# Precalculus

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# Precalculus

A 2-in-1 value: Thinkwell's Precalculus combines concepts from College Algebra with Trigonometry for a comprehensive experience of precalculus mathematics. Our Precalculus has hundreds of video tutorials and thousands of automatically graded exercises with step-by-step feedback, covering everything in the most popular textbooks, so you have all of the pre-calculus math help you need to prepare for Calculus.

Thinkwell's Precalculus video tutorials feature award-winning teacher Edward Burger, who has a unique ability to break down concepts and explain examples in ways that stick with students. Between having the best math teacher, 24/7 availability, and one fixed price instead of an hourly rate, Thinkwell Pre-Calculus is better than a tutor. It's the ultimate pre-calculus study aid.

**Our complete Precalculus package includes:**

- 12-month Online Subscription to our complete Pre-calculus course with video lessons, automatically graded exercises, and much more.
- Workbook (optional) with lecture notes, sample problems, and exercises so that you can study even when away from the computer.

*Workbook requires the purchase of an online subscription.*

## Precalculus Materials

### Online Subscription, *12-month access*

Access to a complete online package that includes everything you need:

- High-quality video lessons explain all of the Pre-calculus Math topics and concepts
- Automatically graded exercises with immediate feedback allow you to track your progress
- Printable full-color illustrated notes help you review what you've learned in the video lesson
- Subscriptions start when you are ready. Buy now and activate your course anytime you like. Wait up to one year to activate your subscription; your 12-month subscription doesn't begin until you say so!

### Workbook, *Notes, sample problems, exercises, and practice problems*

Study without a computer. Our workbook companion contains the same lecture notes and sample problems that are delivered online, as well as some additional exercises, all in a convenient print format. Answers to the odd-numbered exercises are in the back of the book. Online Subscription is required; workbook not sold separately.

### Precalculus Details

- Equivalent to 10th- or 11th-grade Algebra 2, plus 11th- or 12th-grade Trigonometry
- More than 330 video lessons (see sample)
- 1000+ interactive exercises with immediate feedback allow you to track your progress (see sample)
- Pre-Calculus practice tests and final tests for all 8 chapters, as well as a midterm and a final (only available in the homeschool version)
- Printable illustrated notes for each topic
- Real-world application examples in both lectures and exercises
- Closed captioning for all videos
- Glossary of more than 200 mathematical terms
- Engaging content to help students advance their mathematical knowledge:
- Review of algebraic concepts such as exponents, radicals, polynomials, factoring, and complex numbers
- Linear and quadratic equations and inequalities
- Rational and radical expressions
- Absolute value
- Graphing linear and quadratic functions
- Shifts, stretches, symmetry, and reflections
- Synthetic division and long division
- Exponential and logarithmic functions
- Graphing trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant
- Inverse trigonometric functions
- Trigonometric identities
- Applications of trigonometry: the law of sines, the law of cosines, vectors, and polar coordinates
- Systems of equations and matrices
- Conic sections: parabolas, ellipses, and hyperbolas
- Combinations and probability

### Table of Contents

1. Basic Algebra Review- 1.1 Introduction
- 1.1.1 The Top Ten List of Mistakes

- 1.2 Inequalities
- 1.2.1 Concepts of Inequality

- 1.2.2 Inequalities and Interval Notation

- 1.3 Absolute Value
- 1.3.1 Properties of Absolute Value

- 1.3.2 Evaluating Absolute Value Expressions

- 1.4 Exponents
- 1.4.1 An Introduction to Exponents

- 1.4.2 Evaluating Exponential Expressions

- 1.4.3 Applying the Rules of Exponents

- 1.4.4 Evaluating Expressions with Negative Exponents

- 1.5 Converting between Notations
- 1.5.1 Converting between Decimal and Scientific Notation

