Introductory and Intermediate Algebra
1.1a The Real Number Line and Inequalities
1.1b Introduction to Absolute Values
- Examples
- Example 5: Absolute Value
- Bonus Videos
- Bonus 1: Introduction to Absolute Values
1.2 Addition with Real Numbers
1.3 Subtraction with Real Numbers
1.4 Multiplication and Division with Real Numbers
1.5 Exponents, Prime Numbers, and LCM
- Examples
- Example 1: Writing Exponents
- Example 2: Translating Expressions with Exponents
- Example 3: Prime Numbers
- Example 4: Composite Numbers
- Example 5: Prime Factorization
- Example 6: Prime Factorization
- Example 7: Least Common Multiple (LCM)
- Example 8: Least Common Multiple (LCM)
- Example 9: LCM with Variables
- Bonus Videos
- Bonus 1: Exponents, Prime Numbers, and LCM
1.6a Reducing Fractions
1.6b Multiplication and Division with Fractions
- Examples
- Example 3: Fraction of a Number
- Example 4: Dividing Fractions with Negative Numbers
- Example 5: Dividing Fractions with Variables
- Example 6: Multiplication and Division of Fractions
- Example 7: Multiplication and Division of Fractions
- Bonus Videos
- Bonus 1: Multiplication and Division with Fractions
- Bonus 2: Multiplication and Division with Fractions
1.7 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with Like Denominators
- Example 2: Adding Fractions with Unlike Denominators
- Example 3: Subtracting Fractions with Like Denominators
- Example 4: Subtracting Fractions with Unlike Denominators
- Bonus Videos
- Bonus 1: Addition and Subtraction with Fractions
- Bonus 2: Addition and Subtraction with Fractions
1.8 Order of Operations
1.9 Properties of Real Numbers
2.1a Variables and Algebraic Expressions
- Examples
- Example 1: Like Terms
- Bonus Videos
- Bonus 1: Variables and Algebraic Expressions
2.1b Simplifying Expressions
2.1c Evaluating Algebraic Expressions
2.2 Translating Phrases into Algebraic Expressions
2.3a Solving Linear Equations Using Addition and Subtraction
2.3b Solving Linear Equations Using Multiplication and Division
2.4 Solving Linear Equations
2.5 More Linear Equations: ax + b = cx + d
- Examples
- Example 1: Solving Equations of the Form ax + b = cx + d
- Example 2: Solving Equations of the Form ax + b = cx + d
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations with Fractional Coefficients
- Example 5: Solving Equations with Parentheses
- Example 6: Solving Equations with Parentheses
- Example 8: Solutions of Equations
- Example 9: Solutions of Equations
- Example 10: Solutions of Equations
- Bonus Videos
- Bonus 1: More Linear Equations: ax + b = cx + d
- Bonus 2: More Linear Equations: ax + b = cx + d
2.6a Applications: Number Problems and Consecutive Integers
2.6b Applications of Linear Equations: Addition and Subtraction
2.6c Applications of Linear Equations: Multiplication and Division
2.7 Applications with Percent
3.1 Working with Formulas
3.2 Formulas in Geometry
3.3 Applications
3.4 Solving Linear Inequalities
- Examples
- Example 1: Graphing Intervals
- Example 2: Sets of Real Numbers Illustrating Union
- Example 3: Sets of Real Numbers Illustrating Intersection
- Example 4: Solving Linear Inequalities
- Example 5: Solving Compound Inequalities
- Example 6: Application with an Inequality
- Example 7: Application with an Inequality
- Bonus Videos
- Bonus 1: Solving Linear Inequalities
- Bonus 2: Solving Linear Inequalities
3.5a Solving Absolute Value Equations
3.5b Solving Absolute Value Inequalities
4.1 Introduction to the Cartesian Coordinate System
4.2 Graphing Linear Equations by Plotting Points
4.3 Graphing Linear Equations in Slope-Intercept Form
4.4a 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
4.4b Graphing Linear Equations in Point-Slope Form
4.5 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
4.6 Graphing Linear Inequalities
- Examples
- Example 1: Graphing Linear Inequalities
- Bonus Videos
- Bonus 1: Graphing Linear Inequalities
5.1 Simplifying Integer Exponents I
- Examples
- Example 1: Product Rule for Exponents
- Example 2: Product Rule for Exponents
- Example 3: The Exponent 0
- Example 4: Quotient Rule for Exponents
- Example 5: Dividing Terms with Coefficients
- Example 6: Negative Exponents
- Example 7: Combining Rules for Exponents
- Bonus Videos
- Bonus 1: Simplifying Integer Exponents I
5.2a Simplifying Integer Exponents II
- Examples
- Example 1: Power Rule for Exponents
- Example 2: Rule for Power of a Product
- Example 3: Rule for Power of a Quotient
- Example 4: Using Combinations of Rules for Exponents
- Example 5: Two Approaches with Fractional Expressions and Negative Exponents
- Example 6: A More Complex Example
- Bonus Videos
- Bonus 1: Simplifying Integer Exponents II
5.2b Scientific Notation
5.3 Identifying and Evaluating Polynomials
5.4 Adding and Subtracting Polynomials
5.5 Multiplying Polynomials
- Examples
- Example 1: Multiplication with Polynomials
- Bonus Videos
- Bonus 1: Multiplying Polynomials
5.6a The FOIL Method
- Examples
- Example 1: FOIL Method
- Bonus Videos
- Bonus 1: The FOIL Method
5.6b Special Products
