GE 115 - College Algebra


Table of Contents


Chapter P: Fundamental Concepts of Algebra

Section P.1: Algebraic Expressions and Real Numbers
  1. Algebraic Expressions
  2. Example 1.1
  3. Evaluating Algebraic Expressions - The Order of Operations
  4. Examples 1.2 - 1.4
  5. Formulas and Mathematical Models
  6. Sets
  7. The Set of Real Numbers
  8. The Real Number Line
  9. Ordering the Real Numbers
  10. Absolute Value
  11. Distance between Points on a Real Number Line
  12. Properties of Real Numbers and Algebraic Expressions
  13. Simplifying Algebraic Expressions
  14. Properties of Negatives
Section P.2: Exponents and Scientific Notation
  1. The Product and Quotient Rules
  2. Zero as an Exponent
  3. Negative Integers as Exponents
  4. The Power Rule for Exponents (Powere to Powers)
  5. The Products-to-Powers Rule for Exponents
  6. The Quotients-to-Powers Rule for Exponents
  7. Simplifying Exponential Expressions
  8. Scientific Notation
  9. Converting from Scientific to Decimal Notation
  10. Converting from Decimal to Scientific Notation
  11. Computations with Scientific Notation
  12. Applications:  Putting Numbers in Perspective
Section P.3: Radicals and Rational Exponents
  1. Square Roots
  2. Simplifying Expressions of the Form SQRT(a^2)
  3. The Product Rule for Square Roots
  4. The Quotient Rule for Square Roots
  5. Adding and Subtracting Square Roots
  6. Rationalizing Denominators and Numerators
  7. Other Kinds of Roots
  8. Rational Exponents
Section P.4: Polynomials
  1. How We Describe Polynomials
  2. Adding and Subtracting Polynomials
  3. Multiplying Polynomials
  4. The Product of Two Binomials:  FOIL
  5. Multiplying the Sum and Difference of Two Terms
  6. The Square of a Binomial
  7. Special Products
  8. Polynomials in Several Variables
Section P.5: Factoring Polynomials
  1. Common Factors
  2. Factoring by Grouping
  3. Factoring Trinomials
  4. Factoring the Difference of Two Squares
  5. Factoring Perfect Square Trinomials
  6. Factoring the Sum and Difference of Two Cubes
  7. A Strategy for Factoring Polynomials
  8. Factoring Algebraic Expressions Containing Fractional and Negative Exponents
Section P.6: Rational Expressions
  1. Rational Expressions
  2. Simplifying Rational Expressions
  3. Multiplying Rational Expressions
  4. Dividing Rational Expressions
  5. Adding and Subtracting Rational Expressions with the Same Denominator
  6. Adding and Subtracting Rational Expressions with the Different Denominators
  7. Complex Rational Expressions

Chapter 1: Equations and Inequalities

Section 1.1: Graphs and Graphing Utilities
  1. Points and Ordered Pairs
  2. Example 1.1.1
  3. Graphs of Equations
  4. Example 1.1.2
  5. Graphing Equations and Creating Tales Using a Graphing Utility
  6. Intercepts
  7. Interpreting Information Given by Graphs
  8. Example 1.1.3
Section 1.2: Linear Equations and Rational Equations
  1. Solving Linear Equations in One Variable
  2. Linear Equations with Fractions
  3. Rational Equations
  4. Types of Equations
Section 1.3: Models and Applications
  1. Problem Solving with Linear Equations
  2. Solving a Formula for One of its Variables
Section 1.4: Complex Numbers
  1. The Imaginary Unit i
  2. Operations with Complex Numbers
  3. Example 1.4.1
  4. Multiplying Complex Numbers
  5. Example 1.4.2
  6. Example 1.4.3
  7. Example 1.4.4
  8. Complex Conjugates and Division
  9. Example 1.4.5
  10. Roots of Negative Numbers
  11. Example 1.4.6
  12. Example 1.4.7
  13. Example 1.4.8
Section 1.5: Quadratic Equations
  1. Solving Quadratic Equations by Factoring
  2. Solving Quadratic Equations by the Square Root Property
  3. Completing the Square
  4. Solving Quadratic Equations Using the Quadratic Formula
  5. The Discriminant
  6. Determining Which Method to Use
  7. Applications
Section 1.6: Other Types of Equations
  1. Polynomial Equations
  2. Radical Equations
  3. Equations with Rational Exponents
  4. Equations That Are Quadratic in Form
  5. Equations Involving Absolute Value
Section 1.7: Linear Inequalities and Absolute Value Inequalities
  1. Interval Notation
  2. Intersections and Unions of Intervals
  3. Solving Linear Inequalities in One Variable
  4. Inequalities with Unsual Solution Sets
  5. Solving Compound Inequalities
  6. Solving Inequalities with Absolute Value
  7. Applications
Chapter 2: Functons and Graphs

