College Algebra
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College Algebra details
College Algebra is an advanced core math course offered at two- and four-year colleges. The course includes general concepts of polynomials, inequalities, sequences, and functions.
For most high school students, our Algebra 2 course provides a more appropriate college-prep course.
Thinkwell's College Algebra has all the features your home school needs:
- More than 270 video lessons
- 136 available contact hours (What is this?)
The number of contact hours in a course reflects the amount of time a student will typically spend completing the assignments in each course (i.e. watching videos, doing exercises, taking exams, etc...). Many people think about contact hours as the "seat time" for a course. Thinkwell provides this information so you can ensure that the amount of instruction in a Thinkwell course meets the standards and requirements for your state or region.
- 36-week lesson plan with daily assignments (see lesson plan)
- 1000+ interactive exercises with immediate feedback allow you to track your progress
(See sample) - College Algebra practice tests and final tests for all 8 chapters, as well as a midterm and a final
- Printable illustrated notes for each topic
- Interactive animations with audio
- Real-world application examples in both lectures and exercises
- Closed captioning for all video
- Glossary of more than 350 mathematical terms
About the Author
Table of Contents
(Expand All - Close All)1. Prerequisites
- 1.1 Introduction
- 1.1.1 Introduction to Algebra
- 1.1.2 The Top Ten List of Mistakes
- 1.2 Inequalities
- 1.2.1 Concepts of Inequality
- 1.2.2 Inequalities and Interval Notation
- 1.3 Absolute Value
- 1.3.1 Properties of Absolute Value
- 1.3.2 Evaluating Absolute Value Expressions
- 1.4 Exponents
- 1.4.1 An Introduction to Exponents
- 1.4.2 Evaluating Exponential Expressions
- 1.4.3 Applying the Rules of Exponents
- 1.4.4 Evaluating Expressions with Negative Exponents
- 1.5 Converting between Notations
- 1.5.1 Converting between Decimal and Scientific Notation
- 1.5.2 Converting Rational Exponents and Radicals
- 1.6 Radical Expressions
- 1.6.1 Simplifying Radical Expressions
- 1.6.2 Simplifying Radical Expressions with Variables
- 1.6.3 Rationalizing Denominators
- 1.7 Polynomial Expressions
- 1.7.1 Determining Components and Degree
- 1.7.2 Adding, Subtracting, and Multiplying Polynomials
- 1.7.3 Multiplying Big Products
- 1.7.4 Using Special Products
- 1.8 Factoring
- 1.8.1 Factoring Using the Greatest Common Factor
- 1.8.2 Factoring by Grouping
- 1.8.3 Factoring Trinomials Completely
- 1.9 Factoring Patterns
- 1.9.1 Factoring Perfect Square Trinomials
- 1.9.2 Factoring the Difference of Two Squares
- 1.9.3 Factoring Sums and Differences of Cubes
- 1.9.4 Factoring by Any Method
- 1.10 Rational Expressions
- 1.10.1 Rational Expressions and Domain
- 1.10.2 Working with Fractions
- 1.10.3 Writing Rational Expressions in Lowest Terms
- 1.11 Working with Rationals
- 1.11.1 Multiplying and Dividing Rational Expressions
- 1.11.2 Adding and Subtracting Rational Expressions
- 1.11.3 Rewriting Complex Fractions
- 1.12 Complex Numbers
- 1.12.1 Introducing and Writing Complex Numbers
- 1.12.2 Rewriting Powers of i
- 1.12.3 Adding and Subtracting Complex Numbers
- 1.12.4 Multiplying Complex Numbers
- 1.12.5 Dividing Complex Numbers
