Pre-Calculus All-in-One For Dummies: Book + Chapter Quizzes Online

Title Page
Copyright Page
Table of Contents
Introduction
	About This Book
	Foolish Assumptions
	Icons Used in This Book
	Beyond the Book
	Where to Go from Here
Unit 1: Getting Started with Pre-Calculus
	Chapter 1: Preparing for Pre-Calculus
		Recapping Pre-Calculus: An Overview
		Checking in on Number Basics and Processes
			Understanding the multitude of number types: Terms to know
			Looking at the fundamental operations you can perform on numbers
			Knowing the properties of numbers: Truths to remember
		Looking at Visual Statements: When Math Follows Form with Function
			Using basic terms and concepts
			Graphing linear equalities and inequalities
			Gathering information from graphs
		Getting Yourself a Graphing Calculator
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 1 Quiz
		Answers to Chapter 1 Quiz
	Chapter 2: Operating with Real Numbers
		Describing Numbers on the Number Line
		Solving Inequalities
			Recapping inequality how-tos
			Solving equations and inequalities involving absolute value
			Expressing solutions for inequalities with interval notation
		Working with Radicals and Exponents
			Defining and relating radicals and exponents
			Rewriting radicals as exponents (or, creating rational exponents)
			Getting a radical out of a denominator: Rationalizing
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 2 Quiz
		Answers to Chapter 2 Quiz
	Chapter 3: Cementing the Building Blocks of Pre-Calculus Functions
		Identifying Special Function Types and Their Graphs
			Even and odd functions
			One-to-one functions
		Dealing with Parent Functions and Their Graphs
			Linear functions
			Quadratic functions
			Square-root functions
			Absolute-value functions
			Cubic functions
			Cube-root functions
		Setting the Stage for Rational Functions
			Searching for vertical asymptotes and holes
			Searching for horizontal asymptotes
			Seeking out oblique asymptotes
			Locating the x- and y-intercepts
		Putting the Results to Work: Graphing Rational Functions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 3 Quiz
		Answers to Chapter 3 Quiz
	Chapter 4: Operating on Functions
		Transforming the Parent Graphs
			Stretching and flattening
			Graphing translations
			Seeing reflections
			Combining various transformations (a transformation in itself!)
			Transforming functions point by point
		Sharpen Your Scalpel: Operating on Functions
			Adding and subtracting
			Multiplying and dividing
			Breaking down a composition of functions
			Adjusting the domain and range of combined functions (if applicable)
		Turning Inside Out with Inverse Functions
			Graphing an inverse
			Inverting a function to find its inverse
			Verifying an inverse
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 4 Quiz
		Answers to Chapter 4 Quiz
Unit 2: Getting the Grip on Graphing
	Chapter 5: Graphing Polynomial Functions
		Understanding Degrees and Roots
		Factoring a Polynomial Expression
			Always the first step: Looking for a GCF
			Unwrapping the box containing a trinomial
			Recognizing and factoring special polynomials
			Grouping to factor four or more terms
		Finding the Roots of a Factored Equation
		Cracking a Quadratic Equation When It Won’t Factor
			Using the quadratic formula
			Completing the square
		Solving Polynomial Equations with a Degree Higher Than Two
			Counting a polynomial’s total roots
			Tallying the real roots: Descartes’s rule of signs
			Accounting for imaginary roots: The fundamental theorem of algebra
			Guessing and checking the real roots
		Put It in Reverse: Using Solutions to Find Factors
		Graphing Polynomials
			Graphing when all the roots are real numbers
			Graphing when roots are imaginary numbers: Combining all techniques
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 5 Quiz
		Answers to Chapter 5 Quiz
	Chapter 6: Exponential and Logarithmic Functions
		Exploring Exponential Functions
			Searching the ins and outs of exponential functions
			Graphing and transforming exponential functions
		Logarithms: The Inverse of Exponential Functions
			Getting a better handle on logarithms
			Managing the properties and identities of logs
			Changing a log’s base
			Calculating a number when you know its log: Inverse logs
			Graphing logs
		Base Jumping to Simplify and Solve Equations
			Stepping through the process of solving exponential equations
			Solving logarithmic equations
		Growing Exponentially: Word Problems in the Kitchen
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 6 Quiz
		Answers to Chapter 6 Quiz
	Chapter 7: Piece-Wise and Greatest-Integer Functions
		Looking at Functions with More Than One Rule: Piece-Wise Functions
			Graphing piece-wise functions
