Algebra for College Students
1.1 Prime Numbers, Exponents, and LCM
1.2a Name that Real Number
1.2b Properties of Real Numbers
1.3a Introduction to Absolute Values
- Examples
- Example 1: Absolute Value
- Bonus Videos
- Bonus 1: Introduction to Absolute Values
1.3b Addition with Real Numbers
1.3c Subtraction with Real Numbers
1.3d Multiplication and Division with Real Numbers
1.3e Order of Operations
1.4a Simplifying Expressions
- Examples
- Example 1: Combining Like Terms
- Bonus Videos
- Bonus 1: Simplifying Expressions
1.4b Solving Linear Equations
1.4c Solving Absolute Value Equations
1.5a Evaluating Formulas
- Examples
- Example 1: Triangle
- Bonus Videos
- Bonus 1: Evaluating Formulas
1.5b Solving Formulas
- Examples
- Example 2: Solving Formulas
- Bonus Videos
- Bonus 1: Solving Formulas
1.6 Applications
1.7a Solving Linear Inequalities
1.7b Solving Absolute Value Inequalities
2.1a Introduction to the Cartesian Coordinate System
2.1b Graphing Linear Equations by Plotting Points
2.2 Graphing Linear Equations in Slope-Intercept Form
2.3a Finding the Equation of a Line
- Examples
- Example 1: Graphing a Line Given a Point and the Slope
- Example 2: Finding Equations of Lines Using the Slope and a Point
- Example 3: Using Two Points to Find the Equation of a Line
- Bonus Videos
- Bonus 1: Finding the Equation of a Line
- Bonus 2: Finding the Equation of a Line
- Bonus 3: Finding the Equation of a Line
- Bonus 4: Finding the Equation of a Line
- Bonus 5: Finding the Equation of a Line
2.3b Graphing Linear Equations in Point-Slope Form
2.4 Introduction to Functions and Function Notation
- Examples
- Example 1: Finding the Domain and Range
- Example 2: Reading the Domain and Range from the Graph of a Relation
- Example 3: Functions
- Example 4: Vertical Line Test
- Example 5: Domain
- Example 6: Function Evaluation
- Example 7: Nonlinear Function Evaluation
- Bonus Videos
- Bonus 1: Introduction to Functions and Function Notation
- Bonus 2: Introduction to Functions and Function Notation
2.5 Graphing Linear Inequalities
- Examples
- Example 1: Graphing Linear Inequalities
- Bonus Videos
- Bonus 1: Graphing Linear Inequalities
3.1a Solving Systems of Linear Equations by Graphing
3.1b Solving Systems of Linear Equations by Substitution
3.1c Solving Systems of Linear Equations by Addition
3.2 Applications: Systems of Equations
3.3 Solving Systems of Linear Equations with Three Variables
- Examples
- Example 1: Three Variables (a System with One Solution)
- Example 2: Three Variables (a System with No Solution)
- Example 3: Three Variables (A System with Infinitely Many Solutions)
- Example 4: Three Variables (Application)
- Bonus Videos
- Bonus 1: Solving Systems of Linear Equations with Three Variables
3.4 Matrices and Gaussian Elimination
3.5 Determinants
3.6 Determinants and Systems of Linear Equations: Cramer's Rule
3.7 Systems of Linear Inequalities
4.1a Simplifying Integer Exponents I
4.1b Simplifying Integer Exponents II
4.1c Scientific Notation
4.2a Identifying Polynomials
- Bonus Videos
- Bonus 1: Identifying Polynomials
4.2b Adding and Subtracting Polynomials
4.3a Multiplying Polynomials
4.3b The FOIL Method
- Examples
- Example 1: FOIL Method
- Bonus Videos
- Bonus 1: The FOIL Method
4.4a Division by a Monomial
- Examples
- Example 1: Dividing by a Monomial
- Bonus Videos
- Bonus 1: Division by a Monomial
4.4b The Division Algorithm
4.5a GCF of a Polynomial
4.5b Factoring by Grouping
- Examples
- Example 3: Factoring by Grouping
- Bonus Videos
- Bonus 1: Factoring by Grouping
4.6a Factoring Trinomials by Trial and Error
4.6b Factoring Trinomials by the ac-Method
4.7a Special Factorizations - Squares
4.7b Special Factorizations - Cubes
4.8 Solving Equations by Factoring
4.9 Using a Graphing Calculator to Solve Equations
5.1a Defining Rational Expressions
5.1b Multiplication and Division with Rational Expressions
5.2 Addition and Subtraction with Rational Expressions
- Examples
- Example 1: Adding Rational Expressions with a Common Denominator
- Example 2: Adding Rational Expressions with Different Denominators
- Example 4: Subtracting Rational Expressions with a Common Denominator
- Example 5: Subtracting Rational Expressions with Different Denominators
- Bonus Videos
- Bonus 1: Addition and Subtraction with Rational Expressions
- Bonus 2: Addition and Subtraction with Rational Expressions
- Bonus 3: Addition and Subtraction with Rational Expressions
5.3 Complex Fractions
5.4 Solving Equations with Rational Expressions
- Examples
- Example 1: Proportions
- Example 2: Application of Proportions
- Example 3: Similar Triangles
- Example 4: Solving Equations Involving Rational Expressions
- Example 5: Solving a Formula for a Specified Variable
- Bonus Videos
- Bonus 1: Solving Equations with Rational Expressions
- Bonus 2: Solving Equations with Rational Expressions
