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E-raamat: Pre-Calculus For Dummies: 1,001 Practice Problems

4.64/5 (20 hinnangut Goodreads-ist)

Mary Jane Sterling (Bradley University, Peoria, IL)

Formaat: PDF+DRM
Ilmumisaeg: 09-Sep-2014
Kirjastus: For Dummies
Keel: eng
ISBN-13: 9781118852811

Teised raamatud teemal:

Pre-calculus

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Formaat: PDF+DRM
Ilmumisaeg: 09-Sep-2014
Kirjastus: For Dummies
Keel: eng
ISBN-13: 9781118852811

Teised raamatud teemal:

Pre-calculus

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Moving from easy to increasingly difficult, a pre-calculus study guide helps students practice their math skills and gain confidence by completing more than 1,000 problems with multiple-choice answers and step-by-step solution walkthroughs. Include free one-year access to an online question bank. Original.

Provides over one thousand practice problems reviewing topics covered in a pre-calculus course, including algebra basics, graphing and transforming functions, polynomials, trigonometry basics, and conic sections, with detailed answer explanations.

Prepare for calculus the smart way, with customizable pre-calculus practice

1,001 Pre-Calculus Practice Problems For Dummies offers 1,001 opportunities to gain confidence in your math skills. Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, or computer, the online component works in conjunction with the book to polish your skills and confidence in preparation for calculus.

Calculus-level math proficiency is required for college STEM majors. Pre-calculus introduces you to the concepts you'll learn in calculus, and provides you with a solid foundation of methods and skills that are essential to calculus success. 1,001 Pre-Calculus Practice Problems For Dummies gives you the practice you need to master the skills and conquer pre-calculus. Companion website includes:

All 1,001 practice problems in multiple choice format
Customizable practice sets for self-directed study
Problems ranked as easy, medium, and hard
Free one-year access to the online question bank

Math is notorious for giving students trouble, and calculus is the #1 offender. Fear not! Pre-calculus is the perfect calculus prep, and 1,001 Pre-Calculus Practice Problems For Dummies gives you 1,001 opportunities to get it right.

Introduction

(6)

What You'll Find

(1)

How This Workbook Is Organized

(1)

Part I The Questions

(1)

Part II The Answers

(1)

Beyond the Book

(1)

What you'll find online

(1)

How to register

(1)

Where to Go for Additional Help

(3)

Part I The Questions

(118)

Chapter 1 Getting Started with Algebra Basics

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Identifying Which System or Systems a Number Belongs To

(1)

Recognizing Properties of Number Systems

(1)

Simplifying Expressions with the Order of Operations

(1)

Graphing Inequalities

(1)

Using Graphing Formulas

(1)

Applying Graphing Formulas

(2)

Chapter 2 Solving Some Equations and Inequalities

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Interval and Inequality Notation

(1)

Solving Linear Inequalities

(1)

Solving Quadratic Inequalities

(1)

Solving Absolute Value Inequalities

(1)

Working with Radicals and Fractional Notation

(1)

Performing Operations Using Fractional Exponents

(1)

Factoring Using Fractional Notation

(1)

Solving Radical Equations

(1)

Rationalizing Denominators

(1)

Chapter 3 Function Basics

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Function Notation to Evaluate Function Values

(1)

Determining the Domain and Range of a Function

(1)

Recognizing Even Functions

(1)

Identifying Odd Functions

(1)

Ruling Out Even and Odd Functions

(1)

Recognizing One-to-One Functions from Given Relations

(2)

Identifying One-to-One Functions from Equations

(1)

Recognizing a Function's Inverse

(1)

Determining a Function's Inverse

(1)

Executing Operations on Functions

(1)

Performing Function Composition

(1)

Doing More Function Composition

(1)

Using the Difference Quotient

(1)

Chapter 4 Graphing and Transforming Functions

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Functions and Their Inverses

(1)

Sketching Quadratic Functions from Their Equations

(1)

Writing Equations from Graphs of Parabolas

(1)

Investigating and Graphing Radical Functions

(1)

Investigating Absolute Value Functions

(1)

Investigating the Graphs of Polynomial Functions

(1)

Investigating Rational Functions

(1)

Transformation of Functions

(1)

Transforming Selected Points Using Functions

(1)

Sketching Graphs Using Basic Functions and Transformations

(1)

Sketching More Graphs Using Basic Functions and Transformations

(2)