2. Equations and Inequalities
- 2.1 Linear Equations
- 2.1.1 An Introduction to Solving Equations
- 2.1.2 Solving a Linear Equation
- 2.1.3 Solving a Linear Equation with Rationals
- 2.1.4 Solving a Linear Equation That Has Restrictions
- 2.2 Word Problems with Linear Equations: Math Topics
- 2.2.1 An Introduction to Solving Word Problems
- 2.2.2 Solving for Perimeter
- 2.2.3 Solving a Linear Geometry Problem
- 2.2.4 Solving for Consecutive Numbers
- 2.2.5 Solving to Find the Average
- 2.3 Word Problems with Linear Equations: Applications
- 2.3.1 Solving for Constant Velocity
- 2.3.2 Solving a Problem about Work
- 2.3.3 Solving a Mixture Problem
- 2.3.4 Solving an Investment Problem
- 2.3.5 Solving Business Problems
- 2.4 Quadratic Equations: Some Solution Techniques
- 2.4.1 Solving Quadratics by Factoring
- 2.4.2 Solving Quadratics by Completing the Square
- 2.4.3 Completing the Square: Another Example
- 2.5 Quadratic Equations and the Quadratic Formula
- 2.5.1 Proving the Quadratic Formula
- 2.5.2 Using the Quadratic Formula
- 2.5.3 Predicting the Type of Solutions Using the Discriminant
- 2.6 Quadratic Equations: Special Topics
- 2.6.1 Solving for a Squared Variable
- 2.6.2 Finding Real Number Restrictions
- 2.6.3 Solving Fancy Quadratics
- 2.7 Word Problems with Quadratics: Math Topics
- 2.7.1 An Introduction to Word Problems with Quadratics
- 2.7.2 Solving a Quadratic Geometry Problem
- 2.7.3 Solving with the Pythagorean Theorem
- 2.8 Word Problems with Quadratics: Applications
- 2.8.1 Solving a Motion Problem
- 2.8.2 Solving a Projectile Problem
- 2.8.3 Solving Other Problems
- 2.9 Radical Equations
- 2.9.1 Determining Extraneous Roots
- 2.9.2 Solving an Equation Containing a Radical
- 2.9.3 Solving an Equation with Two Radicals
- 2.9.4 Solving an Equation with Rational Exponents
- 2.10 Variation
- 2.10.1 An Introduction to Variation
- 2.10.2 Direct Proportion
- 2.10.3 Inverse Proportion
- 2.11 Solving Inequalities
- 2.11.1 An Introduction to Solving Inequalities
- 2.11.2 Solving Compound Inequalities
- 2.11.3 More on Compound Inequalities
- 2.11.4 Solving Word Problems Involving Inequalities
- 2.12 Inequalities: Quadratics
- 2.12.1 Solving Quadratic Inequalities
- 2.12.2 Solving Quadratic Inequalities: Another Example
- 2.13 Inequalities: Rationals and Radicals
- 2.13.1 Solving Rational Inequalities
- 2.13.2 Solving Rational Inequalities: Another Example
- 2.13.3 Determining the Domains of Expressions with Radicals
- 2.14 Absolute Value
- 2.14.1 Matching Number Lines with Absolute Values
- 2.14.2 Solving Absolute Value Equations
- 2.14.3 Solving Equations with Two Absolute Value Expressions
- 2.14.4 Solving Absolute Value Inequalities
- 2.14.5 Solving Absolute Value Inequalities: More Examples
3. Relations and Functions
- 3.1 Graphing Basics
- 3.1.1 Using the Cartesian System
- 3.1.2 Thinking Visually
- 3.2 Relationships between Two Points
- 3.2.1 Finding the Distance between Two Points
- 3.2.2 Finding the Second Endpoint of a Segment
- 3.3 Relationships among Three Points
- 3.3.1 Collinearity and Distance
- 3.3.2 Triangles
- 3.4 Circles
- 3.4.1 Finding the Center-Radius Form of the Equation of a Circle
- 3.4.2 Finding the Center and Radius of a Circle
- 3.4.3 Decoding the Circle Formula
- 3.4.4 Solving Word Problems Involving Circles
- 3.5 Graphing Equations
- 3.5.1 Graphing Equations by Locating Points
- 3.5.2 Finding the x- and y-Intercepts of an Equation