- 1.5.2 Converting Rational Exponents and Radicals

- 1.6 Radical Expressions
- 1.6.1 Simplifying Radical Expressions

- 1.6.2 Simplifying Radical Expressions with Variables

- 1.6.3 Rationalizing Denominators

- 1.7 Polynomial Expressions
- 1.7.1 Determining Components and Degree

- 1.7.2 Adding, Subtracting, and Multiplying Polynomials

- 1.7.3 Multiplying Big Products

- 1.7.4 Using Special Products

- 1.8 Factoring
- 1.8.1 Factoring Using the Greatest Common Factor

- 1.8.2 Factoring by Grouping

- 1.8.3 Factoring Trinomials Completely

- 1.8.4 Factoring Trinomials: The Grouping Method

- 1.9 Factoring Patterns
- 1.9.1 Factoring Perfect Square Trinomials

- 1.9.2 Factoring the Difference of Two Squares

- 1.9.3 Factoring the Sums and Differences of Cubes

- 1.9.4 Factoring by Any Method

- 1.10 Rational Expressions
- 1.10.1 Rational Expressions and Domain

- 1.10.2 Working with Fractions

- 1.10.3 Writing Rational Expressions in Lowest Terms

- 1.11 Working with Rationals
- 1.11.1 Multiplying and Dividing Rational Expressions

- 1.11.2 Adding and Subtracting Rational Expressions

- 1.11.3 Rewriting Complex Fractions

- 1.12 Complex Numbers
- 1.12.1 Introducing and Writing Complex Numbers

- 1.12.2 Rewriting Powers of i

- 1.12.3 Adding and Subtracting Complex Numbers

- 1.12.4 Multiplying Complex Numbers

- 1.12.5 Dividing Complex Numbers

#### 2. Equations and Inequalities

- 2.1 Linear Equations
- 2.1.1 An Introduction to Solving Equations

- 2.1.2 Solving a Linear Equation

- 2.1.3 Solving a Linear Equation with Rationals

- 2.1.4 Solving a Linear Equation That Has Restrictions

- 2.2 Word Problems with Linear Equations: Math Topics
- 2.2.1 An Introduction to Solving Word Problems

- 2.2.2 Solving for Perimeter

- 2.2.3 Solving a Linear Geometry Problem

- 2.2.4 Solving for Consecutive Numbers

- 2.2.5 Solving to Find the Average

- 2.3 Word Problems with Linear Equations: Applications
- 2.3.1 Solving for Constant Velocity

- 2.3.2 Solving a Problem about Work

- 2.3.3 Solving a Mixture Problem

- 2.3.4 Solving an Investment Problem

- 2.3.5 Solving Business Problems

- 2.4 Quadratic Equations: Some Solution Techniques
- 2.4.1 Solving Quadratics by Factoring

- 2.4.2 Solving Quadratics by Completing the Square

- 2.4.3 Completing the Square: Another Example

- 2.5 Quadratic Equations and the Quadratic Formula
- 2.5.1 Proving the Quadratic Formula

- 2.5.2 Using the Quadratic Formula

- 2.5.3 Predicting the Type of Solutions Using the Discriminant

- 2.6 Quadratic Equations: Special Topics
- 2.6.1 Solving for a Squared Variable

- 2.6.2 Finding Real Number Restrictions

- 2.6.3 Solving Fancy Quadratics

- 2.7 Word Problems with Quadratics: Math Topics
- 2.7.1 An Introduction to Word Problems with Quadratics

- 2.7.2 Solving a Quadratic Geometry Problem

- 2.7.3 Solving with the Pythagorean Theorem

- 2.7.4 The Pythagorean Theorem: Another Example

- 2.8 Word Problems with Quadratics: Applications
- 2.8.1 Solving a Motion Problem