Chapter 5 Polynomials

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Factoring to Solve Quadratic Equations

(1)

Solving Quadratic Equations by Using the Quadratic Formula

(1)

Using Completing the Square to Solve Quadratic Equations

(1)

Solving Polynomial Equations for Intercepts

(1)

Using Factoring by Grouping to Solve Polynomial Equations

(1)

Applying Descartes's Rule of Signs

(1)

Listing Possible Roots of a Polynomial Equation

(1)

Dividing Polynomials

(1)

Using Synthetic Division to Divide Polynomials

(1)

Checking for Roots of a Polynomial by Using Synthetic Division

(1)

Writing Polynomial Expressions from Given Roots

(1)

Writing Polynomial Expressions When Given Roots and a Point

(1)

Graphing Polynomials

(1)

Writing Equations from Graphs of Polynomials

(2)

Chapter 6 Exponential and Logarithmic Functions

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Understanding Function Notation

(1)

Graphing Exponential Functions

(1)

Solving Exponential Equations

(1)

Using the Equivalence bx = y ⇔ logb y = x to Rewrite Expressions

(1)

Using the Equivalence logb y = x ⇔ bx = y to Rewrite Expressions

(1)

Rewriting Logarithmic Expressions

(1)

Rewriting Logs of Products and Quotients as Sums and Differences

(1)

Solving Logarithmic Equations

(1)

Applying Function Transformations to Log Functions

(1)

Applying Logarithms to Everyday Life

(2)

Chapter 7 Trigonometry Basics

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Right Triangles to Determine Trig Functions

(1)

Solving Problems by Using Right Triangles and Their Functions

(1)

Working with Special Right Triangles

(1)

Changing Radians to Degrees

(1)

Changing Degrees to Radians

(1)

Finding Angle Measures (in Degrees) in Standard Position

(1)

Determining Angle Measures (in Radians) in Standard Position

(1)

Identifying Reference Angles

(1)

Determining Trig Functions by Using the Unit Circle

(1)

Calculating Trig Functions by Using Other Functions and Terminal Side Positions

(1)

Using the Arc Length Formula

(1)

Evaluating Inverse Functions

(1)

Solving Trig Equations for x in Degrees

(1)

Calculating Trig Equations for x in Radians

(1)

Chapter 8 Graphing Trig Functions

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Recognizing Basic Trig Graphs

(2)

Graphing Sine and Cosine

(1)

Applying Function Transformations to Graphs of Trig Functions

(1)

Writing New Trig Functions Using Transformations

(1)

Graphing Tangent and Cotangent

(1)

Interpreting Transformations of Trig Functions

(1)

Graphing Secant and Cosecant

(1)

Interpreting Transformations from Function Rules

(1)

Chapter 9 Getting Started with Trig Identities

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Proving Basic Trig Identities

(1)

Returning to Basic Sine and Cosine to Solve Identities

(1)

Using Multiplication by a Conjugate to Solve Identities

(1)

Solving Identities After Raising a Binomial to a Power

(1)

Solving Identities After Factoring out a Common Function

(1)

Solving Identities After Combining Fractions

(1)

Performing Algebraic Processes to Make Identities More Solvable

(2)

Chapter 10 Continuing with Trig Identities

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Using Identities That Add or Subtract Angle Measures

(1)

Confirming Double-Angle Identities

(1)

Using Identities That Double the Size of the Angle

(1)

Confirming the Statements of Multiple-Angle Identities

(1)

Creating Half-Angle Identities from Double-Angle Identities

(1)

Creating a Half-Angle Identity for Tangent

(1)

Using Half-Angle Identities to Simplify Expressions

(1)

Creating Products of Trig Functions from Sums and Differences

(1)

Using Product-to-Sum Identities to Evaluate Expressions

(1)

Using Sum-to-Product Identities to Evaluate Expressions

(1)

Applying Power-Reducing Identities

(1)

Using Identities to Determine Values of Functions at Various Angles

(1)

Working through Identities Using Multiple Methods

(2)

Chapter 11 Working with Triangles and Trigonometry

(10)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Applying the Law of Sines to Find Sides

(1)

Utilizing the Law of Sines to Find Angles

(1)

Using the Law of Sines for Practical Applications

(1)

Investigating the Ambiguous Case of the Law of Sines

(1)

Determining All Angles and Sides of a Triangle

(1)

Finding Side Measures by Using the Law of Cosines

(1)

