Precalculus plus Integrated Review, 2nd 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 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 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.4 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.5 Decimals 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 8: Application: Changing Fractions to Percents
• Example 10: Changing Percents to Fractions
• Example 11: Changing Percents to Mixed Numbers

1.R.6 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

1.R.7 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.8 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

1.1a 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

1.1b 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

1.2a Properties of Exponents

• Examples
• Example 1: Natural Number Exponents
• Example 2: Simplifying Exponents
• Example 3: Properties of Exponents

1.2b Scientific Notation and Geometric Problems Using Exponents

• Examples
• Example 1: Scientific Notation
• Example 2: Simplifying Expressions with Scientific Notation
• Example 3: Geometric Formulas

1.2c Properties of Radicals

• Examples
• Example 1: Radical Notation
• Example 2: The Pythagorean Theorem
• Example 3: Simplifying Radical Expressions
• Example 4: Rationalizing the Denominator
• Example 5: Rationalizing the Numerator

1.2d Rational Number Exponents

• Examples
• Example 1: Combining Radicals
• Example 2: Simplifying Expressions
• Example 3: Simplifying Radical Expressions
• Example 4: Finding Areas with Heron's Formula

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 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

1.4 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

1.5a 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

1.5b 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

1.6 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

1.7a 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

1.7b Higher Degree Polynomial Equations

• Examples
• Example 1: Quadratic-Like Equations
• Example 2: Solving Equations by Factoring
• Example 3: Solving Equations by Factoring

1.8a 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

1.8b Radical Equations

• Examples
• Example 1: Causing Extraneous Solutions
• Example 2: Radical Equations
• Example 3: Escape Speed
• Example 4: Rational Exponents

2.R.1 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.2 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

2.1 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 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

2.3 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

2.4 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

2.5 Linear Inequalities in Two Variables

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

2.6 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

3.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

3.R.2 Identifying Like Terms

• Examples
• Example 1: Identifying Like Terms

3.R.3 Simplifying Expressions

• Examples
• Example 1: Combining Like Terms

3.R.4 Translating English Phrases and Algebraic Expression

• 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

3.1 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 5: Evaluating Functions
• Example 6: Domain, Codomain, and Range
• Example 7: Implied Domain of a Function

3.2a Linear and Quadratic Functions

• Examples
• Example 1: Graphing Linear Functions
• Example 2: Graphing Quadratic Functions
• Example 3: Using the Vertex Formula

3.2b Max/Min Applications of Quadratic Functions

• Examples
• Example 1: Fencing a Garden

3.3 Other Common Functions

• Examples
• Example 1: Functions of the Form axⁿ
• Example 2: Functions of the Form ${\displaystyle \frac{a}{x^n}}$
• Example 3: The Absolute Value Function
• Example 4: Piecewise-Defined Function

3.4 Variation and Multi-Variable Functions

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

3.5 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

3.6 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

3.7 Inverses of Functions

• Examples
• Example 1: Finding the Inverse of a Relation
• Example 2: Inverse Functions
• Example 3: Finding Formulas of Inverse Functions

4.R.1 Greatest Common Factor (GCF) of a Set of Terms

• Examples
• Example 1: Finding the GCF

4.R.2 Factoring Trinomials by Grouping

• Examples
• Example 1: Using the ac-Method
• Example 2: Using the ac-Method
• Example 3: Using the ac-Method

4.R.3 Review of Factoring Techniques

4.R.4 Introduction to Rational Expressions

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

4.1 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

4.2 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

4.3 Locating Real Zeros of Polynomials

• 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

4.4 The Fundamental Theorem of Algebra

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

4.5a Rational Functions

• Examples
• Example 1: Vertical Asymptotes
• Example 2: Horizontal and Oblique Asymptotes
• Example 3: Graphing Rational Functions

4.5b Rational Inequalities

• Examples
• Example 1: Solving Rational Inequalities
• Example 2: Rational Inequalities

5.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

5.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

5.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

5.1 Exponential Functions and their Graphs

• Examples
• Example 1: Graphing Exponential Functions
• Example 2: Graphing Exponential Functions
• Example 3: Solving Elementary Exponential Equations