			Using piece-wise functions in real-world applications
		Grappling with the Greatest-Integer Function
			Observing the greatest-integer function
			Making use of the greatest-integer function
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 7 Quiz
		Answers to Chapter 7 Quiz
Unit 3: The Essentials of Trigonometry
	Chapter 8: Circling In on Angles
		Introducing Radians and Relating to Degrees
		Trig Ratios: Taking Right Triangles a Step Further
			Following the sine
			Looking for a cosine
			Going out on a tangent
			Discovering the flip side: Reciprocal trig functions
			Working in reverse: Inverse trig functions
			Defining ranges of inverse trig functions
		Understanding How Trig Ratios Work on the Coordinate Plane
		Digesting Special Triangle Ratios
			The 45er: Isosceles right triangle
			The 30–60–90 right triangle
		Triangles and the Unit Circle: Working Together for the Common Good
			Placing the major angles correctly
			Retrieving trig-function values on the unit circle
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 8 Quiz
		Answers to Chapter 8 Quiz
	Chapter 9: Homing In on the Friendliest Angles
		Building on the Unit Circle
			Familiarizing yourself with the most common angles
			Finding the reference angle to solve for functions of angles
			Relating reference angles to their parents
			Drawing uncommon angles
		Solving Equations Using Inverse Functions
		Measuring Arcs: When the Circle Is Put in Motion
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 9 Quiz
		Answers to Chapter 9 Quiz
	Chapter 10: Picturing Basic Trig Functions and Reciprocal Functions
		Drafting the Sine and Cosine Parent Graphs
			Sketching sine
			Looking at cosine
		Graphing Tangent and Cotangent Parent Graphs
			Tackling tangent
			Clarifying cotangent
		Putting Secant and Cosecant in Parent Graphs Pictures
			Graphing secant
			Checking out cosecant
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 10 Quiz
		Answers to Chapter 10 Quiz
	Chapter 11: Graphing and Transforming Trig Functions
		Transforming Trig Graphs
			Messing with sine and cosine graphs
			Tweaking tangent and cotangent graphs
			Transforming the graphs of secant and cosecant
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 11 Quiz
		Answers to Chapter 11 Quiz
Unit 4: Identities and Special Triangles
	Chapter 12: Identifying with Trig Identities: The Basics
		Keeping the End in Mind: A Quick Primer on Identities
		Lining Up the Means to the End: Basic Trig Identities
			Reciprocal and ratio identities
			Pythagorean identities
			Even/odd identities
			Co-function identities
			Periodicity identities
		Tackling Difficult Trig Proofs: Some Techniques to Know
			Dealing with demanding denominators
			Going solo on each side
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 12 Quiz
		Answers to Chapter 12 Quiz
	Chapter 13: Advancing with Advanced Identities
		Finding Trig Functions of Sums and Differences
			Searching out the sine of a  b 
			Calculating the cosine of a  b 
			Taming the tangent of a  b 
		Doubling an Angle and Finding Its Trig Value
			Finding the sine of a doubled angle
			Calculating cosines for two
			Squaring your cares away
			Having twice the fun with tangents
		Taking Trig Functions of Common Angles Divided in Two
		A Glimpse of Calculus: Traveling from Products to Sums and Back
			Expressing products as sums (or differences)
			Transporting from sums (or differences) to products
		Eliminating Exponents with Power-Reducing Formulas
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 13 Quiz
		Answers to Chapter 13 Quiz
	Chapter 14: Getting the Slant on Oblique Triangles
		Solving a Triangle with the Law of Sines
			When you know two angle measures
			When you know two consecutive side lengths
		Conquering a Triangle with the Law of Cosines
			SSS: Finding angles using only sides
			SAS: Tagging the angle in the middle (and the two sides)
		Filling in the Triangle by Calculating Area
			Finding area with two sides and an included angle (for SAS scenarios)
			Using Heron’s Formula (for SSS scenarios)
		Making Triangles Work for You
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 14 Quiz
		Answers to Chapter 14 Quiz
Unit 5: Analytic Geometry
	Chapter 15: Coordinating with Complex Numbers
		Understanding Real versus Imaginary
		Combining Real and Imaginary: The Complex Number System
			Simplifying expressions when complex numbers are created
			Performing operations with complex numbers
		Graphing Complex Numbers
		Grasping the usefulness of complex numbers
			Solving quadratic equations with complex answers
			Analyzing the graphs of quadratics
			Keeping pace with polynomials
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 15 Quiz
		Answers to Chapter 15 Quiz
	Chapter 16: Warming Up to Polar Coordinates