- 3.6 Function Basics
- 3.6.1 Functions and the Vertical Line Test
- 3.6.2 Identifying Functions
- 3.6.3 Function Notation and Finding Function Values
- 3.7 Working with Functions
- 3.7.1 Determining Intervals Over Which a Function Is Increasing
- 3.7.2 Evaluating Piecewise-Defined Functions for Given Values
- 3.7.3 Solving Word Problems Involving Functions
- 3.8 Function Domain and Range
- 3.8.1 Finding the Domain and Range of a Function
- 3.8.2 Domain and Range: One Explicit Example
- 3.8.3 Satisfying the Domain of a Function
- 3.9 Linear Functions: Slope
- 3.9.1 An Introduction to Slope
- 3.9.2 Finding the Slope of a Line Given Two Points
- 3.9.3 Interpreting Slope from a Graph
- 3.9.4 Graphing a Line Using Point and Slope
- 3.10 Equations of a Line
- 3.10.1 Writing an Equation in Slope-Intercept Form
- 3.10.2 Writing an Equation Given Two Points
- 3.10.3 Writing an Equation in Point-Slope Form
- 3.10.4 Matching a Slope-Intercept Equation with Its Graph
- 3.10.5 Slope with Parallel and Perpendicular Lines
- 3.11 Linear Functions: Applications
- 3.11.1 Constructing Linear Function Models of a Set of Data
- 3.11.2 Linear Cost and Revenue Functions
- 3.12 Graphing Functions
- 3.12.1 Graphing Some Important Functions
- 3.12.2 Graphing Piecewise-Defined Functions
- 3.12.3 Matching Equations with Their Graphs
- 3.13 The Greatest Integer Function
- 3.13.1 The Greatest Integer Function
- 3.13.2 Graphing the Greatest Integer Function
- 3.14 Composite Functions
- 3.14.1 Using Operations on Functions
- 3.14.2 Composite Functions
- 3.14.3 Components of Composite Functions
- 3.14.4 Finding Functions That Form a Given Composite
- 3.14.5 Finding the Difference Quotient of a Function
- 3.15 Quadratic Functions: Basics
- 3.15.1 Deconstructing the Graph of a Quadratic Function
- 3.15.2 Nice-Looking Parabolas
- 3.15.3 Using Discriminants to Graph Parabolas
- 3.15.4 Maximum Height in the Real World
- 3.16 Quadratic Functions: The Vertex
- 3.16.1 Finding the Vertex by Completing the Square
- 3.16.2 Using the Vertex to Write the Quadratic Equation
- 3.16.3 Finding the Maximum or Minimum of a Quadratic
- 3.16.4 Graphing Parabolas
- 3.17 Manipulating Graphs: Shifts and Stretches
- 3.17.1 Shifting Curves along Axes
- 3.17.2 Shifting or Translating Curves along Axes
- 3.17.3 Stretching a Graph
- 3.17.4 Graphing Quadratics Using Patterns
- 3.18 Manipulating Graphs: Symmetry and Reflections
- 3.18.1 Determining Symmetry
- 3.18.2 Reflections
- 3.18.3 Reflecting Specific Functions
4. Polynomial and Rational Functions
- 4.1 Polynomials: Long Division
- 4.1.1 Using Long Division with Polynomials
- 4.1.2 Long Division: Another Example
- 4.2 Polynomials: Synthetic Division
- 4.2.1 Using Synthetic Division with Polynomials
- 4.2.2 More Synthetic Division
- 4.3 The Remainder Theorem
- 4.3.1 The Remainder Theorem
- 4.3.2 More on the Remainder Theorem
- 4.4 The Factor Theorem
- 4.4.1 The Factor Theorem and Its Uses
- 4.4.2 Factoring a Polynomial Given a Zero
- 4.5 The Rational Root Theorem
- 4.5.1 Presenting the Rational Zero Theorem
- 4.5.2 Considering Possible Solutions
- 4.6 Zeros of Polynomials
- 4.6.1 Finding Polynomials Given Zeros, Degree, and One Point
- 4.6.2 Finding all Zeros and Multiplicities of a Polynomial
- 4.6.3 Finding the Real Zeros for a Polynomial
- 4.6.4 Using Descartes' Rule of Signs
- 4.6.5 Finding the Zeros of a Polynomial from Start to Finish