- 2.8.2 Solving a Projectile Problem

- 2.8.3 Solving Other Problems

- 2.9 Radical Equations
- 2.9.1 Determining Extraneous Roots

- 2.9.2 Solving an Equation Containing a Radical

- 2.9.3 Solving an Equation with Two Radicals

- 2.9.4 Solving an Equation with Rational Exponents

- 2.10 Variation
- 2.10.1 An Introduction to Variation

- 2.10.2 Direct Proportion

- 2.10.3 Inverse Proportion

- 2.11 Solving Inequalities
- 2.11.1 An Introduction to Solving Inequalities

- 2.11.2 Solving Compound Inequalities

- 2.11.3 More on Compound Inequalities

- 2.11.4 Solving Word Problems Involving Inequalities

- 2.12 Inequalities: Quadratics
- 2.12.1 Solving Quadratic Inequalities

- 2.12.2 Solving Quadratic Inequalities: Another Example

- 2.13 Inequalities: Rationals and Radicals
- 2.13.1 Solving Rational Inequalities

- 2.13.2 Solving Rational Inequalities: Another Example

- 2.13.3 Determining the Domains of Expressions with Radicals

- 2.14 Absolute Value
- 2.14.1 Matching Number Lines with Absolute Values

- 2.14.2 Solving Absolute Value Equations

- 2.14.3 Solving Equations with Two Absolute Value Expressions

- 2.14.4 Solving Absolute Value Inequalities

- 2.14.5 Solving Absolute Value Inequalities: More Examples

#### 3. Relations and Functions

- 3.1 Graphing Basics
- 3.1.1 Using the Cartesian System

- 3.1.2 Thinking Visually

- 3.2 Relationships between Two Points
- 3.2.1 Finding the Distance between Two Points

- 3.2.2 Finding the Second Endpoint of a Segment

- 3.3 Relationships among Three Points
- 3.3.1 Collinearity and Distance

- 3.3.2 Triangles

- 3.4 Circles
- 3.4.1 Finding the Center-Radius Form of the Equation of a Circle

- 3.4.2 Decoding the Circle Formula

- 3.4.3 Finding the Center and Radius of a Circle

- 3.4.4 Solving Word Problems Involving Circles

- 3.5 Graphing Equations
- 3.5.1 Graphing Equations by Locating Points

- 3.5.2 Finding the x- and y-Intercepts of an Equation

- 3.6 Function Basics
- 3.6.1 Functions and the Vertical Line Test

- 3.6.2 Identifying Functions

- 3.6.3 Function Notation and Finding Function Values

- 3.7 Working with Functions
- 3.7.1 Determining Intervals Over Which a Function Is Increasing

- 3.7.2 Evaluating Piecewise-Defined Functions for Given Values

- 3.7.3 Solving Word Problems Involving Functions

- 3.8 Function Domain and Range
- 3.8.1 Finding the Domain and Range of a Function

- 3.8.2 Domain and Range: One Explicit Example

- 3.8.3 Satisfying the Domain of a Function

- 3.9 Linear Functions: Slope
- 3.9.1 An Introduction to Slope

- 3.9.2 Finding the Slope of a Line Given Two Points

- 3.9.3 Interpreting Slope from a Graph

- 3.9.4 Graphing a Line Using Point and Slope

- 3.10 Equations of a Line
- 3.10.1 Writing an Equation in Slope-Intercept Form

- 3.10.2 Writing an Equation Given Two Points

- 3.10.3 Writing an Equation in Point-Slope Form

- 3.10.4 Matching a Slope-Intercept Equation with Its Graph

- 3.10.5 Slope for Parallel and Perpendicular Lines

- 3.11 Linear Functions: Applications
- 3.11.1 Constructing Linear Function Models of Data

- 3.11.2 Linear Cost and Revenue Functions

- 3.12 Graphing Functions
- 3.12.1 Graphing Some Important Functions

- 3.12.2 Graphing Piecewise-Defined Functions

- 3.12.3 Matching Equations with Their Graphs

- 3.13 The Greatest Integer Function
- 3.13.1 The Greatest Integer Function

- 3.13.2 Graphing the Greatest Integer Function

- 3.14 Quadratic Functions: Basics
- 3.14.1 Deconstructing the Graph of a Quadratic Function

