College Algebra
1.1 The Real Number System
- Examples
- Example 1: Types of Real Numbers
- Example 2: Drawing the Real Number Line
- Example 3: Working with Order
- Example 4: Set-Builder Notation
- Example 5: Intervals of Real Numbers
- Example 6: Absolute Value
- Example 7: Using Absolute Value Properties
- Example 8: Working With Repeating Digits
- Bonus Videos
- Bonus 1: The Real Number System
- Bonus 2: The Real Number System
1.2 The Arithmetic of Algebraic Expressions
- Examples
- Example 1: Terminology of Algebraic Expressions
- Example 2: Evaluating Algebraic Expressions
- Example 3: Applying the Field Properties
- Example 4: Visualizing the Distributive Property
- Example 5: Properties of Real Numbers
- Example 6: Order of Operations
- Example 7: Union and Intersection of Intervals
- Example 8: Union and Intersection
- Bonus Videos
- Bonus 1: The Arithmetic of Algebraic Expressions
1.3a Properties of Exponents
1.3b Scientific Notation and Geometric Problems Using Exponents
1.4a Properties of Radicals
1.4b Rational Number Exponents
1.5 Polynomials and Factoring
- Examples
- Example 1: Polynomial Expressions
- Example 2: Adding and Subtracting Polynomials
- Example 3: Multiplying Polynomials
- Example 4: The FOIL Method
- Example 5: The Greatest Common Factor Method
- Example 6: Factoring by Grouping
- Example 7: Factoring Special Binomials
- Example 8: Factoring a Trinomial
- Example 9: Factoring a Trinomial by Grouping
- Example 10: Perfect Square Trinomials
- Example 11: Factoring Expressions with Fractional Exponents
- Bonus Videos
- Bonus 1: Polynomials and Factoring
- Bonus 2: Polynomials and Factoring
1.6 The Complex Number System
- Examples
- Example 1: The Number i
- Example 2: Powers of i
- Example 3: Simplifying Complex Expressions
- Example 4: Dividing Complex Numbers
- Example 5: Roots and Complex Numbers
- Bonus Videos
- Bonus 1: The Complex Number System
- Bonus 2: The Complex Number System
- Bonus 3: The Complex Number System
- Bonus 4: The Complex Number System
2.1a Linear Equations in One Variable
- Examples
- Example 1: Solving Linear Equations in One Variable
- Example 2: Solving Linear Equations in One Variable
- Example 3: Solving Absolute Value Equations
- Example 4: Solving Absolute Value Equations Geometrically
- Bonus Videos
- Bonus 1: Linear Equations in One Variable
- Bonus 2: Linear Equations in One Variable
- Bonus 3: Linear Equations in One Variable
- Bonus 4: Linear Equations in One Variable
- Bonus 5: Linear Equations in One Variable
2.1b Applications of Linear Equations in One Variable
- Examples
- Example 1: Solving Linear Equations for One Variable
- Example 2: Calculating Distance
- Example 3: Calculating Average Interest
- Bonus Videos
- Bonus 1: Applications of Linear Equations in One Variable
- Bonus 2: Applications of Linear Equations in One Variable
- Bonus 3: Applications of Linear Equations in One Variable
- Bonus 4: Applications of Linear Equations in One Variable
- Bonus 5: Applications of Linear Equations in One Variable
2.2 Linear Inequalities in One Variable
- Examples
- Example 1: Multiplying Inequalities by Negative Numbers
- Example 2: Solving Linear Inequalities
- Example 3: Graphing Intervals of Real Numbers
- Example 4: Calculating Final Grades
- Example 5: Compound Linear Inequalities
- Example 6: Absolute Value Inequalities
- Example 7: Translating Inequality Phrases
- Example 8: Applications of Inequalities
- Bonus Videos
- Bonus 1: Linear Inequalities in One Variable
- Bonus 2: Linear Inequalities in One Variable
- Bonus 3: Linear Inequalities in One Variable
- Bonus 4: Linear Inequalities in One Variable
2.3 Quadratic Equations in One Variable
- Examples