5.5 Applications Involving Rational Expressions
5.6 Applications: Variation
6.1a Evaluating Radicals
6.1b Simplifying Radicals
- Examples
- Example 1: Simplifying Numerical Expressions with Square Roots
- Example 2: Simplifying Radical Expressions
- Example 3: Simplifying Square Roots with Variables
- Example 4: Simplifying Square Roots
- Example 5: Simplifying Expressions with Cube Roots
- Bonus Videos
- Bonus 1: Simplifying Radicals
- Bonus 2: Simplifying Radicals
6.2 Rational Exponents
- Examples
- Example 1: Evaluating Principal nth Roots
- Example 3: Conversion from Exponential Notation to Radical Notation
- Example 4: Simplifying Expressions with Rational Exponents
- Example 5: Simplifying Radical Notation by Changing to Exponential Notation
- Bonus Videos
- Bonus 1: Rational Exponents
- Bonus 2: Rational Exponents
6.3a Addition and Subtraction with Radicals
6.3b Multiplication with Radicals
- Examples
- Example 2: Multiplication of Radicals
- Bonus Videos
- Bonus 1: Multiplication with Radicals
6.3c Rationalizing Denominators
6.4 Solving Radical Equations
6.5 Functions with Radicals
6.6 Complex Numbers
6.7 Multiplication and Division with Complex Numbers
7.1a Quadratic Equations: The Square Root Method
7.1b Quadratic Equations: Completing the Square
7.2 Quadratic Equations: The Quadratic Formula
7.3 Applications: Quadratic Equations
7.4 Equations in Quadratic Form
7.5 Graphing Parabolas
7.6a Solving Quadratic Inequalities
7.6b Solving Inequalities with Rational Expressions
8.1 Algebra of Functions
8.2 Composition of Functions and Inverse Functions
8.3 Exponential Functions and the Number e
8.4 Logarithmic Functions
8.5 Properties of Logarithmic Functions
- Examples
- Example 1: Using the Product Rule of Logarithms
- Example 2: Using the Quotient Rule of Logarithms
- Example 3: Using the Power Rule
- Example 4: Using the Properties of Logarithms to Expand Expressions
- Example 5: Using the Properties of Logarithms to Write Single Logarithm Expressions
- Bonus Videos
- Bonus 1: Properties of Logarithmic Functions
8.6 Common Logarithms and Natural Logarithms
8.7 Exponential and Logarithmic Equations
8.8 Applications: Exponential and Logarithmic Functions
9.1 Translations
- Examples
- Example 1: Using Notation
- Example 2: Finding the Difference Quotient for a Given Function
- Example 3: Horizontal and Vertical Translations of the Function y = |x|
- Example 4: Reflections and Translations of the Function y = |x|
- Example 5: Translations of Functions with Graphs Given
- Bonus Videos
- Bonus 1: Translations
9.2 Parabolas as Conic Sections
- Examples
- Example 1: Horizontal Parabolas
- Bonus Videos
- Bonus 1: Parabolas as Conic Sections
9.3 Distance Formula and Circles
9.4 Ellipses and Hyperbolas
- Examples
- Example 1: Equation of an Ellipse-Major Axis Horizontal
- Example 2: Equation of an Ellipse-Major Axis Vertical
- Example 3: Hyperbola Opening Left and Right
- Example 4: Hyperbola Opening Up and Down
- Example 5: Ellipse with Center at
- Example 6: Hyperbola with Center at (h, k)
- Bonus Videos
- Bonus 1: Ellipses and Hyperbolas
9.5 Nonlinear Systems of Equations
10.1 Sequences
- Examples
- Example 1: Writing Terms of a Sequence
- Example 2: Finding the General Formula of a Sequence
- Example 3: Application
- Example 4: An Alternating Sequence
- Example 5: A Decreasing Sequence
- Example 6: An Increasing Sequence
- Example 7: A Sequence that is Neither Increasing Nor Decreasing
- Bonus Videos
- Bonus 1: Sequences
10.2 Sigma Notation
10.3 Arithmetic Sequences
- Examples
- Example 1: An Arithmetic Sequence
- Example 2: A Sequence that is Not Arithmetic
- Example 3: Finding a Specific Term in an Arithmetic Sequence
- Example 4: Finding n Given Certain Conditions
- Example 5: Finding Partial Sums of Arithmetic Sequences
- Example 6: An Application of an Arithmetic Sequence
- Bonus Videos
- Bonus 1: Arithmetic Sequences
10.4 Geometric Sequences and Series
- Examples
- Example 1: A Geometric Sequence
- Example 2: A Sequence that is Not Geometric
- Example 3: Finding a Specified Term of a Geometric Sequence
- Example 4: Finding a1 and r for a Geometric Sequence
- Example 5: Partial Sums of Geometric Sequences
- Example 6: Partial Sums of Geometric Sequences
- Example 7: Geometric Series
- Bonus Videos
- Bonus 1: Geometric Sequences and Series
10.5 The Binomial Theorem
A.1 Review of Fractions
A.2 Synthetic Division
A.3 Applications of Linear Equations
- Examples
- Example 1: Solving x + b = c
- Example 2: Solving x + b = c
- Example 3: Solving x + b = c
- Example 4: An Application Solving ax = c
- Example 5: Solving ax = c
- Example 6: Solving ax = c
- Example 7: Solving ax = c
- Bonus Videos
- Bonus 1: Applications of Linear Equations
- Bonus 2: Applications of Linear Equations
A.4 Permutations
A.5 Combinations
- Examples
- Example 1: Combinations
- Example 2: Combinations
- Bonus Videos
- Bonus 1: Combinations