Using the Law of Cosines to Determine an Angle

(1)

Applying the Law of Cosines to Real-World Situations

(1)

Finding Areas of Triangles by Using the Sine

(1)

Applying the Trig Formula for Area of a Triangle

(1)

Using the Trig Formula for Area in Various Situations

(1)

Solving Area Problems Needing Additional Computations

(1)

Finding Areas of Triangles by Using Heron's Formula

(1)

Applying Heron's Formula

(1)

Practical Applications Using Heron's Formula

(1)

Tackling Practical Applications by Using Triangular Formulas

(2)

Chapter 12 Complex Numbers and Polar Coordinates

(8)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Writing Powers of i in Their Simplest Form

(1)

Adding and Subtracting Complex Numbers

(1)

Multiplying Complex Numbers

(1)

Using Multiplication to Divide Complex Numbers

(1)

Solving Quadratic Equations with Complex Solutions

(1)

Graphing Complex Numbers

(2)

Identifying Points with Polar Coordinates

(1)

Identifying Points Whose Angles Have Negative Measures

(1)

Converting Polar to Rectangular Coordinates

(1)

Converting Rectangular to Polar Coordinates

(1)

Recognizing Polar Curves

(1)

Chapter 13 Conic Sections

(6)

The Problems You'll Work On

(1)

What to Watch Out For

(1)

Identifying Conics from Their Equations

(1)

Rewriting Conic Equations in Standard Form

(1)

Writing Equations for Circles

(1)

Determining Foci and Axes of Symmetry of Parabolas

(1)

Finding the Vertices and Directrixes of Parabolas

(1)

Writing Equations of Parabolas

100

(1)

Determining Centers and Foci of Ellipses

100

(1)

Writing Equations of Ellipses

100

(1)

Determining Asymptotes of Hyperbolas

101

(1)

Writing Equations of Hyperbolas

101

(1)

Changing Equation Format from Trig Functions to Algebraic

101

(1)

Changing Equation Format from Algebraic to Trig

102

(1)

Chapter 14 Systems of Equations and Inequalities

103

(8)

The Problems You'll Work On

103

(1)

What to Watch Out For

104

(1)

Using Substitution to Solve Systems of Linear Equations with Two Variables

104

(1)

Using Elimination to Solve Systems of Linear Equations with Two Variables

104

(1)

Solving Systems of Equations Involving Nonlinear Functions

105

(1)

Solving Systems of Linear Equations

105

(1)

Solving Systems of Linear Equations with Four Variables

106

(1)

Graphing Systems of Inequalities

106

(1)

Decomposition of Fractions

107

(1)

Operating on Matrices

107

(1)

Changing Matrices to the Echelon Form

108

(1)

Solving Systems of Equations Using Augmented Matrices

108

(1)

Solving Systems of Equations Using the Inverse of the Coefficient Matrix

109

(1)

Applying Cramer's Rule to Solve Systems of Equations

110

(1)

Chapter 15 Sequences and Series

111

(6)

The Problems You'll Work On

111

(1)

What to Watch Out For

111

(1)

Finding Terms of Sequences

112

(1)

Determining Rules for Sequences

112

(1)

Working with Recursively Defined Sequences

112

(1)

Adding Terms in an Arithmetic Series

113

(1)

Summing Terms of a Series

113

(1)

Finding Rules and Summing Terms of a Series

113

(1)

Calculating the Sum of a Geometric Series

114

(1)

Determining Formulas and Finding Sums

114

(1)

Counting Items by Using Combinations

114

(1)

Constructing Pascal's Triangle

115

(1)

Applying Pascal's Triangle

115

(1)

Utilizing the Binomial Theorem

115

(2)

Chapter 16 Introducing Limits and Continuity

117

(8)

The Problems You'll Work On

117

(1)

What to Watch Out For

117

(1)

Determining Limits from Graphs

118

(1)

Determining One-Sided Limits

119

(1)

Determining Limits from Function Values

120

(1)

Determining Limits from Function Rules

121

(1)

Applying Laws of Limits

122

(1)

Investigating Continuity

123

(2)

Part II The Answers

125

(402)

Chapter 17 Answers

127

(400)

Index

527

Mary Jane Sterling is the author of several books, including Algebra I For Dummies, Algebra II For Dummies, Trigonometry For Dummies, and Linear Algebra For Dummies. She taught at Bradley University in Peoria, Illinois, for more than 35 years.

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