Pre-Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice) (For Dummies

Title Page
Copyright Page
Table of Contents
Introduction
	What You’ll Find
	How This Workbook Is Organized
		Part I: The Questions
		Part II: The Answers
	Beyond the Book
		What you’ll find online
		How to register
	Where to Go for Additional Help
Part I: The Questions
	Chapter 1: Getting Started with Algebra Basics
		The Problems You’ll Work On
		What to Watch Out For
		Identifying Which System or Systems a Number Belongs To
		Recognizing Properties of Number Systems
		Simplifying Expressions with the Order of Operations
		Graphing Inequalities
		Using Graphing Formulas
		Applying Graphing Formulas
	Chapter 2: Solving Some Equations and Inequalities
		The Problems You’ll Work On
		What to Watch Out For
		Using Interval and Inequality Notation
		Solving Linear Inequalities
		Solving Quadratic Inequalities
		Solving Absolute Value Inequalities
		Working with Radicals and Fractional Notation
		Performing Operations Using Fractional Exponents
		Factoring Using Fractional Notation
		Solving Radical Equations
		Rationalizing Denominators
	Chapter 3: Function Basics
		The Problems You’ll Work On
		What to Watch Out For
		Using Function Notation to Evaluate Function Values
		Determining the Domain and Range of a Function
		Recognizing Even Functions
		Identifying Odd Functions
		Ruling Out Even and Odd Functions
		Recognizing One-to-One Functions from Given Relations
		Identifying One-to-One Functions from Equations
		Recognizing a Function’s Inverse
		Determining a Function’s Inverse
		Executing Operations on Functions
		Performing Function Composition
		Doing More Function Composition
		Using the Difference Quotient
	Chapter 4: Graphing and Transforming Functions
		The Problems You’ll Work On
		What to Watch Out For
		Functions and Their Inverses
		Sketching Quadratic Functions from Their Equations
		Writing Equations from Graphs of Parabolas
		Investigating and Graphing Radical Functions
		Investigating Absolute Value Functions
		Investigating the Graphs of Polynomial Functions
		Investigating Rational Functions
		Transformation of Functions
		Transforming Selected Points Using Functions
		Sketching Graphs Using Basic Functions and Transformations
		Sketching More Graphs Using Basic Functions and Transformations
	Chapter 5: Polynomials
		The Problems You’ll Work On
		What to Watch Out For
		Using Factoring to Solve Quadratic Equations
		Solving Quadratic Equations by Using the Quadratic Formula
		Using Completing the Square to Solve Quadratic Equations
		Solving Polynomial Equations for Intercepts
		Using Factoring by Grouping to Solve Polynomial Equations
		Applying Descartes’s Rule of Signs
		Listing Possible Roots of a Polynomial Equation
		Dividing Polynomials
		Using Synthetic Division to Divide Polynomials
		Checking for Roots of a Polynomial by Using Synthetic Division
		Writing Polynomial Expressions from Given Roots
		Writing Polynomial Expressions When Given Roots and a Point
		Graphing Polynomials
		Writing Equations from Graphs of Polynomials
	Chapter 6: Exponential and Logarithmic Functions
		The Problems You’ll Work On
		What to Watch Out For
		Understanding Function Notation
		Graphing Exponential Functions
		Solving Exponential Equations
		Using the Equivalence bx = y ⇔ logb y = x to Rewrite Expressions
		Using the Equivalence logb y = x ⇔ bx = y to Rewrite Expressions
		Rewriting Logarithmic Expressions
		Rewriting Logs of Products and Quotients as Sums and Differences
		Solving Logarithmic Equations
		Applying Function Transformations to Log Functions
		Applying Logarithms to Everyday Life
	Chapter 7: Trigonometry Basics
		The Problems You’ll Work On
		What to Watch Out For
		Using Right Triangles to Determine Trig Functions
		Solving Problems by Using Right Triangles and Their Functions
		Working with Special Right Triangles
		Changing Radians to Degrees
		Changing Degrees to Radians
		Finding Angle Measures (in Degrees) in Standard Position
		Determining Angle Measures (in Radians) in Standard Position
		Identifying Reference Angles
		Determining Trig Functions by Using the Unit Circle
		Calculating Trig Functions by Using Other Functions and Terminal Side Positions
		Using the Arc Length Formula
		Evaluating Inverse Functions
		Solving Trig Equations for x in Degrees
		Calculating Trig Equations for x in Radians
	Chapter 8: Graphing Trig Functions
		The Problems You’ll Work On
		What to Watch Out For
		Recognizing Basic Trig Graphs
		Graphing Sine and Cosine
		Applying Function Transformations to Graphs of Trig Functions
		Writing New Trig Functions Using Transformations
		Graphing Tangent and Cotangent
		Interpreting Transformations of Trig Functions
		Graphing Secant and Cosecant
		Interpreting Transformations from Function Rules
	Chapter 9: Get ting Star ted with Trig Identities
		The Problems You’ll Work On