- 4.7 Graphing Polynomials
- 4.7.1 Matching Graphs to Polynomial Functions
- 4.7.2 Sketching the Graphs of Basic Polynomial Functions
- 4.8 Rational Functions
- 4.8.1 Understanding Rational Functions
- 4.8.2 Basic Rational Functions
- 4.9 Graphing Rational Functions
- 4.9.1 Vertical Asymptotes
- 4.9.2 Horizontal Asymptotes
- 4.9.3 Graphing Rational Functions
- 4.9.4 Graphing Rational Functions: More Examples
5. Exponential and Logarithmic Functions
- 5.1 Function Inverses
- 5.1.1 Understanding Inverse Functions
- 5.1.2 The Horizontal Line Test
- 5.1.3 Are Two Functions Inverses of Each Other?
- 5.1.4 Graphing the Inverse
- 5.2 Finding Function Inverses
- 5.2.1 Finding the Inverse of a Function
- 5.2.2 Finding the Inverse of a Function with Higher Powers
- 5.3 Exponential Functions
- 5.3.1 An Introduction to Exponential Functions
- 5.3.2 Graphing Exponential Functions: Useful Patterns
- 5.3.3 Graphing Exponential Functions: More Examples
- 5.4 Applying Exponential Functions
- 5.4.1 Using Properties of Exponents to Solve Exponential Equations
- 5.4.2 Finding Present Value and Future Value
- 5.4.3 Finding an Interest Rate to Match Given Goals
- 5.5 The Number e
- 5.5.1 e
- 5.5.2 Applying Exponential Functions
- 5.6 Logarithmic Functions
- 5.6.1 An Introduction to Logarithmic Functions
- 5.6.2 Converting between Exponential and Logarithmic Functions
- 5.7 Solving Logarithmic Functions
- 5.7.1 Finding the Value of a Logarithmic Function
- 5.7.2 Solving for x in Logarithmic Equations
- 5.7.3 Graphing Logarithmic Functions
- 5.7.4 Matching Logarithmic Functions with Their Graphs
- 5.8 Properties of Logarithms
- 5.8.1 Properties of Logarithms
- 5.8.2 Expanding a Logarithmic Expression Using Properties
- 5.8.3 Combining Logarithmic Expressions
- 5.9 Evaluating Logarithmic Functions
- 5.9.1 Evaluating Logarithmic Functions Using a Calculator
- 5.9.2 Using the Change of Base Formula
- 5.10 Applying Logarithmic Functions
- 5.10.1 The Richter Scale
- 5.10.2 The Distance Modulus Formula
- 5.11 Solving Exponential and Logarithmic Equations
- 5.11.1 Solving Exponential Equations
- 5.11.2 Solving Logarithmic Equations
- 5.11.3 Solving Equations with Logarithmic Exponents
- 5.12 Applying Exponents and Logarithms
- 5.12.1 Compound Interest
- 5.12.2 Predicting Change
- 5.13 Word Problems Involving Exponential Growth and Decay
- 5.13.1 An Introduction to Exponential Growth and Decay
- 5.13.2 Half-Life
- 5.13.3 Newton's Law of Cooling
- 5.13.4 Continuously Compounded Interest
6. Systems of Equations
- 6.1 Linear Systems of Equations
- 6.1.1 An Introduction to Linear Systems
- 6.1.2 Solving Systems with Substitution
- 6.1.3 Solving Systems by Elimination
- 6.2 Linear Systems in Three Variables
- 6.2.1 An Introduction to Linear Systems in Three Variables
- 6.2.2 Solving Linear Systems in Three Variables
- 6.2.3 Solving Inconsistent Systems
- 6.2.4 Solving Dependent Systems
- 6.2.5 Solving Systems with Two Equations
- 6.3 Applying Linear Systems
- 6.3.1 Investments
- 6.3.2 Solving with Partial Fractions
- 6.4 Nonlinear Systems of Equations
- 6.4.1 Solving Nonlinear Systems Using Elimination
- 6.4.2 Solving Nonlinear Systems with Substitution
- 6.5 Matrices
- 6.5.1 An Introduction to Matrices
- 6.5.2 The Arithmetic of Matrices
- 6.5.3 Multiplying Matrices by a Scalar
- 6.5.4 Multiplying Matrices
- 6.5.5 Multiplying Matrices: Can They Multiply?
