Precalculus plus Integrated Review, 3rd Edition

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 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

1.R.3 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

1.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

1.R.5 Decimals, Fractions, and Percents

• Examples
• Example 1: Changing Fractions with Denominators of $100$ 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.6 The Real Number Line and Absolute Value

• Examples
• Example 1: Finding the Opposite of an Integer
• Example 2: Graphing Integers on a Number Line
• Example 3: Identifying Types of Numbers
• Example 4: Graphing Sets of Numbers
• Example 5: Graphing Sets of Numbers
• Example 6: Verifying Inequalities
• Example 7: Finding Absolute Values
• Example 8: Verifying Absolute Value Inequalities
• Example 9: Solving Absolute Value Equations
• Example 10: Solving Absolute Value Equations
• Example 11: Application: Solving Absolute Value Equations

1.R.7 Addition with Real Numbers

• Examples
• Example 1: Adding Real Numbers with Like Signs
• Example 2: Adding Real Numbers with Unlike Signs
• Example 3: Adding More Than Two Real Numbers
• Example 4: Adding Three or More Real Numbers

1.R.8 Subtraction with Real Numbers

• Examples
• Example 1: Finding Additive Inverses
• Example 2: Subtracting Real Numbers
• Example 3: Application: Calculating Change in Value
• Example 4: Application: Calculating Change in Value
• Example 5: Application: Calculating Net Change
• Example 6: Application: Calculating Net Change

1.R.9 Multiplication and Division with Real Numbers

• Examples
• Example 1: Multiplying Positive and Negative Real Numbers
• Example 2: Multiplying Two Negative Real Numbers
• Example 3: Multiplication by $0$
• Example 4: Dividing Real Numbers
• Example 5: Dividing Fractions and Decimals
• Example 6: Application: Calculating an Average
• Example 7: Application: Calculating an Average
• Example 8: Application: Calculating an Average

1.1 Real Numbers and Algebraic Expressions

• 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: Union and Intersection of Intervals
• Example 7: Union and Intersection
• Example 8: Absolute Value
• Example 9: Using Absolute Value Properties
• Example 10: Terminology of Algebraic Expressions
• Example 11: Evaluating Algebraic Expressions
• Example 12: Using the Field Properties
• Example 14: Using the Cancellation and Zero-Factor Properties

1.2 Properties of Exponents and Radicals

• Examples
• Example 1: Using Natural Number Exponents
• Example 2: Simplifying Exponents
• Example 3: Using Properties of Exponents
• Example 4: Using Scientific Notation
• Example 5: Simplifying Expressions with Scientific Notation
• Example 6: Using Geometric Formulas
• Example 7: Using Radical Notation
• Example 8: Using Radical Notation
• Example 9: Simplifying Radical Expressions
• Example 11: Rationalizing the Numerator
• Example 12: Combining Radical Expressions
• Example 13: Simplifying Expressions
• Example 14: Simplifying Radical Expressions

1.3 Polynomials and Factoring

• Examples
• Example 1: Polynomial Expressions
• Example 2: Adding and Subtracting Polynomials
• Example 3: Multiplying Polynomials
• Example 4: The FOIL Method
• Example 8: Factoring Special Binomials
• Example 9: Factoring a Trinomial
• Example 10: Factoring a Trinomial by Grouping
• Example 11: Perfect Square Trinomials
• Example 12: Factoring Expressions with Noninteger Rational Exponents

1.4 Rational Expressions

• Examples
• Example 1: Simplifying Rational Expressions
• Example 2: Combining Rational Expressions
• Example 3: Combining Rational Expressions
• Example 4: Simplifying Complex Rational Expressions

1.5 Complex Numbers

• Examples
• Example 1: The Number i
• Example 2: Powers of i
• Example 4: Dividing Complex Numbers
• Example 5: Roots and Complex Numbers

1.6 Linear Equations in One Variable

• Examples
• Example 3: Solving Absolute Value Equations
• Example 4: Solving Linear Equations for One Variable
• Example 5: Calculating Average Speed
• Example 6: Calculating Average Interest Rate

1.7 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: Solving Double Linear Inequalities
• Example 6: Solving Linear Absolute Value Inequalities
• Example 7: Translating Inequality Phrases
• Example 8: Applications of Inequalities

