Algebra II All-in-One For Dummies

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
Part1 Getting to First Base with the Basics
	Chapter 1 Beginning at the Beginning of Algebra
		Following the Order of Operations and Other Properties
			Ordering your operations
			Examining various properties
		Specializing in Products and “FOIL”
			First-Outer-Inner-Last
			Raising binomials to powers
		Expounding on Exponential Rules
			Multiplying and dividing exponents
			Getting to the roots of exponents
			Raising or lowering the roof with exponents
			Making nice with negative exponents
		Taking On Special Operators
			Working with absolute value
			Doing great with the greatest integer function
			Getting the facts with factorial
		Simplifying Radical Expressions
		Factoring in Some Factoring Techniques
			Factoring two terms
			Taking on three terms
			Factoring four or more terms by grouping
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 1 Quiz
		Answers to Chapter 1 Quiz
	Chapter 2 Taking on Linear Equations and Inequalities
		Variables on the Side: Solving Linear Equations
			Tackling basic linear equations
			Clearing out the grouping symbols
		Making Fractional Terms More Manageable
		Solving for a Variable
		Making Linear Inequalities More Equitable
			Solving linear inequalities
			Introducing interval notation
		Compounding the Situation with Compound Statements
		Dealing with Linear Absolute Value Equations and Inequalities
			Being absolutely fair with equations
			Seeing through absolute value inequality
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 2 Quiz
		Answers to Chapter 2 Quiz
	Chapter 3 Handling Quadratic and Other Polynomial Equations
		Implementing the Square Root Rule
		Successfully Factoring for Solutions
			Factoring binomials
			Factoring trinomials
			Factoring by grouping
		Resorting to the Quadratic Formula
			Finding rational solutions
			Straightening out irrational solutions
		Solving Quadratics by Completing the Square
			Squaring up a quadratic equation
			Completing the square twice over
		Tackling Higher-Powered Polynomials
			Handling the sum or difference of cubes
			Solving quadratic-like trinomials
		Using the Rational Root Theorem and Synthetic Division
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 3 Quiz
		Answers to Chapter 3 Quiz
	Chapter 4 Controlling Quadratic and Rational Inequalities
		Checking Out Quadratic Inequalities
			Taking on Rational Inequalities and Non-Solutions
			Increasing the Factors in Polynomial Inequalities
			Considering Absolute Value Inequalities
		Compounding the Situation with Compound Inequalities
		Solving Inequality Word Problems
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 4 Quiz
		Answers to Chapter 4 Quiz
	Chapter 5 Soothing the Rational, the Radical, and the Negative
		Systematically Solving Rational Equations
		Simplifying and Solving Proportions
			Reducing every which way but loose
			Using cross-products to solve a rational equation
		Ridding Yourself of a Radical
			Squaring both sides of a radical equation
			Calming two radicals
		Changing Negative Attitudes toward Negative Exponents
			Flipping negative exponents out of the picture
			Factoring out negatives to solve equations
		Solving Equations with Fractional Exponents
			Combining terms with fractional exponents
			Factoring fractional exponents
			Solving equations by working with fractional exponents
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 5 Quiz
		Answers to Chapter 5 Quiz
	Chapter 6 Giving Graphing a Gander
		Coordinating Axes, Points, and Quadrants
			Identifying the parts of the coordinate plane
			Plotting from dot to dot
		Crossing the Line Using Intercepts and Symmetry
			Finding x- and y-intercepts
			Reflecting on a graph’s symmetry
		Preparing to Graph Lines
			Finding the slope of a line
			Facing two types of equations for lines
		Identifying Parallel and Perpendicular Lines
		Graphing the Ten Basic Forms
			Lines and quadratics
			Cubics and quartics
			Radicals and rationals
			Exponential and logarithmic curves
			Absolute values and circles
		Enter the Machines: Using a Graphing Calculator
			Entering equations into graphing calculators correctly
			Looking through the graphing window
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 6 Quiz
		Answers to Chapter 6 Quiz
Part2 Figuring on Functions
	Chapter 7 Formulating Functions
		Featuring Functions
			Introducing function notation
			Evaluating functions
		Homing In on Domain and Range
			Determining a function’s domain
			Describing a function’s range
		Recognizing Even, Odd, and One-to-One Functions
			Classifying even and odd functions
			Applying even and odd functions to graphs
			Defining one-to-one functions
			Eliminating one-to-one violators
		Going to Pieces with Piecewise Functions
			Doing piecework
			Applying piecewise functions
		Composing Functions and Applying the Difference Quotient
			Performing compositions
			Simplifying the difference quotient
		Dealing with Inverse Functions
			Determining if functions are inverses
			Solving for the inverse of a function
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 7 Quiz