		What to Watch Out For
		Proving Basic Trig Identities
		Returning to Basic Sine and Cosine to Solve Identities
		Using Multiplication by a Conjugate to Solve Identities
		Solving Identities After Raising a Binomial to a Power
		Solving Identities After Factoring out a Common Function
		Solving Identities After Combining Fractions
		Performing Algebraic Processes to Make Identities More Solvable
	Chapter 10: Continuing with Trig Identities
		The Problems You’ll Work On
		What to Watch Out For
		Using Identities That Add or Subtract Angle Measures
		Confirming Double-Angle Identities
		Using Identities That Double the Size of the Angle
		Confirming the Statements of Multiple-Angle Identities
		Creating Half-Angle Identities from Double-Angle Identities
		Creating a Half-Angle Identity for Tangent
		Using Half-Angle Identities to Simplify Expressions
		Creating Products of Trig Functions from Sums and Differences
		Using Product-to-Sum Identities to Evaluate Expressions
		Using Sum-to-Product Identities to Evaluate Expressions
		Applying Power-Reducing Identities
		Using Identities to Determine Values of Functions at Various Angles
		Working through Identities Using Multiple Methods
	Chapter 11: Working with Triangles and Trigonometry
		The Problems You’ll Work On
		What to Watch Out For
		Applying the Law of Sines to Find Sides
		Utilizing the Law of Sines to Find Angles
		Using the Law of Sines for Practical Applications
		Investigating the Ambiguous Case of the Law of Sines
		Determining All Angles and Sides of a Triangle
		Finding Side Measures by Using the Law of Cosines
		Using the Law of Cosines to Determine an Angle
		Applying the Law of Cosines to Real-World Situations
		Finding Areas of Triangles by Using the Sine
		Applying the Trig Formula for Area of a Triangle
		Using the Trig Formula for Area in Various Situations
		Solving Area Problems Needing Additional Computations
		Finding Areas of Triangles by Using Heron’s Formula
		Applying Heron’s Formula
		Practical Applications Using Heron’s Formula
		Tackling Practical Applications by Using Triangular Formulas
	Chapter 12: Complex Numbers and Polar Coordinates
		The Problems You’ll Work On
		What to Watch Out For
		Writing Powers of i in Their Simplest Form
		Adding and Subtracting Complex Numbers
		Multiplying Complex Numbers
		Using Multiplication to Divide Complex Numbers
		Solving Quadratic Equations with Complex Solutions
		Graphing Complex Numbers
		Identifying Points with Polar Coordinates
		Identifying Points Whose Angles Have Negative Measures
		Converting Polar to Rectangular Coordinates
		Converting Rectangular to Polar Coordinates
		Recognizing Polar Curves
	Chapter 13: Conic Sections
		The Problems You’ll Work On
		What to Watch Out For
		Identifying Conics from Their Equations
		Rewriting Conic Equations in Standard Form
		Writing Equations for Circles
		Determining Foci and Axes of Symmetry of Parabolas
		Finding the Vertices and Directrixes of Parabolas
		Writing Equations of Parabolas
		Determining Centers and Foci of Ellipses
		Writing Equations of Ellipses
		Determining Asymptotes of Hyperbolas
		Writing Equations of Hyperbolas
		Changing Equation Format from Trig Functions to Algebraic
		Changing Equation Format from Algebraic to Trig
	Chapter 14: Systems of Equations and Inequalities
		The Problems You’ll Work On
		What to Watch Out For
		Using Substitution to Solve Systems of Linear Equations with Two Variables
		Using Elimination to Solve Systems of Linear Equations with Two Variables
		Solving Systems of Equations Involving Nonlinear Functions
		Solving Systems of Linear Equations
		Solving Systems of Linear Equations with Four Variables
		Graphing Systems of Inequalities
		Decomposition of Fractions
		Operating on Matrices
		Changing Matrices to the Echelon Form
		Solving Systems of Equations Using Augmented Matrices
		Solving Systems of Equations Using the Inverse of the Coeffi cient Matrix
		Applying Cramer’s Rule to Solve Systems of Equations
	Chapter 15: Sequences and Series
		The Problems You’ll Work On
		What to Watch Out For
		Finding Terms of Sequences
		Determining Rules for Sequences
		Working with Recursively Defi ned Sequences
		Adding Terms in an Arithmetic Series
		Summing Terms of a Series
		Finding Rules and Summing Terms of a Series
		Calculating the Sum of a Geometric Series
		Determining Formulas and Finding Sums
		Counting Items by Using Combinations
		Constructing Pascal’s Triangle
		Applying Pascal’s Triangle
		Utilizing the Binomial Theorem
	Chapter 16: Introducing Limits and Continuity
		The Problems You’ll Work On
		What to Watch Out For
		Determining Limits from Graphs
		Determining One-Sided Limits
		Determining Limits from Function Values
		Determining Limits from Function Rules
		Applying Laws of Limits
		Investigating Continuity
Part II: The Answers
	Chapter 17: Answers
Index
EULA