1.8 Polynomial and Polynomial-Like Equations in One Variable

• Examples
• 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
• Example 8: Quadratic-Like Equations
• Example 9: Solving Equations by Factoring
• Example 10: Solving Equations by Factoring

1.9 Rational and Radical Equations in One Variable

• Examples
• Example 1: Solving Rational Equations
• Example 3: Filling a Pool
• Example 4: Filling a Pool Poorly
• Example 5: Causing Extraneous Solutions
• Example 6: Radical Equations
• Example 7: Rational Exponents
• Example 8: Escape Speed

2.R.1 Formulas in Geometry

• 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
• Example 7: Calculating the Area of a Triangle Using a Formula
• Example 8: Calculating the Area of a Trapezoid Using a Formula
• Example 9: Calculating the Area of a Composite Figure
• Example 10: Calculating Area
• Example 11: Calculating Area
• Example 12: Application: Calculating Perimeter and Area
• Example 13: Calculating the Circumference and Area of a Circle
• Example 14: Calculating the Circumference and Area of a Circle
• Example 15: Calculating the Perimeter
• Example 16: Calculating the Area of a Washer
• Example 17: Calculating Perimeter and Area
• Example 18: Calculating the Perimeter and Area
• Example 19: Calculating the Volume of a Rectangular Solid
• Example 20: Calculating the Volume of a Sphere
• Example 21: Calculating the Volume of a Cone
• Example 22: Calculating the Volume of a Solid
• Example 23: Finding the Volume of a Cube
• Example 24: Calculating the Surface Area of a Rectangular Solid
• Example 25: Calculating the Surface Area of a Cylinder

2.R.2 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

2.R.3 Evaluating Radicals

• Examples
• Example 1: Evaluating Square Roots
• Example 2: Evaluating Square Roots
• Example 3: Estimating Square Roots
• Example 4: Evaluating Cube Roots

2.R.4 Simplifying Radicals

• Examples
• Example 1: Simplifying Radical Expressions with Square Roots
• Example 2: Simplifying Square Roots with Variables
• Example 3: Simplifying Square Roots with Variables
• Example 4: Simplifying Expressions with Cube Roots

2.R.5 Introduction to the Cartesian Coordinate System

• Examples
• Example 1: Plotting Ordered Pairs
• Example 2: Plotting Ordered Pairs
• Example 3: Finding Ordered Pairs
• Example 4: Finding Ordered Pairs
• Example 6: Locating Points on the Graph of a Line

2.R.6 Solving Linear Equations: ax + b = c

• Examples
• Example 1: Solving Linear Equations of the Form ax + b = c
• Example 2: Solving Linear Equations of the Form ax + b = c
• Example 3: Solving Linear Equations Involving Decimals
• Example 4: Solving Linear Equations Involving Decimals
• Example 5: Solving Linear Equations Involving Fractions
• Example 6: Solving Linear Equations Involving Fractions

2.R.7 Solving 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 Involving Fractions
• Example 5: Solving Equations Involving Parentheses
• Example 6: Solving Equations Involving Parentheses
• Example 8: Determining Types of Equations
• Example 9: Determining Types of Equations
• Example 10: Determining Types of Equations

2.R.8 Solving Linear Inequalities in One Variable

• Examples
• Example 1: Graphing Intervals
• Example 2: Graphing Intervals
• Example 3: Graphing Intervals
• Example 4: Graphing Intervals
• Example 5: Solving an Inequality and Graphing the Solution Set
• Example 6: Solving an Inequality and Graphing the Solution Set
• Example 7: Solving an Inequality and Graphing the Solution Set
• Example 8: Solving an Inequality and Graphing the Solution Set
• Example 9: Solving Linear Inequalities
• Example 10: Solving Linear Inequalities
• Example 11: Solving Linear Inequalities
• Example 13: Application: Using Inequalities

2.R.9 Solving Radical Equations

• Examples
• Example 1: Solving Equations with One Radical
• Example 2: Solving Equations with One Radical
• Example 3: Solving Equations with One Radical
• Example 4: Solving Equations with One Radical
• Example 6: Solving Equations with Two Radicals
• Example 7: Solving Equations with Two Radicals
• Example 8: Solving Equations containing a Cube Root