- 3.14.2 Nice-Looking Parabolas

- 3.14.3 Using Discriminants to Graph Parabolas

- 3.14.4 Maximum Height in the Real World

- 3.15 Quadratic Functions: The Vertex
- 3.15.1 Finding the Vertex by Completing the Square

- 3.15.2 Using the Vertex to Write the Quadratic Equation

- 3.15.3 Finding the Maximum or Minimum of a Quadratic

- 3.15.4 Graphing Parabolas

- 3.16 Manipulating Graphs: Shifts and Stretches
- 3.16.1 Shifting Curves along Axes

- 3.16.2 Shifting or Translating Curves along Axes

- 3.16.3 Stretching a Graph

- 3.16.4 Graphing Quadratics Using Patterns

- 3.17 Manipulating Graphs: Symmetry and Reflections
- 3.17.1 Determining Symmetry

- 3.17.2 Reflections

- 3.17.3 Reflecting Specific Functions

- 3.18 Composite Functions
- 3.18.1 Using Operations on Functions

- 3.18.2 Composite Functions

- 3.18.3 Components of Composite Functions

- 3.18.4 Finding Functions That Form a Given Composite

- 3.18.5 Finding the Difference Quotient of a Function

- 3.18.6 Calculating the Average Rate of Change

#### 4. Polynomial and Rational Functions

- 4.1 Polynomials: Long Division
- 4.1.1 Using Long Division with Polynomials

- 4.1.2 Long Division: Another Example

- 4.2 Polynomials: Synthetic Division
- 4.2.1 Using Synthetic Division with Polynomials

- 4.2.2 More Synthetic Division

- 4.3 The Remainder Theorem
- 4.3.1 The Remainder Theorem

- 4.3.2 More on the Remainder Theorem

- 4.4 The Factor Theorem
- 4.4.1 The Factor Theorem and Its Uses

- 4.4.2 Factoring a Polynomial Given a Zero

- 4.5 The Rational Zero Theorem
- 4.5.1 Presenting the Rational Zero Theorem

- 4.5.2 Considering Possible Solutions

- 4.6 Zeros of Polynomials
- 4.6.1 Finding Polynomials Given Zeros, Degree, and One Point

- 4.6.2 Finding all Zeros and Multiplicities of a Polynomial

- 4.6.3 Finding the Real Zeros for a Polynomial

- 4.6.4 Using Descartes' Rule of Signs

- 4.6.5 Finding the Zeros of a Polynomial from Start to Finish

- 4.6.6 The Fundamental Theorem of Algebra

- 4.6.7 The Conjugate Pair Theorem

- 4.7 Graphing Simple Polynomial Functions
- 4.7.1 Matching Graphs to Polynomial Functions

- 4.7.2 Sketching the Graphs of Basic Polynomial Functions

- 4.7.3 Graphing Polynomial Functions: Another Example

- 4.8 Rational Functions
- 4.8.1 Understanding Rational Functions

- 4.8.2 Basic Rational Functions

- 4.9 Graphing Rational Functions
- 4.9.1 Vertical Asymptotes

- 4.9.2 Horizontal Asymptotes

- 4.9.3 Graphing Rational Functions

- 4.9.4 Graphing Rational Functions: More Examples

- 4.9.5 Oblique Asymptotes

- 4.9.6 Oblique Asymptotes: Another Example

#### 5. Exponential and Logarithmic Functions

- 5.1 Function Inverses
- 5.1.1 Understanding Inverse Functions

- 5.1.2 The Horizontal Line Test

- 5.1.3 Are Two Functions Inverses of Each Other?