- 6.6 The Gauss-Jordan Method of Solving Matrices
- 6.6.1 Using the Gauss-Jordan Method
- 6.6.2 Using Gauss-Jordan: Another Example
- 6.7 Evaluating Determinants
- 6.7.1 Evaluating 2x2 Determinants
- 6.7.2 Evaluating nxn Determinants
- 6.7.3 Applying Determinants
- 6.8 Cramer's Rule
- 6.8.1 Using Cramer's Rule
- 6.8.2 Using Cramer's Rule in a 3x3 Matrix
- 6.9 Inverses and Matrices
- 6.9.1 An Introduction to Inverses
- 6.9.2 Inverses: 2x2 Matrices
- 6.9.3 Another Look at 2x2 Inverses
- 6.9.4 Inverses: 3x3 Matrices
- 6.9.5 Solving a System of Equations with Inverses
- 6.10 Working with Inequalities
- 6.10.1 An Introduction to Graphing Linear Inequalities
- 6.10.2 Graphing Linear and Nonlinear Inequalities
- 6.10.3 Graphing the Solution Set of a System of Inequalities
- 6.11 Linear Programming
- 6.11.1 Solving for Maxima-Minima
- 6.11.2 Applying Linear Programming
7. Conic Sections
- 7.1 Parabolas
- 7.1.1 An Introduction to Conic Sections
- 7.1.2 An Introduction to Parabolas
- 7.1.3 Determining Information about a Parabola from Its Equation
- 7.1.4 Writing an Equation for a Parabola
- 7.2 Ellipses
- 7.2.1 An Introduction to Ellipses
- 7.2.2 Finding the Equation for an Ellipse
- 7.2.3 Applying Ellipses: Satellites
- 7.3 Hyperbolas
- 7.3.1 An Introduction to Hyperbolas
- 7.3.2 Finding the Equation for a Hyperbola
- 7.3.3 Applying Hyperbolas: Navigation
- 7.4 Conic Sections
- 7.4.1 Identifying a Conic
- 7.4.2 Name That Conic
8. Further Topics in Algebra
- 8.1 The Binomial Theorem
- 8.1.1 Using the Binomial Theorem
- 8.1.2 Binomial Coefficients
- 8.2 Sequences
- 8.2.1 Understanding Sequence Problems
- 8.2.2 Solving Problems Involving Arithmetic Sequences
- 8.2.3 Solving Problems Involving Geometric Sequences
- 8.3 Induction
- 8.3.1 Proving Formulas Using Mathematical Induction
- 8.3.2 Examples of Induction
- 8.4 Combinations and Probability
- 8.4.1 Solving Problems Involving Permutations
- 8.4.2 Solving Problems Involving Combinations
- 8.4.3 Independent Events
- 8.4.4 Inclusive and Exclusive Events
9. Conclusion
- 9.1 Conclusion
- 9.1.1 Final Close