2.1 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

2.2 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

2.3 Linear Equations in Two Variables

• Examples
• Example 1: Linear Equations in Two Variables
• Example 2: Finding Intercepts and Graphing Linear Equations
• Example 3: Graphing Horizontal and Vertical Lines

2.4 Slope and 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: Using the Point-Slope Form of a Line
• Example 6: Using the Point-Slope Form of a Line

2.5 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

2.6 Linear Inequalities in Two Variables

• Examples
• Example 1: Solving Linear Inequalities
• Example 2: Solving Linear Inequalities
• Example 3: Solving Absolute Value Linear Inequalities

3.R.1 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: Determining if a Relation is a Function
• Example 4: Using the Vertical Line Test
• Example 5: Finding the Domain of a Function
• Example 6: Evaluating Functions
• Example 7: Evaluating Nonlinear Functions
• Example 8: Evaluating Functions From a Graph

3.R.2 Translating English Phrases and Algebraic Expressions

• Examples
• Example 1: Translating English Phrases into Algebraic Expressions
• Example 2: Application: Translating English Phrases
• Example 3: Translating Algebraic Expressions to English Phrases
• Example 4: Translating Equations into Word Problems

3.R.3 Applications: Number Problems and Consecutive Integers

• Examples
• Example 1: Solving Number Problems
• Example 2: Solving Number Problems
• Example 3: Solving Number Problems
• Example 4: Finding Consecutive Integers
• Example 5: Finding Consecutive Integers
• Example 6: Application: Calculating Living Expenses
• Example 7: Application: Calculating Costs of Purchases

3.R.4 Greatest Common Factor (GCF) and Factoring by Grouping

• Examples
• Example 1: Finding the GCF
• Example 2: Factoring Out the GCF of a Polynomial
• Example 3: Factoring Out the GCF of a Polynomial
• Example 4: Factoring Out the GCF of a Polynomial
• Example 5: Factoring Out the GCF of a Multi-Variable Polynomial
• Example 6: Factoring Out a Common Binomial Factor
• Example 7: Factoring Polynomials by Grouping
• Example 8: Factoring Polynomials by Grouping
• Example 9: Factoring Polynomials by Grouping
• Example 10: Factoring Polynomials by Grouping
• Example 11: Factoring Polynomials by Grouping

3.R.5 Factoring Trinomials: x^2 + bx + c

• Examples
• Example 1: Factoring Trinomials with Leading Coefficient 1
• Example 2: Factoring Trinomials with Leading Coefficients of 1
• Example 4: Finding a Common Monomial Factor

3.R.6 Factoring Trinomials: ax^2 + bx + c

• Examples
• Example 1: Using the Trial-and-Error Method
• Example 2: Factoring Trinomials
• Example 3: Using the ac-Method
• Example 4: Using the ac-Method
• Example 5: Using the ac-Method

3.R.7 Review of Factoring Techniques

3.R.8 Solving Quadratic Equations by Factoring

• Examples
• Example 1: Solving Factored Quadratic Equations
• Example 2: Solving Quadratic Equations by Factoring
• Example 3: Solving Quadratic Equations by Factoring
• Example 4: Solving Quadratic Equations by Factoring
• Example 5: Solving Quadratic Equations by Factoring
• Example 6: Solving Quadratic Equations by Factoring
• Example 7: Solving Quadratic Equations by Factoring
• Example 9: Solving Higher Degree Equations
• Example 10: Finding Equations with Given Roots

3.R.9 Multiplication and Division with Complex Numbers

• Examples
• Example 1: Multiplying with Complex Numbers
• Example 2: Dividing with Complex Numbers
• Example 3: Simplifying Powers of i

3.R.10 Quadratic Equations: The Quadratic Formula

• Examples
• Example 1: The Quadratic Formula
• Example 2: The Quadratic Formula
• Example 3: The Quadratic Formula
• Example 4: The Quadratic Formula
• Example 5: Cubic Equations
• Example 6: Finding the Discriminant
• Example 7: Understanding the Discriminant
• Example 8: Understanding the Discriminant

3.1 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: Function Notation
• Example 6: Evaluating Functions
• Example 7: Domain, Codomain, and Range
• Example 8: Implied Domain of a Function