		Plotting around a Pole: Polar Coordinates
			Wrapping your brain around the polar coordinate plane
			Graphing polar coordinates with negative values
			Changing to and from polar coordinates
		Picturing polar equations
			Circling around with two circles
			Spiraling and planting roses
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 16 Quiz
		Answers to Chapter 16 Quiz
	Chapter 17: Relating Conics to Sliced Cones
		Cone to Cone: Identifying the Four Conic Sections
			Picturing the conics — graph form
			Writing conic equations — printed form
		Going Round and Round: Graphing Circles
			Graphing circles at the origin
			Graphing circles away from the origin
			Writing in center–radius form
		Riding the Ups and Downs with Parabolas
			Labeling the parts
			Understanding the characteristics of a standard parabola
			Plotting the variations: Parabolas all over the plane
			The vertex, axis of symmetry, focus, and directrix
			Identifying the extremes of vertical parabolas
		The Fat and the Skinny on the Ellipse
			Labeling ellipses and expressing them with algebra
			Identifying the parts from the equation
		Join Two Curves and Get a Hyperbola
			Visualizing the two types of hyperbolas and their bits and pieces
			Finding the equations of asymptotes
		Expressing Conics Outside the Realm of Cartesian Coordinates
			Graphing conic sections in parametric form
			The equations of conic sections on the polar coordinate plane
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 17 Quiz
		Answers to Chapter 17 Quiz
Unit 6: Systems, Sequences, and Series
	Chapter 18: Streamlining Systems of Equations
		A Primer on Your System-Solving Options
		Graphing Equations to Find Solutions
			Common solutions of linear equations
			Common solutions of a linear and a quadratic equation
			Common solutions of two polynomials
		Algebraic Solutions of Two-Equation Systems
			Solving linear systems
			Working nonlinear systems
		Solving Systems with More Than Two Equations
		Decomposing Partial Fractions
		Surveying Systems of Inequalities
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 18 Quiz
		Answers to Chapter 18 Quiz
	Chapter 19: Making Matrices Work
		Introducing Matrices: The Basics
			Applying basic operations to matrices
			Multiplying matrices by each other
		Simplifying Matrices to Ease the Solving Process
			Writing a system in matrix form
			Reduced row-echelon form
			Augmented form
		Making Matrices Work for You
			Using Gaussian elimination to solve systems
			Multiplying a matrix by its inverse
			Using determinants: Cramer’s Rule
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 19 Quiz
		Answers to Chapter 19 Quiz
	Chapter 20: Sequences and Series
		Speaking Sequentially: Grasping the General Method
			Determining a sequence’s terms
			Working in reverse: Forming an expression from terms
			Recognizing recursive formulas: A type of general sequence
		Finding the Difference between Terms: Arithmetic Sequences
			Using consecutive terms to find another
			Using any two terms
		Looking at Ratios and Consecutive Paired Terms: Geometric Sequences
			Embracing some basic concepts
			Going out of order: Dealing with nonconsecutive terms
		Creating a Series: Summing Terms of a Sequence
			Reviewing general summation notation
			Summing an arithmetic sequence
			Seeing how a geometric sequence adds up
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 20 Quiz
		Answers to Chapter 20 Quiz
	Chapter 21: Expanding Binomials for the Real World
		Expanding with the Binomial Theorem
			Concocting binomial coefficients
			Breaking down the binomial theorem
			Expanding by using the binomial theorem
		Working Backwards
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 21 Quiz
		Answers to Chapter 21 Quiz
Unit 7: Onward to Calculus
	Chapter 22: Lining Up the Tools
		Scoping Out the Changes: Pre-Calculus to Calculus
		Understanding Your Limits
		Finding the Limit of a Function
			Graphically
			Analytically
			Algebraically
		Operating on Limits: The Limit Laws
		Calculating the Average Rate of Change
		Exploring Continuity in Functions
			Determining whether a function is continuous
			Discontinuity in rational functions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 22 Quiz
		Answers to Chapter 22 Quiz
	Chapter 23: Proceeding with Successful Procedures
		Figure Out What the Problem Is Asking
		Draw Pictures (the More the Better)
		Plan Your Attack: Identify Your Targets
		Write Down Any Formulas
		Show Each Step of Your Work
		Know When to Quit
		Check Your Answers
		Practice Plenty of Problems
		Keep Track of the Order of Operations
		Use Caution When Dealing with Fractions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 23 Quiz
		Answers to Chapter 23 Quiz
Index
EULA