- Example 1: Solving Quadratic Equations by Factoring
- Example 2: Perfect Square Quadratic Equations
- Example 3: Completing the Square
- Example 4: Using the Quadratic Formula
- Example 5: The Discriminant
- Example 6: Methods of Solving Quadratic Equations
- Example 7: Gravity Problems
- Bonus Videos
- Bonus 1: Quadratic Equations in One Variable
- Bonus 2: Quadratic Equations in One Variable
- Bonus 3: Quadratic Equations in One Variable
- Bonus 4: Quadratic Equations in One Variable
2.4 Higher Degree Polynomial Equations
- Examples
- Example 1: Quadratic-Like Equations
- Example 2: Solving Equations by Factoring
- Example 3: Solving Equations by Factoring
- Bonus Videos
- Bonus 1: Higher Degree Polynomial Equations
- Bonus 2: Higher Degree Polynomial Equations
- Bonus 3: Higher Degree Polynomial Equations
- Bonus 4: Higher Degree Polynomial Equations
2.5 Rational Expressions and Equations
- Examples
- Example 1: Rational Expressions
- Example 2: Combining Rational Expressions
- Example 3: Combining Rational Expressions
- Example 4: Complex Rational Expressions
- Example 5: Solving Rational Equations
- Example 6: Filling a Pool
- Example 7: Filling a Pool Poorly
- Bonus Videos
- Bonus 1: Rational Expressions and Equations
- Bonus 2: Rational Expressions and Equations
- Bonus 3: Rational Expressions and Equations
2.6 Radical Equations
3.1 The Cartesian Coordinate System
- Examples
- Example 1: Plotting Points in the Cartesian Coordinate System
- Example 2: Graphing Equations in Two Variables
- Example 3: Using the Distance Formula
- Example 4: Using the Midpoint Formula
- Bonus Videos
- Bonus 1: The Cartesian Coordinate System
- Bonus 2: The Cartesian Coordinate System
- Bonus 3: The Cartesian Coordinate System
- Bonus 4: The Cartesian Coordinate System
- Bonus 5: The Cartesian Coordinate System
3.2 Linear Equations in Two Variables
3.3 Forms of Linear Equations
- Examples
- Example 1: Calculating the Slope of a Line
- Example 2: Calculating the Slope of a Line
- Example 3: Slope-Intercept Form of a Line
- Example 4: Slope-Intercept Form of a Line
- Example 5: Point-Slope Form of a Line
- Example 6: Point-Slope Form of a Line
- Bonus Videos
- Bonus 1: Forms of Linear Equations
- Bonus 2: Forms of Linear Equations
- Bonus 3: Forms of Linear Equations
- Bonus 4: Forms of Linear Equations
3.4 Parallel and Perpendicular Lines
- Examples
- Example 1: Finding Equations of Parallel Lines
- Example 2: Finding Equations of Parallel Lines
- Example 3: Identifying a Quadrilateral
- Example 4: Finding Equations of Perpendicular Lines
- Example 5: Finding Equations of Perpendicular Lines
- Example 6: Identifying Parallel and Perpendicular Lines
- Bonus Videos
- Bonus 1: Parallel and Perpendicular Lines
- Bonus 2: Parallel and Perpendicular Lines
- Bonus 3: Parallel and Perpendicular Lines
- Bonus 4: Parallel and Perpendicular Lines
3.5 Linear Inequalities in Two Variables
- Examples
- Example 1: Solving Linear Inequalities
- Example 2: Solving Linear Inequalities
- Example 3: Solving Absolute Value Linear Inequalities
- Example 4: Graphing Regions of Constraint
- Example 5: Orchard Business
- Bonus Videos
- Bonus 1: Linear Inequalities in Two Variables
- Bonus 2: Linear Inequalities in Two Variables
3.6 Introduction to Circles
- Examples
- Example 1: Standard Form of a Circle
- Example 2: Standard Form of a Circle
- Example 3: Standard Form of a Circle
- Example 4: Graphing Circles
- Example 5: Graphing Circles and Completing the Square
- Bonus Videos
- Bonus 1: Introduction to Circles
- Bonus 2: Introduction to Circles
- Bonus 3: Introduction to Circles
4.1 Relations and Functions
- Examples
- Example 1: Relations, Domains, and Ranges
- Example 2: Is the Relation a Function?