3.2 Linear Functions

• Examples
• Example 1: Graphing Linear Functions

3.3 Quadratic Functions

• Examples
• Example 1: Graphing Quadratic Functions
• Example 2: Using the Vertex Formula
• Example 6: Fencing a Garden

3.4 Other Common Functions

• Examples
• Example 1: Power Functions of the Form axⁿ
• Example 3: The Absolute Value Function
• Example 4: Piecewise-Defined Function

3.5 Variation and Multivariable Functions

• Examples
• Example 1: Direct Variation
• Example 2: Inverse Variation
• Example 3: Joint Variation
• Example 4: Finding the Force of Gravity

3.6 Mathematical Models

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 Simplifying and Evaluating Algebraic Expressions

• Examples
• Example 1: Identifying Like Terms
• Example 2: Combining Like Terms
• Example 3: Evaluating Algebraic Expressions
• Example 4: Simplifying and Evaluating Algebraic Expressions
• Example 5: Simplifying and Evaluating Algebraic Expressions
• Example 6: Simplifying and Evaluating Algebraic Expressions

4.R.3 Multiplication with Polynomials

• Examples
• Example 1: Multiplying Polynomials and Monomials
• Example 3: Multiplying Two Binomials
• Example 5: Multiplying Polynomials
• Example 6: Multiplying Polynomials
• Example 7: Multiplying Polynomials
• Example 8: Multiplying Polynomials
• Example 9: Using the FOIL Method to Multiply Binomials
• Example 10: Using the FOIL Method to Multiply Binomials

4.R.4 Division with Polynomials

• Examples
• Example 1: Dividing by a Monomial
• Example 2: Using the Division Algorithm
• Example 3: Using Long Division (Remainder 0)
• Example 4: Using Long Division (Terms Missing)

4.R.5 Introduction to Rational Expressions

• Examples
• Example 1: Finding Restrictions on the Variable
• Example 2: Evaluating Rational Expressions
• Example 3: Reducing Rational Expressions

4.R.6 Multiplication and Division with Rational Expressions

• Examples
• Example 1: Multiplication with Rational Expressions
• Example 2: Multiplying with Rational Expressions
• Example 3: Multiplying with Rational Expressions
• Example 4: Multiplying with Rational Expressions
• Example 6: Dividing with Rational Expressions
• Example 7: Dividing with Rational Expressions
• Example 8: Dividing with Rational Expressions

4.R.7 Simplifying Complex Fractions

• Examples
• Example 1: First Method for Simplifying Complex Fractions
• Example 2: First Method for Simplifying Complex Fractions
• Example 3: First Method for Simplifying Complex Fractions
• Example 4: Second Method for Simplifying Complex Fractions
• Example 5: Second Method for Simplifying Complex Fractions
• Example 6: Simplifying Complex Algebraic Expressions

4.1 Transformations of Functions

• Examples
• Example 1: Horizontal Shifting/Translation
• Example 3: Horizontal and Vertical Shifting
• Example 5: Vertical Stretching and Compressing
• Example 8: Order of Transformations

4.2 Properties of Functions

• Examples
• Example 1: Using Symmetry to Graph Relations
• Example 2: Determining Intervals of Monotonicity
• Example 3: Modeling the Water Level of a River

4.3 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

4.4 Inverses of Functions

• Examples
• Example 1: Finding the Inverse of a Relation
• Example 2: Inverse Functions

5.1 Polynomial Functions and Polynomial Inequalities

• Examples
• Example 1: Solutions of Polynomial Equations
• Example 2: Graphing Polynomial Functions
• Example 4: Solving Polynomial Inequalities Using a Graph

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 5: Synthetic Division (with Complex Numbers)
• Example 6: Constructing Polynomials

5.3 Locating Real Zeros of Polynomial Functions

• Examples
• Example 1: The Rational Zero Theorem
• Example 2: Descartes' Rule of Signs
• Example 3: Finding Bounds of Real Zeros
• Example 4: Finding the Zeros of a Polynomial
• Example 5: Intermediate Value Theorem

5.4 The Fundamental Theorem of Algebra

• Examples
• Example 1: Graphing Polynomial Functions
• Example 2: Factoring Polynomials
• Example 3: Constructing Polynomials