- 5.1.4 Graphing the Inverse

- 5.2 Finding Function Inverses
- 5.2.1 Finding the Inverse of a Function

- 5.2.2 Finding the Inverse of a Function with Higher Powers

- 5.3 Exponential Functions
- 5.3.1 An Introduction to Exponential Functions

- 5.3.2 Graphing Exponential Functions: Useful Patterns

- 5.3.3 Graphing Exponential Functions: More Examples

- 5.4 Applying Exponential Functions
- 5.4.1 Using Properties of Exponents to Solve Exponential Equations

- 5.4.2 Finding Present Value and Future Value

- 5.4.3 Finding an Interest Rate to Match Given Goals

- 5.5 The Number e
- 5.5.1 e

- 5.5.2 Applying Exponential Functions

- 5.6 Logarithmic Functions
- 5.6.1 An Introduction to Logarithmic Functions

- 5.6.2 Converting between Exponential and Logarithmic Functions

- 5.7 Solving Logarithmic Functions
- 5.7.1 Finding the Value of a Logarithmic Function

- 5.7.2 Solving for x in Logarithmic Equations

- 5.7.3 Graphing Logarithmic Functions

- 5.7.4 Matching Logarithmic Functions with Their Graphs

- 5.8 Properties of Logarithms
- 5.8.1 Properties of Logarithms

- 5.8.2 Expanding a Logarithmic Expression Using Properties

- 5.8.3 Combining Logarithmic Expressions

- 5.9 Evaluating Logarithms
- 5.9.1 Evaluating Logarithmic Functions Using a Calculator

- 5.9.2 Using the Change of Base Formula

- 5.10 Applying Logarithmic Functions
- 5.10.1 The Richter Scale

- 5.10.2 The Distance Modulus Formula

- 5.11 Solving Exponential and Logarithmic Equations
- 5.11.1 Solving Exponential Equations

- 5.11.2 Solving Logarithmic Equations

- 5.11.3 Solving Equations with Logarithmic Exponents

- 5.12 Applying Exponents and Logarithms
- 5.12.1 Compound Interest

- 5.12.2 Predicting Change

- 5.13 Word Problems Involving Exponential Growth and Decay
- 5.13.1 An Introduction to Exponential Growth and Decay

- 5.13.2 Half-Life

- 5.13.3 Newton's Law of Cooling

- 5.13.4 Continuously Compounded Interest

#### 6. The Trigonometric Functions

- 6.1 Angles and Radian Measure
- 6.1.1 Finding the Quadrant in Which an Angle Lies

- 6.1.2 Finding Coterminal Angles

- 6.1.3 Finding the Complement and Supplement of an Angle

- 6.1.4 Converting between Degrees and Radians

- 6.1.5 Using the Arc Length Formula

- 6.2 Right Angle Trigonometry
- 6.2.1 An Introduction to the Trigonometric Functions

- 6.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle

- 6.2.3 Finding an Angle Given the Value of a Trigonometric Function

- 6.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles

- 6.2.5 Finding the Height of a Building

- 6.3 The Trigonometric Functions
- 6.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane

- 6.3.2 Evaluating Trigonometric Functions Using the Reference Angle

- 6.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions

- 6.3.4 Trigonometric Functions of Important Angles

- 6.4 Graphing Sine and Cosine Functions
- 6.4.1 An Introduction to the Graphs of Sine and Cosine Functions

- 6.4.2 Graphing Sine or Cosine Functions with Different Coefficients

- 6.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine

- 6.4.4 Solving Word Problems Involving Sine or Cosine Functions

- 6.5 Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts
- 6.5.1 Graphing Sine and Cosine Functions with Phase Shifts

- 6.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift

- 6.6 Graphing Other Trigonometric Functions
- 6.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions

- 6.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent

- 6.6.3 Identifying a Trigonometric Function from its Graph

- 6.7 Inverse Trigonometric Functions
- 6.7.1 An Introduction to Inverse Trigonometric Functions

- 6.7.2 Evaluating Inverse Trigonometric Functions

- 6.7.3 Solving an Equation Involving an Inverse Trigonometric Function

- 6.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse

- 6.7.5 Applying Trigonometric Functions: Is He Speeding?

