College Algebra plus Integrated Review, 2nd Edition
0.1 How to Read a Math Textbook
0.2 Tips for Success in a Math Course
0.3 Tips for Improving Math Test Scores
0.4 Practice, Patience, and Persistence!
0.5 Note Taking
0.6 Do I Need a Math Tutor?
0.7 Tips for Improving Your Memory
0.8 Overcoming Anxiety
0.9 Online Resources
0.10 Preparing for a Final Math Exam
0.11 Managing Your Time Effectively
1.R.1 Exponents, Prime Numbers, and LCM
- Examples
- Example 1: Identifying the Base and Exponent
- Example 3: Evaluating Exponential Expressions
- Example 4: Evaluating Exponential Expressions
- Example 5: Using the Order of Operations with Whole Numbers
- Example 6: Using the Order of Operations with Whole Numbers
- Example 7: Divisibility by 2
- Example 8: Divisibility by 3
- Example 9: Divisibility by 4
- Example 10: Divisibility by 5
- Example 11: Divisibility by 6
- Example 12: Divisibility by 9
- Example 13: Divisibility by 10
- Example 15: Determining Prime Numbers
- Example 16: Determining Composite Numbers
- Example 17: Determining Whether a Number is Prime
- Example 18: Determining Whether a Number is Prime
- Example 20: Finding the Prime Factorization of a Number
- Example 22: Finding the Factors of a Composite Number
- Example 24: Finding the Least Common Multiple (LCM)
- Example 25: Finding the Least Common Multiple (LCM)
- Example 27: Finding the Least Common Multiple (LCM)
- Example 28: Finding the Least Common Multiple (LCM)
- Example 30: Application: Finding the LCM
- Example 31: Finding Equivalent Fractions
- Example 32: Finding Equivalent Fractions
1.R.2 Reducing Fractions to Lowest Terms
- Examples
- Example 1: Reducing Fractions to Lowest Terms
- Example 2: Reducing Fractions to Lowest Terms
- Example 4: Application: Reducing Fractions to Lowest Terms
- Example 5: Multiplying and Reducing Using Prime Factors
- Example 6: Multiplying and Reducing Using Prime Factors
- Example 7: Multiplying and Reducing Using Prime Factors
- Example 9: Application: Multiplying and Reducing Fractions
- Example 10: Multiplying and Reducing Using the Division Method
- Example 11: Multiplying and Reducing Using the Division Method
- Example 12: Multiplying and Reducing Using the Division Method
- Example 13: Multiplying and Reducing Using the Division Method
1.R.3 Decimals and Percents
- Examples
- Example 1: Changing Fractions with Denominators of to Percents
- Example 2: Changing Decimal Numbers to Percents
- Example 3: Changing Percents to Decimal Numbers
- Example 4: Changing Fractions to Percents
- Example 5: Changing Fractions to Percents
- Example 6: Changing Mixed Numbers to Percents
- Example 8: Changing Fractions to Percents
- Example 9: Application: Changing Fractions to Percents
- Example 10: Changing Percents to Fractions
- Example 11: Changing Percents to Mixed Numbers
1.R.4 Simplifying Radicals
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.R.1 Multiplication and Division with Fractions
- Examples
- Example 1: Multiplying Fractions
- Example 2: Multiplying Fractions
- Example 3: Application: Multiplying Fractions
- Example 4: Recognizing the Properties of Multiplication
- Example 5: Reducing Fractions to Lowest Terms
- Example 6: Reducing Fractions to Lowest Terms
- Example 8: Application: Reducing Fractions to Lowest Terms
- Example 9: Multiplying and Reducing Using Prime Factors
- Example 10: Multiplying and Reducing Using Prime Factors
- Example 11: Multiplying and Reducing Using Prime Factors
- Example 13: Application: Multiplying and Reducing Fractions
- Example 14: Multiplying and Reducing Using the Division Method
- Example 15: Multiplying and Reducing Using the Division Method
- Example 16: Multiplying and Reducing Using the Division Method
- Example 17: Multiplying and Reducing Using the Division Method
- Example 18: Finding Reciprocals
- Example 19: Finding Reciprocals
- Example 20: Dividing Fractions
- Example 21: Dividing Fractions
- Example 22: Dividing and Reducing Fractions
- Example 23: Dividing and Reducing Fractions
- Example 26: Finding a Missing Number
- Example 27: Application: Dividing Fractions
- Example 28: Application: Multiplying and Dividing Fractions
2.R.2 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with the Same Denominator
- Example 2: Finding the Least Common Denominator (LCD)
- Example 3: Adding Fractions with Different Denominators
- Example 4: Adding Fractions with Different Denominators
- Example 5: Adding Three Fractions with Different Denominators
- Example 6: Application: Adding Fractions
- Example 7: Application: Adding Fractions
- Example 8: Subtracting Fractions with the Same Denominator
- Example 9: Subtracting Fractions with Different Denominators
- Example 10: Subtracting Fractions with Different Denominators
- Example 11: Subtracting Fractions with Different Denominators
- Example 12: Application: Subtracting Fractions with Different Denominators
2.R.3 Applications: Number Problems and Consecutive Integers
2.R.4 Proportions
- Examples
- Example 1: Verifying Proportions
- Example 3: Solving Proportions
- Example 4: Solving Proportions
- Example 5: Solving Proportions
- Example 6: Solving Proportions
- Example 8: Application: Solving Proportions
- Example 9: Application: Solving Proportions
- Example 10: Application: Solving Proportions
- Example 13: Application: Solving Proportions Written in Medical Notation
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.R.1 Order of Operations with Real Numbers
- Examples
- Example 1: Using the Order of Operations with Real Numbers
- Example 2: Using the Order of Operations with Real Numbers
- Example 3: Using the Order of Operations with Real Numbers
- Example 4: Using the Order of Operations with Real Numbers
- Example 6: Using the Order of Operations with Real Numbers
- Example 7: Using the Order of Operations with Real Numbers
4.R.2 Identifying Like Terms
4.R.3 Simplifying Expressions
- Examples
- Example 1: Combining Like Terms
4.R.4 Translating English Phrases and Algebraic Expressions
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.R.1 Rules for Exponents
7.R.2 Power Rules for Exponents
- Examples
- Example 1: Using the Power Rule for Exponents
- Example 2: Using the Rule for Power of a Product
- Example 3: Using the Rule for Power of a Quotient
- Example 4: Using Combinations of Rules for Exponents
- Example 5: Using Two Approaches with Fractional Expressions and Negative Exponents
- Example 6: Simplifying a More Complex Example
7.R.3 Rational Exponents
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.R.1 Systems of Linear Equations: Solutions by Graphing
- Examples
- Example 1: Checking Solutions to Systems (Solution)
- Example 2: Checking Solutions to Systems (Not a Solution)
- Example 3: Solving Systems (One Solution/A Consistent System)
- Example 4: Solving Systems (No Solution/An Inconsistent System)
- Example 5: Solving Systems (Infinite Solutions/A Dependent System)
- Example 6: Solving a System that Requires Estimation
8.R.2 Systems of Linear Inequalities
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