5.5 Rational Functions and Rational Inequalities

• Examples
• Example 1: Vertical Asymptotes
• Example 2: Horizontal and Oblique Asymptotes
• Example 3: Graphing Rational Functions
• Example 4: Solving Rational Inequalities
• Example 5: Solving Rational Inequalities

6.R.1 Rules for Exponents

• Examples
• Example 1: Using the Product Rule for Exponents
• Example 2: Using the Product Rule for Exponents
• Example 3: Evaluating the Exponent 0
• Example 4: Using the Quotient Rule for Exponents
• Example 5: Dividing Terms with Coefficients
• Example 6: Negative Exponents
• Example 7: Combining Rules for Exponents

6.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

6.R.3 Rational Exponents

• Examples
• Example 1: Evaluating $n^{\mathrm{th}}$ Roots
• Example 2: Converting from Exponential Notation to Radical Notation
• Example 3: Simplifying Expressions with Rational Exponents
• Example 4: Simplifying Radical Notation by Changing to Exponential Notation

6.R.4 Introduction to Logarithmic Functions

• Examples
• Example 1: Translating Between Exponential and Logarithmic Form
• Example 2: Evaluating Logarithms
• Example 3: Solving Logarithmic Equations
• Example 4: Solving Logarithmic Equations

6.1 Exponential Functions and Their Graphs

• Examples
• Example 1: Graphing Exponential Functions
• Example 3: Solving Elementary Exponential Equations

6.2 Exponential Models

• Examples
• Example 1: Population Growth
• Example 3: Compound Interest Formula
• Example 4: Compound Interest Formula
• Example 5: Continuous Compounding Formula

6.3 Logarithmic Functions and Their Graphs

• Examples
• Example 1: Exponential and Logarithmic Equations
• Example 2: Graphing Logarithmic Functions
• Example 5: Solving Logarithmic Equations
• Example 6: Evaluating Logarithmic Expressions

6.4 Logarithmic Properties and Models

• 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 8: The Decibel Scale

6.5 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

7.R.1 Angles

7.R.2 Triangles

• Examples
• Example 1: Classifying a Triangle by Its Sides
• Example 2: Determining Whether a Triangle Exists
• Example 3: Analyzing Triangles
• Example 4: Determining Whether Triangles are Similar
• Example 5: Finding Unknown Values Using Similar Triangles
• Example 6: Application: Finding Unknown Values Using Similar Triangles
• Example 7: Determining Whether Triangles are Congruent

7.1 Radian and Degree Measure

• Examples
• Example 1: Converting between Degrees and Radians
• Example 2: Determining the Measure of an Angle
• Example 3: Applying the Arc Length Formula
• Example 4: Finding the Angular and Linear Speeds
• Example 5: Finding the Area of a Sector

7.2 Trigonometric Functions and Right Triangles

• Examples
• Example 1: Finding the Values of the Six Trigonometric Functions
• Example 2: Evaluating Trigonometric Functions
• Example 4: Using Trigonometric Functions
• Example 5: Using Trigonometric Functions
• Example 6: Using Trigonometric Functions

7.3 Trigonometric Functions and the Unit Circle

• Examples
• Example 4: Finding the Reference Angle
• Example 6: Using Cofunction Identities
• Example 7: Using the Relationships between Trigonometric Functions
• Example 8: Using the Relationships between Trigonometric Functions

7.4 Graphs of Sine and Cosine Functions

• Examples
• Example 7: Graphing Transformed Trigonometric Functions
• Example 8: Using Simple Harmonic Motion
• Example 9: Modeling Damped Harmonic Motion

7.5 Graphs of Other Trigonometric Functions

7.6 Inverse Trigonometric Functions

• Examples
• Example 2: Evaluating Compositions of Trigonometric Functions
• Example 3: Evaluating Compositions of Trigonometric Functions
• Example 4: Using Inverse Trigonometric Functions
• Example 5: Using Inverse Trigonometric Functions

8.1 Fundamental Trigonometric Identities

• Examples
• Example 1: Simplifying Trigonometric Expressions
• Example 2: Simplifying Trigonometric Expressions
• Example 3: Verifying Trigonometric Identities
• Example 4: Verifying Trigonometric Identities
• Example 5: Verifying Trigonometric Identities
• Example 6: Using Trigonometric Substitutions