#### 7. Trigonometric Identities

- 7.1 Basic Trigonometric Identities
- 7.1.1 Fundamental Trigonometric Identities

- 7.1.2 Finding All Function Values

- 7.2 Simplifying Trigonometric Expressions
- 7.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities

- 7.2.2 Simplifying Trigonometric Expressions Involving Fractions

- 7.2.3 Simplifying Products of Binomials Involving Trigonometric Functions

- 7.2.4 Factoring Trigonometric Expressions

- 7.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither

- 7.3 Proving Trigonometric Identities
- 7.3.1 Proving an Identity

- 7.3.2 Proving an Identity: Other Examples

- 7.4 Solving Trigonometric Equations
- 7.4.1 Solving Trigonometric Equations

- 7.4.2 Solving Trigonometric Equations by Factoring

- 7.4.3 Solving Trigonometric Equations with Coefficients in the Argument

- 7.4.4 Solving Trigonometric Equations Using the Quadratic Formula

- 7.4.5 Solving Word Problems Involving Trigonometric Equations

- 7.5 The Sum and Difference Identities
- 7.5.1 Identities for Sums and Differences of Angles

- 7.5.2 Using Sum and Difference Identities

- 7.5.3 Using Sum and Difference Identities to Simplify an Expression

- 7.6 Double-Angle Identities
- 7.6.1 Confirming a Double-Angle Identity

- 7.6.2 Using Double-Angle Identities

- 7.6.3 Solving Word Problems Involving Multiple-Angle Identities

- 7.7 Other Advanced Identities
- 7.7.1 Using a Cofunction Identity

- 7.7.2 Using a Power-Reducing Identity

- 7.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation

#### 8. Applications of Trigonometry

- 8.1 The Law of Sines
- 8.1.1 The Law of Sines

- 8.1.2 Solving a Triangle Given Two Sides and One Angle

- 8.1.3 Solving a Triangle (SAS): Another Example

- 8.1.4 The Law of Sines: An Application

- 8.2 The Law of Cosines
- 8.2.1 The Law of Cosines

- 8.2.2 The Law of Cosines (SSS)

- 8.2.3 The Law of Cosines (SAS): An Application

- 8.2.4 Heron's Formula

- 8.3 Vector Basics
- 8.3.1 An Introduction to Vectors

- 8.3.2 Finding the Magnitude and Direction of a Vector

- 8.3.3 Vector Addition and Scalar Multiplication

- 8.4 Components of Vectors and Unit Vectors
- 8.4.1 Finding the Components of a Vector

- 8.4.2 Finding a Unit Vector

- 8.4.3 Solving Word Problems Involving Velocity or Forces

- 8.5 Complex Numbers in Trigonometric Form
- 8.5.1 Graphing a Complex Number and Finding Its Absolute Value

- 8.5.2 Expressing a Complex Number in Trigonometric or Polar Form

- 8.5.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

- 8.6 Powers and Roots of Complex Numbers
- 8.6.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power

- 8.6.2 Roots of Complex Numbers

- 8.6.3 More Roots of Complex Numbers

- 8.6.4 Roots of Unity

- 8.7 Polar Coordinates
- 8.7.1 An Introduction to Polar Coordinates

- 8.7.2 Converting between Polar and Rectangular Coordinates

- 8.7.3 Converting between Polar and Rectangular Equations

- 8.7.4 Graphing Simple Polar Equations

- 8.7.5 Graphing Special Polar Equations

#### 9. Systems of Equations and Matrices

- 9.1 Linear Systems of Equations
- 9.1.1 An Introduction to Linear Systems

- 9.1.2 Solving a System by Substitution

- 9.1.3 Solving a System by Elimination

- 9.2 Linear Systems of Equations in Three Variables
- 9.2.1 An Introduction to Linear Systems in Three Variables

