formula - Notes
Carbon-14 Dating
   Class Notes  - All
   C-14 Dating  -  Notes1Notes1- Large Print
 
  Reliability of C-14 Dating  -  Reliability
   Half-life of C-14  -  half-life
   Research Report submitted  - 
Report
River Levels and Flow Rate
   "Periodic" Functions - Graphs
   Rivers in Florida
   Rivers in the USA
   Flow Rates:  the Y-axis:  Linear Scale vs. Logarithmic Scale - Graph

Population Growth
Population Growth - formula
Where did the Population Growth Function come from?  Differential Equation
Exponential Growth of Rabbits in Australia
   Modeling the growth of rabbits -  Notes ,
   The problem continues -  Unintended Consequences
Exponential function vs. Logistics function -   , 
   Comparing the functions -  Graphs
   Growth of Mosquitoes -  Graphs

     
Chapter 6
  Systems of Equations and Matrices
    Systems of Linear Equations
   Summary of 3 Cases -  Notes 
   Example of 3 Methods -  Notes

Solving Systems of Linear Equations Using the TI-83/84 - Notes
Solving Systems of Linear Equations - 3-D Graph - 3-D Graph
Solving Systems of Non-Linear Equations - Notes

Gaussian Elimination
   Matrix Row Transformations - Notes
   Solving Systems of Linear Equations - Handout  ,  Larger Print

Properties of Matrices - Notes

Cramer's Rule - Notes

Partial Fraction Decomposition - Summary