8.2 Sum and Difference Identities

• Examples
• Example 1: Using the Sum and Difference Identities for Exact Evaluation
• Example 3: Using the Sum and Difference Identities for Exact Evaluation
• Example 4: Using the Sum and Difference Identities for Exact Evaluation
• Example 5: Using the Sum and Difference Identities
• Example 7: Using the Sum and Difference Identities
• Example 8: Using the Sum and Difference Identities
• Example 9: Using the Sum of Sines and Cosines Identity

8.3 Product-Sum Identities

• Examples
• Example 1: Using the Double-Angle Identities
• Example 2: Using Trigonometric Identities
• Example 3: Using the Power-Reducing Identities
• Example 4: Using the Half-Angle Identities
• Example 5: Using the Half-Angle Identities for Exact Evaluation
• Example 6: Using the Product-to-Sum Identities
• Example 7: Using the Sum-to-Product Identities

8.4 Trigonometric Equations

• Examples
• Example 1: Solving Equations by Isolating the Trigonometric Function
• Example 2: Solving Equations by Isolating the Trigonometric Function
• Example 3: Solving Trigonometric Equations by Factoring
• Example 4: Solving Equations Using Trigonometric Identities
• Example 5: Solving Trigonometric Equations by Graphing
• Example 6: Solving Equations Using Trigonometric Identities
• Example 7: Solving Equations by Isolating the Trigonometric Function
• Example 8: Solving Equations Using Inverse Trigonometric Functions
• Example 9: Solving Equations Using Inverse Trigonometric Functions

9.1 The Law of Sines

• Examples
• Example 1: Using the Law of Sines in an AAS Situation
• Example 2: Using the Law of Sines in an ASA Situation
• Example 3: Using the Law of Sines in an SSA Situation with Two Solutions
• Example 4: Using the Law of Sines in an SSA Situation with No Solution
• Example 5: Using the Sine Formula to Find the Area of a Triangle

9.2 The Law of Cosines

• Examples
• Example 1: Using the Law of Cosines in an SSS Situation
• Example 2: Using the Law of Cosines in an SAS Situation
• Example 3: Using Heron's Formula to Find the Area of a Triangle

9.3 Polar Coordinates and Polar Equations

• Examples
• Example 1: Plotting in Polar Coordinates
• Example 2: Converting from Polar to Cartesian Coordinates
• Example 4: Rewriting an Equation in Polar Form
• Example 5: Rewriting an Equation in Rectangular Form
• Example 6: Graphing Polar Equations
• Example 7: Graphing Polar Equations
• Example 8: Graphing Common Polar Equations Using Symmetry
• Example 9: Graphing Common Polar Equations Using Symmetry

9.4 Parametric Equations

• Examples
• Example 1: Determining Parametric Equations and Their Graphs
• Example 2: Using Parametric Equations
• Example 3: Eliminating the Parameter
• Example 4: Eliminating the Parameter
• Example 5: Constructing Parametric Equations

9.5 Trigonometric Form of Complex Numbers

• Examples
• Example 1: Finding the Magnitude
• Example 2: Graphing Regions in the Complex Plane
• Example 3: Writing Complex Numbers in Trigonometric Form
• Example 4: Writing Complex Numbers in Standard Form
• Example 5: Multiplying Complex Numbers
• Example 6: Dividing Complex Numbers
• Example 7: Graphing Complex Numbers and Their Product
• Example 8: Using De Moivre's Theorem
• Example 9: Finding Roots of Complex Numbers
• Example 10: Finding Roots of Complex Numbers

9.6 Vectors in the Cartesian Plane

• Examples
• Example 1: Graphing the Sum of Two Vectors
• Example 2: Graphing Vectors
• Example 3: Using Vector Operations
• Example 4: Finding the Unit Vector and Linear Combination of a Vector
• Example 5: Finding the Vector Form of the Velocity
• Example 6: Applying Vector Operations
• Example 7: Applying Vector Operations