- Example 3: Functions and the Vertical Line Test
- Example 4: Functional Notation
- Example 5: Evaluating Functions
- Example 6: Implied Domain of a Function
- Bonus Videos
- Bonus 1: Relations and Functions
- Bonus 2: Relations and Functions
- Bonus 3: Relations and Functions
- Bonus 4: Relations and Functions
- Bonus 5: Relations and Functions
- Bonus 6: Relations and Functions
4.2a Linear and Quadratic Functions
4.2b Max/Min Applications of Quadratic Functions
4.3a Other Common Functions
4.3b Direct and Inverse Variation
4.4 Transformations of Functions
- Examples
- Example 1: Horizontal Shifting/Translation
- Example 3: Horizontal and Vertical Shifting
- Example 5: Vertical Stretching and Compressing
- Example 6: Order of Transformations
- Example 7: Symmetry of Equations
- Example 8
- Example 9
- Bonus Videos
- Bonus 1: Transformations of Functions
- Bonus 2: Transformations of Functions
- Bonus 3: Transformations of Functions
- Bonus 4: Transformations of Functions
4.5 Combining Functions
- Examples
- Example 1: Combining Functions Arithmetically
- Example 2: Combining Functions Arithmetically
- Example 3: Combining Functions Arithmetically
- Example 4: Composing Functions
- Example 5: Domains of Compositions of Functions
- Example 6: Domains of Compositions of Functions
- Example 7: Decomposing Functions
- Bonus Videos
- Bonus 1: Combining Functions
- Bonus 2: Combining Functions
- Bonus 3: Combining Functions
- Bonus 4: Combining Functions
4.6 Inverses of Functions
5.1 Introduction to Polynomial Equations and Graphs
- Examples
- Example 1: Solutions of Polynomial Equations
- Example 2: Graphing Polynomial Functions
- Example 3: Solving Polynomial Inequalities Using a Graph
- Example 4: Solving Polynomial Inequalities: Sign-Test Method
- Bonus Videos
- Bonus 1: Introduction to Polynomial Equations and Graphs
- Bonus 2: Introduction to Polynomial Equations and Graphs
- Bonus 3: Introduction to Polynomial Equations and Graphs
5.2 Polynomial Division and the Division Algorithm
- Examples
- Example 1: Polynomial Long Division
- Example 2: Polynomial Long Division
- Example 3: Polynomial Long Division with Complex Numbers
- Example 4: Synthetic Division
- Example 5: Synthetic Division (with Complex Numbers)
- Example 6: Constructing Polynomials
- Bonus Videos
- Bonus 1: Polynomial Division and the Division Algorithm
- Bonus 2: Polynomial Division and the Division Algorithm
5.3 Locating Real Zeros of Polynomials
5.4 The Fundamental Theorem of Algebra
7.1 Exponential Functions and their Graphs
7.2 Applications of Exponential Functions
- Examples
- Example 1: Population Growth
- Example 2: Radioactive Decay
- Example 3: Compound Interest Formula
- Example 4: Compound Interest Formula
- Example 5: Continuous Compounding Formula
- Bonus Videos
- Bonus 1: Applications of Exponential Functions
- Bonus 2: Applications of Exponential Functions
- Bonus 3: Applications of Exponential Functions
7.3 Logarithmic Functions and their Graphs
- Examples
- Example 1: Exponential and Logarithmic Equations
- Example 2: Graphing Logarithmic Functions
- Example 3: Graphing Logarithmic Functions
- Example 4: Logarithmic Expressions
- Example 5: Solving Logarithmic Equations
- Example 6: Evaluating Logarithmic Expressions
- Bonus Videos
- Bonus 1: Logarithmic Functions and their Graphs
- Bonus 2: Logarithmic Functions and their Graphs
- Bonus 3: Logarithmic Functions and their Graphs
7.4 Properties and Applications of Logarithms
- Examples
- Example 1: Continuously Compounded Interest
- Example 2: Solving Exponential Equations
- Example 3: Expanding Logarithmic Expressions
- Example 4: Condensing Logarithmic Expressions
- Example 5: Change of Base Formula
- Example 6: The pH Scale
- Example 7: The Richter Scale
- Example 8: The Decibel Scale
- Bonus Videos
- Bonus 1: Properties and Applications of Logarithms
- Bonus 2: Properties and Applications of Logarithms
- Bonus 3: Properties and Applications of Logarithms
7.5 Exponential and Logarithmic Equations
- Examples
- Example 1: Solving Exponential Equations
- Example 2: Solving Exponential Equations
- Example 3: Solving Logarithmic Equations
- Example 4: Solving Logarithmic Equations
- Example 5: Compounding Interest
- Example 6: Radiocarbon Dating
- Bonus Videos
- Bonus 1: Exponential and Logarithmic Equations
- Bonus 2: Exponential and Logarithmic Equations
- Bonus 3: Exponential and Logarithmic Equations
- Bonus 4: Exponential and Logarithmic Equations
- Bonus 5: Exponential and Logarithmic Equations
8.1 Solving Systems by Substitution and Elimination