		Answers to Chapter 7 Quiz
	Chapter 8 Specializing in Quadratic Functions
		Setting the Standard to Create a Parabola
			Starting with “a” in the standard form
			Following up with “b” and “c”
		Recognizing the Intercepts and Vertex
			Finding the one and only y-intercept
			Finding the x-intercepts
			Going to the extreme: Finding the vertex
		Making Symmetry Work with an Axis
		Graphing Parabolas
		Applying Quadratics in Real-Life Situations
			Selling candles
			Shooting basketballs
			Launching a water balloon
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 8 Quiz
		Answers to Chapter 8 Quiz
	Chapter 9 Plugging In Polynomials
		Getting into Polynomial Basics and Vocabulary
			Exploring polynomial intercepts and turning points
			Interpreting relative value and absolute value
			Counting intercepts and turning points
		Solving for Polynomial Intercepts
		Finding the Roots of a Polynomial
			Applying factoring patterns and groupings
			Considering the unfactorable
		Saving Your Sanity: The Rational Root Theorem
			Putting the theorem to good use
			Changing from roots to factors
			Letting Descartes make a ruling on signs
			Counting up the positive roots
			Changing the function to count negative roots
		Synthesizing Root Findings
			Using synthetic division to test for roots
			Synthetically dividing by a binomial
			Wringing out the Remainder (Theorem)
		Determining Positive and Negative Intervals
		Graphing Polynomials
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 9 Quiz
		Answers to Chapter 9 Quiz
	Chapter 10 Acting Rationally with Functions
		Exploring the Domain and Intercepts of Rational Functions
			Sizing up domain
			Introducing intercepts
		Adding Asymptotes to the Rational Pot
			Determining the equations of vertical asymptotes
			Heading after horizontal asymptotes
			Graphing vertical and horizontal asymptotes
			Crunching the numbers and graphing oblique asymptotes
		Removing Discontinuities
			Removal by factoring
			Evaluating the removal restrictions
			Showing removable discontinuities on a graph
		Going the Limit: Limits at a Number and Infinity
			Evaluating limits at discontinuities
			Determining an existent limit without tables
			Determining which functions have limits
			Going to infinity
			Catching rational limits at infinity
		Graphing Rational Functions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 10 Quiz
		Answers to Chapter 10 Quiz
	Chapter 11 Exploring Exponential and Logarithmic Functions
		Evaluating e-Expressions and Powers of e
			Exponential functions: it’s all about the base, baby
			Meeting the most frequently used bases: 10 and e
		Solving Exponential Equations
			Taking advantage of matching bases
			Recognizing and using quadratic patterns
			Taking out a greatest common factor
			Factoring like a quadratic trinomial
		Making Cents: Applying Compound Interest
			Applying the compound interest formula
			Measuring the actual compound: effective rates
			Looking at continuous compounding
		Logging On to Logarithmic Functions
			Meeting the properties of logarithms
			Putting your logs to work
			Expanding and contracting expressions with log notation
		Solving Logarithmic Equations
			Setting log equal to log
			Rewriting log equations as exponentials
		Graphing Exponential and Logarithmic Functions
			Expounding on the exponential
			Graphing log functions using intercepts
			Reflecting on inverses of exponential functions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 11 Quiz
		Answers to Chapter 11 Quiz
	Chapter 12 Transforming and Critiquing Functions
		Running through the Transformations
			Translating and understanding the language
			Reflecting on the good feeling graphing gives you
		Scaling the Cliff of Numerical Possibilities
		Multiplying the Opportunities for Transforming
		Noting the Ups, Downs, Highs, and Lows
			Determining increasing and decreasing intervals
			Charting the highs and lows
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 12 Quiz
		Answers to Chapter 12 Quiz
Part3 Using Conics and Systems of Equations
	Chapter 13 Slicing the Way You Like It: Conic Sections
		Carefully Cutting Circular Cones
		Opening Every Which Way with Parabolas
			Looking at parabolas with vertices at the origin
			Observing the general form of parabolic equations
			Converting parabolic equations to the standard form
			Sketching the graphs of parabolas
		Going Round and Round in Circles
			Standardizing the circle
			Specializing in circles
		Preparing for Solar Ellipses
			Raising the standards of an ellipse
			Sketching an elliptical path
		Getting Hyper Excited about Hyperbolas
			Including the asymptotes and vertices
			Graphing hyperbolas
		Identifying Conics from Their Equations
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 13 Quiz
		Answers to Chapter 13 Quiz
	Chapter 14 Solving Systems of Linear Equations
		Looking at the Standard Linear-Systems Form
		Solving Systems of Two Linear Equations by Using Elimination
			Getting to the point with elimination
			Recognizing solutions indicating parallel or coexisting lines
		Making Substitution the Choice
			Variable substitution made easy