Section 2.1: Basics of Functions and Their Graphs
  1. Relations
  2. Functions
  3. Functions as Equations
  4. Function Notation
  5. Graphs of Functions
  6. The Vertical Line Test
  7. Obtaining Information from Graphs
  8. Identifying Domain and Range from a Functions's Graph
  9. Identifying Intercepts from a Function's Graph
Section 2.2: More on Functions and Their Graphs
  1. Functions and Difference Quotients
  2. Piecewise Functions
  3. Increasing and Decreasing Functions
  4. Relative Maxima and Relative Minima
  5. Even and Odd Functions and Symmetry
  6. Step Functions
Section 2.3: Linear Functions and Slope
  1. The Slope of a Line
  2. The Point-Slope Form of the Equation of a Line
  3. The Slope-Intercept Form of the Equation of a Line
  4. Equations of Horizontal and Vertical Lines
  5. The General Form of the Equation of a Line
  6. Using Intercepts to Graph Ax + By + C = 0
  7. Applications
Section 2.4: More on Slope
  1. Parallel and Perpendicular Lines
  2. Slope as Rate of Change
  3. The Average Rate of Change of a Functions
Section 2.5: Transformations of Functions
  1. Graphs of Common Functions
  2. Vertical Shifts
  3. Horizontal Shifts
  4. Reflections of Graphs
  5. Vertical Stretching and Shrinking
  6. Horizontal Stretching and Shrinking
  7. Sequence of Transformations
Section 2.6: Combinations of Functions; Composite Functions
  1. The Domain of a Function
  2. The Algebra of Functions: Sum, Difference, Product, and Quotient of Functions
  3. Composite Functions
  4. Determine Domains for Composite Functions
  5. Decomposing Functions
Section 2.7: Inverse Functions
  1. Verifying Inverse Functions
  2. Finding the Inverse of a Functions
  3. The Horizontal Line Test and One-to-One Functions
  4. Graphs of f and f-1
  5. Finding the Inverse of a Domain-Restricted Function
Section 2.8: Distance and Mid-point Formulas; Circles
  1. The Distance Formula
  2. The Midpoint Formula
  3. The Standard Form of the Equation of a Circle
  4. Using the Standard Form of a Circle's Equation to Graph the Circle
  5. Converting the General Form of a Circle's Equation to Standard Form and Graphing the Circle
Chapter 3: Polynomial and Rational Functions

Section 3.1: Quadratic Functions
  1. Graphs of Quadratic Functions
  2. Graphing Quadratic Functions in Standard Form
  3. Minimum and Maximum Values of Quadratic Functions
  4. Applications of Quadratic Functions
Section 3.2: Polynomial Functions and Their Graphs
  1. Identify Polynomial Functions
  2. Smooth, Continuous Graphs
  3. End Behavior of Polynomial Functions
  4. Zeros of Polynomial Functions
  5. Multiplicities of Zeros
  6. The Intermediate Value Theorem
  7. Turning Points of Polynomial Functions
  8. A Strategy for Graphing Polynomial Functions
Section 3.3: Dividing Polynomials; Remainder and Factor Theorems
  1. Long Division of Polynomials and the Division Algorithm
  2. Dividing Polynomials Using Synthetic Division
  3. The Remainder Theorem
  4. The Factor Theorem
Section 3.4: Zeros of Polynomial Functions
  1. The Rational Zero Theorem
  2. Find Zeros of a Polynomial Function
  3. Solving a Polynomial Equation - The Fundamental Theorem of Algebra
  4. The Linear Factorization Theorem
  5. Descartes's Rule of Signs
Section 3.5: Rational Functions and Their Graphs
  1. Rational Functions
  2. Use Arrow Notation
  3. Vertical Asymtotes of Rational Functions
  4. Horizontal Asymtotes of Rational Functions
  5. Using Transformations to Graph Rational Functons
  6. Graphing Rational Functons
  7. Slant Asymptotes
  8. Applications
Section 3.6: Polynomial and Rational Inequalities
  1. Procedure for Solving Polynomial Inequalities
  2. Solving Rational Inequalities
  3. Applications
Section 3.7: Modeling Using Variation
  1. Direct Variation
  2. Inverse Variation
  3. Combined Variation
  4. Joint Variation
Chapter 5: Systems of Equations and Inequalities

Section 5.1: Systems of Linear Equations in Two Variables
  1. Systems of Linear Equations and Their Solutions
  2. Eliminating a Variable Using the Substitution Method
  3. Eliminating a Variable Using the Addition Method
  4. Linear Systems Having No Solution or Infinitely Many Solutions
  5. Functions of Business: Break-Even Analysis
Section 5.2: Systems of Linear Equations in Three Variables
  1. Systems of Linear Equations in Three Variables and Their Solutions
  2. Solving Systems of Linear Equations in Three Variables by Eliminating Variables
  3. Applications