9.7 The Dot Product

• Examples
• Example 1: Calculating the Dot Product
• Example 2: Using the Properties of the Dot Product
• Example 3: Applying the Dot Product Theorem
• Example 4: Finding an Orthogonal Vector
• Example 5: Finding the Projection of u onto v
• Example 6: Applying the Dot Product
• Example 7: Applying the Dot Product

9.8 Hyperbolic Functions

10.R.1 Special Products of Binomials

• Examples
• Example 1: Difference of Two Squares
• Example 3: Squares of Binomials

10.R.2 Special Factoring Techniques

• Examples
• Example 1: Factoring the Difference of Two Squares
• Example 2: Factoring the Sum of Two Squares (Not Factorable)
• Example 3: Factoring Perfect Square Trinomials

10.1 Ellipses

• Examples
• Example 1: Graphing an Ellipse Centered at the Origin
• Example 2: Graphing an Ellipse with Equation in Standard Form
• Example 3: Graphing an Ellipse with Equation Not in Standard Form
• Example 4: Constructing the Equation for an Ellipse

10.2 Parabolas

• Examples
• Example 1: Graphing a Parabola with Equation in Standard Form
• Example 2: Graphing a Parabola with Equation Not in Standard Form
• Example 3: Standard Form Equation of a Parabola
• Example 4: Parabolic Mirrors

10.3 Hyperbolas

• Examples
• Example 1: Graphing a Hyperbola with Equation in Standard Form
• Example 2: Graphing a Hyperbola with Equation Not in Standard Form
• Example 3: Standard Form of the Equation of a Hyperbola
• Example 4: LORAN

10.4 Rotation of Conic Sections

• Examples
• Example 1: Finding $x^{\mathrm{\prime }}{y}^{\mathrm{\prime }}$-Coordinates
• Example 2: Using the Rotation Relations
• Example 4: Classifying and Graphing Conic Sections

10.5 Polar Equations of Conic Sections

• Examples
• Example 1: Identifying the Type and Directrix of a Conic
• Example 2: Constructing a Polar Equation
• Example 3: Graphing Conic Sections in Polar Form
• Example 4: Graphing Conic Sections in Polar Form
• Example 5: Graphing Conic Sections Using Rotation in Polar Coordinates

11.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

11.R.2 Systems of Linear Equations: Solutions by Substitution

11.R.3 Systems of Linear Equations: Solutions by Addition

11.R.4 Systems of Linear Inequalities

• Examples
• Example 1: Solving Systems of Linear Inequalities
• Example 2: Solving Systems of Linear Inequalities
• Example 3: Solving Systems of Linear Inequalities

11.1 Solving Systems of Linear Equations by Substitution and Elimination

• Examples
• Example 1: Solving an Independent System by Substitution
• Example 2: Solving a Dependent System by Substitution
• Example 3: Solving an Independent System by Elimination
• Example 4: Solving an Inconsistent System by Elimination
• Example 5: Solving an Independent System by Elimination
• Example 6: Solving a Dependent System by Elimination
• Example 7: Mixing Alloys
• Example 8: Determining Ages

11.2 Matrix Notation and Gauss-Jordan 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

11.3 Determinants and Cramer's Rule

• Examples
• Example 1: Determinant of a 2×2 Matrix
• Example 2: Minors and Cofactors
• Example 3: Determinant of an n×n Matrix
• Example 4: Properties of Determinants
• Example 5: Cramer's Rule
• Example 6: Cramer's Rule

11.4 Basic Matrix Operations

• Examples
• Example 1: Matrix Addition
• Example 2: Matrix Equations
• Example 3: Scalar Multiplication
• Example 4: Matrix Subtraction
• Example 5: Matrix Multiplication
• Example 6: Matrix Multiplication

11.5 Inverses of Matrices

• Examples
• Example 1: Matrix Equation
• Example 2: Finding the Inverse of a Matrix
• Example 3: Finding the Inverse of a Matrix
• Example 4: Inverse Matrix Method

11.6 Partial Fraction Decomposition

• Examples
• Example 1: Finding the Partial Fraction Decomposition of a Function
• Example 2: Finding the Partial Fraction Decomposition of a Function
• Example 3: Finding the Partial Fraction Decomposition of a Function
• Example 4: Finding the Partial Fraction Decomposition of a Function
• Example 5: Finding the Partial Fraction Decomposition of a Function