- Examples
- Example 1: Solving a System of Equations by Substitution
- Example 2: Solving a System of Equations by Substitution
- Example 3: Solving a System of Equations by Elimination
- Example 4: Solving a System of Equations by Elimination
- Example 5: Solving a System of Equations by Elimination
- Example 6: Solving a System of Equations by Elimination
- Example 7: Mixing Alloys
- Example 8: Determining Ages
- Bonus Videos
- Bonus 1: Solving Systems by Substitution and Elimination
- Bonus 2: Solving Systems by Substitution and Elimination
8.2 Matrix Notation and Gaussian Elimination
- Examples
- Example 1: Matrices and Matrix Notation
- Example 2: Augmented Matrices
- Example 3: Row Echelon Form
- Example 4: Elementary Row Operations
- Example 5: Gaussian Elimination
- Example 6: Reduced Row Echelon Form
- Bonus Videos
- Bonus 1: Matrix Notation and Gaussian Elimination
- Bonus 2: Matrix Notation and Gaussian Elimination
8.3 Determinants and Cramer's Rule
8.4 The Algebra of Matrices
8.5 Inverses of Matrices
8.6 Linear Programming
8.7 Nonlinear Systems of Equations
- Examples
- Example 1: Solving Nonlinear Systems by Graphing
- Example 2: Solving Nonlinear Systems by Graphing
- Example 3: Solving Nonlinear Systems Algebraically
- Example 4: Solving Nonlinear Systems Algebraically
- Example 5: Solving Nonlinear Systems Algebraically
- Bonus Videos
- Bonus 1: Nonlinear Systems of Equations
9.1 Sequences and Series
9.2 Arithmetic Sequences and Series
9.3 Geometric Sequences and Series
9.4 Mathematical Induction
9.5a An Introduction to Combinatorics - Counting, Permutations, and Combinations
- Examples
- Example 1: Counting Phone Numbers
- Example 2: The Multiplication Principle of Counting
- Example 3: Permutations
- Example 4: Permutations
- Example 5: Permutation Formula
- Example 6: Permutations and Combinations
- Example 7: Forming Committees
- Example 8: Forming "Words"
- Bonus Videos
- Bonus 1: An Introduction to Combinatorics - Counting, Permutations, and Combinations
9.5b An Introduction to Combinatorics - The Binomial and Multinomial Theorems
9.6 An Introduction to Probability
- Examples
- Example 1: Probabilities when Outcomes are Equally Likely
- Example 2: Computing Probabilities
- Example 3: Computing Probabilities
- Example 4: Probability of a Union of Two Events
- Example 5: Unions of Mutually Exclusive Events
- Example 6: Independent Events
- Bonus Videos
- Bonus 1: An Introduction to Probability
A.1 Introduction to Polynomial Equations and Graphs (excluding complex numbers)
A.2 Polynomial Division and the Division Algorithm (excluding complex numbers)
A.3 Locating Real Zeros of Polynomials (excluding complex numbers)
A.4 The Fundamental Theorem of Algebra (excluding complex numbers)
A.5 Mathematical Models
A.6 Properties of Functions
A.7 Angles and Triangles
- Examples
- Example 1: Measuring Angles
- Example 2: Classifying Angles by Their Measure
- Example 3: Identifying Complementary and Supplementary Angles
- Example 4: Calculating Measures of Angles
- Example 5: Identifying Congruent Angles
- Example 6: Calculating Measures of Angles
- Example 7: Finding Adjacent Angles
- Example 8: Calculating Measures of Angles
- Example 9: Classifying a Triangle by Its Sides
- Example 10: Determining Whether a Triangle Exists
- Example 11: Analyzing Triangles
A.8 Perimeter
- Examples
- Example 1: Calculating the Perimeter of a Square
- Example 2: Calculating the Perimeter of a Triangle
- Example 3: Calculating the Perimeter of a Rectangle
- Example 4: Calculating the Perimeter of a Polygon
- Example 5: Calculating the Perimeter of a Polygon
- Example 6: Application: Calculating the Perimeter of a Polygon
A.9 Area
A.10 Circles
A.11 Volume and Surface Area
- Examples
- Example 1: Calculating the Volume of a Rectangular Solid
- Example 2: Calculating the Volume of a Sphere
- Example 3: Calculating the Volume of a Cone
- Example 4: Calculating the Volume of a Solid
- Example 5: Finding the Volume of a Cube
- Example 6: Calculating the Surface Area of a Rectangular Solid
- Example 7: Calculating the Surface Area of a Cylinder
A.12 Similar and Congruent Triangles
A.13 Square Roots and the Pythagorean Theorem
- Examples
- Example 1: Evaluating Perfect Squares
- Example 2: Evaluating Square Roots
- Example 3: Calculating Square Roots Using a Calculator
- Example 4: Verifying Right Triangles
- Example 5: Finding the Length of the Hypotenuse
- Example 6: Finding the Length of the Hypotenuse
- Example 7: Finding the Length of the Hypotenuse