5.2 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

5.3 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

5.4 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

5.5 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

6.R.1 Angles

• 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

6.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

6.1 Radian and Degree Measure of Angles

• 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

6.2 Trigonometric Functions of Acute Angles

• 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

6.3 Trigonometric Functions of Any Angle

• Examples
• Example 1: Finding the Values of the Six Trigonometric Functions
• Example 2: Finding the Values of the Six Trigonometric Functions
• Example 3: Finding the Reference Angle
• Example 4: Evaluating Trigonometric Functions
• Example 5: Using Cofunction Identities
• Example 6: Using the Relationships Between Trigonometric Functions
• Example 7: Using the Relationships Between Trigonometric Functions

6.4 Graphs of Trigonometric Functions

• Examples
• Example 1: Graphing the Cosecant Function
• Example 2: Finding the Period of Trigonometric Functions
• Example 3: Graphing the Tangent Function
• Example 4: Using Simple Harmonic Motion
• Example 5: Graphing Transformed Trigonometric Functions
• Example 6: Graphing Transformed Trigonometric Functions
• Example 7: Graphing Transformed Trigonometric Functions
• Example 8: Modeling Damped Harmonic Motion

6.5 Inverse Trigonometric Functions

• Examples
• Example 1: Defining and Plotting the Arccosine Function
• Example 2: Evaluating Inverse Trigonometric Functions
• Example 3: Evaluating Compositions of Trigonometric Functions
• Example 4: Evaluating Compositions of Trigonometric Functions
• Example 5: Using Inverse Trigonometric Functions
• Example 6: Using Inverse Trigonometric Functions

7.1 Fundamental Identities and their Uses

• 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

7.2 Sum and Difference Identities

• Examples
• Example 1: Using the Sum and Difference Identities for Exact Evaluation
• Example 2: 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 6: Using the Sum and Difference Identities
• Example 7: Using the Sum and Difference Identities
• Example 8: Using the Sum of Sines and Cosines Identity

7.3 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

7.4 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

8.1a The Law of Sines and the Law of Cosines

• 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: Determining If a Triangle Exists
• Example 4: Determining If a Triangle Exists
• Example 5: Using the Law of Cosines in a SSS Situation
• Example 6: Using the Law of Cosines in an SAS Situation

8.1b Area of Triangles

• Examples
• Example 1: Using the Sine Formula to Find the Area of a Triangle
• Example 2: Using Heron's Formula to Find the Area of a Triangle

8.2 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 Coordinates
• Example 5: Rewriting an Equation in Rectangular Coordinates
• 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

8.3a Parametric Equations - Graphing and Applications

• Examples
• Example 1: Determining Parametric Equations and Their Graphs
• Example 2: Using Parametric Equations

8.3b Parametric Equations - Eliminating the Parameter

• Examples
• Example 3: Eliminating the Parameter
• Example 4: Eliminating the Parameter

8.3c Parametric Equations - Constructing Equations

• Examples
• Example 5: Constructing Parametric Equations

8.4a 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

8.4b Operations with Complex Numbers

• Examples
• Example 1: Multiplying Complex Numbers
• Example 2: Dividing Complex Numbers
• Example 3: Graphing Complex Numbers and Their Product
• Example 4: Using De Moivre's Theorem
• Example 5: Finding Roots of Complex Numbers
• Example 6: Finding Roots of Complex Numbers

8.5 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

8.6 The Dot Product and Its Uses

• 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.R.1 Special Products of Binomials

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

9.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

9.1 The Ellipse

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

9.2 The Parabola

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

9.3 The Hyperbola

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

9.4 Rotation of Conics

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

9.5 Polar Form 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

10.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

10.R.2 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

10.1 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

10.2 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

10.3 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

10.4 The Algebra of Matrices

• 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

10.5 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

10.6 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

10.7 Linear Programming

• Examples
• Example 1: Feasible Regions
• Example 2: Linear Programming
• Example 3: Linear Programming
• Example 4: Linear Programming

10.8 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
• Example 6: Solving Nonlinear Systems of Inequalities by Graphing

11.1 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

11.2 Arithmetic Sequences and Series

• Examples
• Example 1: General Term of an Arithmetic Sequence
• Example 2: Modeling Population Growth
• Example 3: Partial Sums of Arithmetic Sequences
• Example 4: Partial Sums of Arithmetic Sequences

11.3 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

11.4 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

11.5a 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"

11.5b An Introduction to Combinatorics - The Binomial and Multinomial Theorems

• Examples
• Example 1: Binomial Expansion
• Example 2: The Binomial Theorem
• Example 3: The Multinomial Theorem

11.6 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

A.1 Mathematical Models

A.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

A.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

A.4 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