			Identifying parallel and coexisting lines
		Graphing Solutions of Linear Systems
			Pinpointing the intersection
			Toeing the same line twice and dealing with parallel lines
		Using Cramer’s Rule to Defeat Unwieldy Fractions
			Setting up the linear system for Cramer
			Applying Cramer’s Rule to a linear system
		Tackling Linear Systems with Three Linear Equations
			Solving three-equation systems with algebra
			Generalizing multiple solutions for linear equations
		Upping the Ante with Larger Systems
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 14 Quiz
		Answers to Chapter 14 Quiz
	Chapter 15 Solving Systems of Nonlinear Equations
		Crossing Parabolas with Lines
			Determining the points where a line and parabola cross paths
			Dealing with a solution that’s no solution
		Intertwining Parabolas and Circles
			Managing multiple intersections
			Sorting out the solutions
		Planning Your Attack on Other Systems of Equations
			Mixing polynomials and lines
			Crossing polynomials
		Navigating Exponential Intersections
		Rounding Up Rational Functions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 15 Quiz
		Answers to Chapter 15 Quiz
	Chapter 16 Solving Systems of Inequalities
		Playing Fair with Inequalities
		Keeping It Linear with Inequalities
			Getting a new slant on linear inequalities
			Taking on more than two linear inequalities
			Graphing areas with curves and lines
		Applying the Systems to Real Life
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 16 Quiz
		Answers to Chapter 16 Quiz
Part4 Making Lists and Checking for Imaginary Numbers
	Chapter 17 Getting More Complex with Imaginary Numbers
		Simplifying Powers of i
			Understanding the Complexity of Complex Numbers
			Operating on complex numbers
			Multiplying by the conjugate to perform division
			Simplifying radicals
		Solving Quadratic Equations with Complex Solutions
		Working Polynomials with Complex Solutions
			Identifying conjugate pairs
			Interpreting complex zeros
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 17 Quiz
		Answers to Chapter 17 Quiz
	Chapter 18 Making Moves with Matrices
		Describing the Different Types of Matrices
			Row and column matrices
			Square matrices
			Zero matrices
			Identity matrices
		Performing Operations on Matrices
			Adding and subtracting matrices
			Multiplying matrices by scalars
			Multiplying two matrices
		Defining Row Operations
		Finding Inverse Matrices
			Determining additive inverses
			Determining multiplicative inverses
		Dividing Matrices by Using Inverses
		Using Matrices to Find Solutions for Systems of Equations
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 18 Quiz
		Answers to Chapter 18 Quiz
	Chapter 19 Seeking Out Sequences and Series
		Understanding Sequence Terminology
			Using sequence notation
			No-fear factorials in sequences
			Alternating sequential patterns
			Looking for sequential patterns
		Taking Note of Arithmetic and Geometric Sequences
			Finding common ground: Arithmetic sequences
			Taking the multiplicative approach: geometric sequences
		Recursively Defining Functions
		Making a Series of Moves
			Introducing summation notation
			Summing arithmetically
			Summing geometrically
		Highlighting Special Formulas
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 19 Quiz
		Answers to Chapter 19 Quiz
	Chapter 20 Everything You Wanted to Know about Sets and Counting
		Revealing the Set Rules
			Listing elements with a roster
			Building sets from scratch
			Going for all (universal set) or nothing (empty set)
			Subbing in with subsets
		Operating on Sets
			Celebrating the union of two sets
			Looking both ways for set intersections
			Feeling complementary about sets
			Counting the elements in sets
		Drawing Venn You Feel Like It
			Applying the Venn diagram
			Adding a set to a Venn diagram
		Focusing on Factorials
			Making factorials manageable
			Simplifying factorials
		How Do I Love Thee? Let Me Count Up the Ways
			Applying the multiplication principle to sets
			Arranging permutations of sets
			Mixing up sets with combinations
		Branching Out with Tree Diagrams
			Picturing a tree diagram for a permutation
			Drawing a tree diagram for a combination
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 20 Quiz
		Answers to Chapter 20 Quiz
Part5 Applying Known Formulas
	Chapter 21 Manipulating Formulas
		Expanding Binomials
			Using the Binomial Theorem
			Applying Pascal’s Triangle
		Taking On the Graphing Formulas
			Formulating properties between two points
			Measuring the distance between a point and a line
		Getting All Geometric
			Telling the plain truth with plane geometry
			Keeping it solid
		Solving a Formula for a Variable
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 21 Quiz
		Answers to Chapter 21 Quiz
	Chapter 22 Taking on Applications
		Making Mixtures Magically Mathematical
			Keeping money matters solvent
			Flowing freely with fluids
			Mixing up many ingredients
		Going the Distance
			Equating distances
			Summing up the distances
		Working through the Challenges
		Acting Your Age
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 22 Quiz
		Answers to Chapter 22 Quiz
Index
	EULA