11.7 Systems of Linear Inequalities and Linear Programming

• Examples
• Example 2: Feasible Regions
• Example 3: Linear Programming
• Example 4: Linear Programming

11.8 Systems of Nonlinear Equations and Inequalities

• Examples
• Example 1: Solving Systems of Nonlinear Equations by Graphing
• Example 2: Solving Systems of Nonlinear Equations by Graphing
• Example 3: Solving Systems of Nonlinear Equations Algebraically
• Example 4: Solving Systems of Nonlinear Equations Algebraically
• Example 5: Solving Systems of Nonlinear Equations Algebraically
• Example 6: Solving Systems of Nonlinear Inequalities by Graphing

12.1 Sequences and Series

• Examples
• Example 1: Sequences
• Example 2: Recursively Defined Sequences
• Example 3: Finding the Formula for a Sequence
• Example 4: Evaluating Sums
• Example 5: Evaluating Sums
• Example 6: Evaluating Partial Sums and Series

12.2 Arithmetic Sequences and Series

• Examples
• Example 1: General Term of an Arithmetic Sequence
• Example 3: Partial Sums of Arithmetic Sequences
• Example 4: Partial Sums of Arithmetic Sequences

12.3 Geometric Sequences and Series

• Examples
• Example 1: General Term of a Geometric Sequence
• Example 2: General Term of a Geometric Sequence
• Example 3: Comparing Salary Offers
• Example 4: Partial Sum of a Geometric Sequence
• Example 5: Infinite Geometric Series

12.4 Mathematical Induction

• Examples
• Example 1: Proof by Mathematical Induction
• Example 2: Proof by Mathematical Induction
• Example 3: Proof by Mathematical Induction
• Example 4: Proof by Mathematical Induction

12.5 Combinatorics

• Examples
• Example 2: Using the Multiplication Principle of Counting
• Example 3: Calculating Permutations
• Example 4: Calculating Permutations
• Example 5: Using the Permutation Formula
• Example 6: Calculating Permutations and Combinations
• Example 7: The Combination Formula and Forming Committees
• Example 8: Counting Rules and Forming "Words"
• Example 11: Using the Multinomial Theorem

12.6 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

13.1 Rates of Change and Tangents

• Examples
• Example 4: Using Difference Quotients to Approximate the Slope of a Tangent Line

13.2 Limits in the Plane

• Examples
• Example 3: Finding One-Sided Limits near Vertical Asymptotes
• Example 4: Finding One-Sided Limits near Vertical Asymptotes
• Example 6: Using Limits at Infinity to Identify Horizontal Asymptotes

13.3 The Mathematical Definition of Limit

• Examples
• Example 2: Using Graphs to Determine Limits
• Example 3: Using the ε-δ Definition of Limit to Prove a Limit Exists
• Example 5: Using the ε-δ Definition of Limit to Prove a Limit Exists
• Example 6: Proving a Limit Does Not Exist
• Example 7: Proving a Limit Does Not Exist

13.4 Determining Limits of Functions

• Examples
• Example 1: Using Graphs and Limit Laws to Determine Limits
• Example 3: Using Limit Laws to Determine Limits
• Example 6: Using Algebraic Techniques to Determine Limits
• Example 7: Using Algebraic Techniques to Determine Limits
• Example 8: Using the Squeeze Theorem to Determine Limits

13.5 Continuity

• Examples
• Example 1: Finding Points of Continuity and Discontinuity
• Example 2: Finding Points of Discontinuity
• Example 5: Using the ε-δ Definition of Continuity
• Example 6: Understanding Rational Functions and Continuity
• Example 7: Using Theorems to Determine Continuity of Functions
• Example 8: Using Alternate Formulations to Prove Functions Are Continuous
• Example 10: Defining Continuous Extensions of Functions
• Example 11: Using the Intermediate Value Theorem

13.6 The Derivative

• Examples
• Example 1: Finding the Equation of a Tangent Line
• Example 2: Finding Instantaneous Velocity
• Example 3: Finding Instantaneous Velocity
• Example 4: Finding Speed
• Example 5: Finding Derivatives and Tangent Lines to Graphs
• Example 6: Finding Break-Even Points and Marginal Profit