- 9.2.2 Solving Linear Systems in Three Variables

- 9.2.3 Solving Inconsistent Systems

- 9.2.4 Solving Dependent Systems

- 9.2.5 Solving Systems with Two Equations

- 9.3 Applying Linear Systems
- 9.3.1 Investments

- 9.3.2 Solving with Partial Fractions

- 9.3.3 Partial Fractions: Another Example

- 9.4 Nonlinear Systems
- 9.4.1 Solving Nonlinear Systems Using Elimination

- 9.4.2 Solving Nonlinear Systems by Substitution

- 9.5 Matrices
- 9.5.1 An Introduction to Matrices

- 9.5.2 The Arithmetic of Matrices

- 9.5.3 Multiplying Matrices by a Scalar

- 9.5.4 Multiplying Matrices

- 9.6 Solving Systems Using the Gauss-Jordan Method
- 9.6.1 Using the Gauss-Jordan Method

- 9.6.2 Using Gauss-Jordan: Another Example

- 9.6.3 Using the Gauss-Jordan Method with Three Equations

- 9.6.4 Gaussian Elimination with Three Equations

- 9.7 Evaluating Determinants
- 9.7.1 Evaluating 2x2 Determinants

- 9.7.2 Evaluating
*n*x*n*Determinants

- 9.7.3 Evaluating a Determinant Using Elementary Row Operations

- 9.7.4 Finding a Determinant using Expanding by Cofactors

- 9.7.5 Applying Determinants

- 9.8 Cramer's Rule
- 9.8.1 Using Cramer's Rule

- 9.8.2 Using Cramer's Rule in a 3x3 Matrix

- 9.9 Inverses and Matrices
- 9.9.1 An Introduction to Inverses

- 9.9.2 Inverses: 2x2 Matrices

- 9.9.3 Another Look at 2x2 Inverses

- 9.9.4 Inverses: 3x3 Matrices

- 9.9.5 Solving a System of Equations with Inverses

- 9.10 Working with Inequalities
- 9.10.1 An Introduction to Graphing Linear Inequalities

- 9.10.2 Graphing Linear and Nonlinear Inequalities

- 9.10.3 Graphing the Solution Set of a System of Inequalities

- 9.11 Linear Programming
- 9.11.1 Solving for Maxima-Minima

- 9.11.2 Applying Linear Programming

#### 10. Special Topics

- 10.1 Conic Sections: Parabolas
- 10.1.1 An Introduction to Conic Sections

- 10.1.2 An Introduction to Parabolas

- 10.1.3 Determining Information about a Parabola from Its Equation

- 10.1.4 Writing an Equation for a Parabola

- 10.2 Conic Sections: Ellipses
- 10.2.1 An Introduction to Ellipses

- 10.2.2 Finding the Equation for an Ellipse

- 10.2.3 Applying Ellipses: Satellites

- 10.2.4 The Eccentricity of an Ellipse

- 10.3 Conic Sections: Hyperbolas
- 10.3.1 An Introduction to Hyperbolas

- 10.3.2 Finding the Equation for a Hyperbola

- 10.3.3 Applying Hyperbolas: Navigation

- 10.4 Conic Sections
- 10.4.1 Identifying a Conic

- 10.4.2 Name That Conic

- 10.4.3 Rotation of Axes

- 10.4.4 Rotating Conics

- 10.5 The Binomial Theorem
- 10.5.1 Using the Binomial Theorem

- 10.5.2 Binomial Coefficients

- 10.5.3 Finding a Term of a Binomial Expansion

- 10.6 Sequences
- 10.6.1 General and Specific Terms

- 10.6.2 Understanding Sequence Problems

- 10.6.3 Series Notation, Definitions and Evaluating

- 10.6.4 Solving Problems Involving Arithmetic Sequences

- 10.6.5 Finding the Sum of an Arithmetic Sequence

- 10.6.6 Solving Problems Involving Geometric Sequences

- 10.6.7 Finding the Sum of a Geometric Sequence

- 10.7 Induction
- 10.7.1 Proving Formulas Using Mathematical Induction

- 10.7.2 Examples of Induction

- 10.8 Combinations and Probability
- 10.8.1 Solving Problems Involving Permutations

- 10.8.2 Solving Problems Involving Combinations

- 10.8.3 Independent Events

- 10.8.4 Inclusive and Exclusive Events