5.7a Division by a Monomial
- Examples
- Example 1: Dividing by a Monomial
- Bonus Videos
- Bonus 1: Division by a Monomial
5.7b The Division Algorithm
6.1a Greatest Common Factor of Two or More Terms
- Examples
- Example 1: Finding the GCF
- Bonus Videos
- Bonus 1: Greatest Common Factor of Two or More Terms
6.1b Greatest Common Factor of a Polynomial
6.1c Factoring Expressions by Grouping
6.2 Factoring Trinomials: Leading Coefficient 1
6.3a Factoring Trinomials by Trial and Error
6.3b Factoring Trinomials by Grouping
6.4a Special Factorizations - Squares
6.4b Special Factorizations - Cubes
6.5 Additional Factoring Practice
6.6 Solving Quadratic Equations by Factoring
6.7 Applications of Quadratic Equations
7.1a Defining Rational Expressions
7.1b Multiplication and Division with Rational Expressions
7.2 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
7.3 Complex Fractions
7.4a Solving Equations: Ratios and Proportions
7.4b Solving Equations with Rational Expressions
7.5 Applications Involving Rational Expressions
7.6 Applications: Variation
8.1 Solving Systems of Linear Equations by Graphing
- Examples
- Example 1: Solution of a System
- Example 2: Not a Solution of a System
- Example 3: A System with One Solution
- Example 4: A System with No Solution
- Example 5: A System with Infinitely Many Solutions
- Example 6: A System that Requires Estimation
- Bonus Videos
- Bonus 1: Solving Systems of Linear Equations by Graphing
8.2 Solving Systems of Linear Equations by Substitution
8.3 Solving Systems of Linear Equations by Addition
8.4 Applications: Distance - Rate - Time, Number Problems, Amounts and Costs
8.5 Applications: Interest and Mixture
8.6 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
8.7 Matrices and Gaussian Elimination
8.8 Systems of Linear Inequalities
9.1 Evaluating Radicals
9.2 Simplifying Radicals
9.3 Rational Exponents
- Examples
- Example 1: Evaluating Principal Roots
- Example 2: Conversion Between Exponential Notation and Radical Notation
- Example 3: Simplifying Expressions with Rational Exponents
- Example 4: Simplifying Radical Notation by Changing to Exponential Notation
- Bonus Videos
- Bonus 1: Rational Exponents
- Bonus 2: Rational Exponents
9.4a Addition and Subtraction with Radicals
9.4b Multiplication with Radicals
- Examples
- Example 2: Multiplication of Radicals
- Bonus Videos
- Bonus 1: Multiplication with Radicals
9.4c Rationalizing Denominators
9.5 Equations with Radicals
9.6 Functions with Radicals
9.7 Complex Numbers
9.8 Multiplication and Division with Complex Numbers
10.1a Quadratic Equations: The Square Root Method
10.1b Quadratic Equations: Completing the Square
10.2 Quadratic Equations: The Quadratic Formula
10.3 Applications: Quadratic Equations
10.4 Equations in Quadratic Form
10.5 Graphing Parabolas
10.6a Solving Quadratic Inequalities
10.6b Solving Inequalities with Rational Expressions
11.1 Algebra of Functions
11.2 Composition of Functions and Inverse Functions
11.3 Exponential Functions
11.4 Logarithmic Functions
11.5 Properties of Logarithms
- 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 Logarithms
11.6 Common Logarithms and Natural Logarithms
11.7 Exponential and Logarithmic Equations
11.8 Applications: Exponential and Logarithmic Functions
12.1 Translations and Reflections
- 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 and Reflections
12.2 Parabolas as Conic Sections
- Examples
- Example 1: Horizontal Parabolas
- Bonus Videos
- Bonus 1: Parabolas as Conic Sections
12.3 The Distance Formula and Circles
12.4 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
12.5 Nonlinear Systems of Equations
13.1 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
13.2 Sigma Notation
13.3 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
13.4 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
13.5 The Binomial Theorem
A.1a Decimals and Percents
- Examples
- Example 1: Adding Decimals
- Example 2: Subtracting Decimals
- Example 3: Monetary Arithmetic
- Example 4: Multiplying Decimals
- Example 5: Dividing Decimals
- Example 6: Dividing Decimals and Rounding
- Example 7: Calculating Price
- Example 8: Converting Decimals to Percents
- Example 9: Converting Percents to Decimals
- Example 10: Converting Fractions to Percents
- Example 11: Calculating Percents
- Bonus Videos
- Bonus 1: Decimals and Percents
A.1b More with Decimals
- Examples
- Example 1: Reading and Writing Decimal Numbers
- Example 2: Reading and Writing Decimal Numbers
- Example 3: Reading and Writing Decimal Numbers
- Example 4: Reading and Writing Decimal Numbers
- Example 5: Reading and Writing Decimal Numbers
- Example 6: Rounding Decimal Numbers
- Example 7: Rounding Decimal Numbers
- Bonus Videos
- Bonus 1: More with Decimals
A.2 Synthetic Division
A.3 Using a Graphing Calculator to Solve Equations
A.4 Determinants
A.5 Determinants and Systems of Linear Equations: Cramer's Rule
A.6 Permutations
A.7 Combinations
- Examples
- Example 1: Combinations
- Example 2: Combinations
- Bonus Videos
- Bonus 1: Combinations