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Algebra II for Dummies

ISBN-10: 0471775819
ISBN-13: 9780471775812
Edition: 2006
List price: $19.99
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Description: Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and  More...

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Book details

List price: $19.99
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/19/2006
Binding: Paperback
Pages: 384
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 1.540
Language: English

Besides being an important area of math for everyday use, algebra is a passport to studying subjects like calculus, trigonometry, number theory, and geometry, just to name a few. To understand algebra is to possess the power to grow your skills and knowledge so you can ace your courses and possibly pursue further study in math. Algebra II For Dummies is the fun and easy way to get a handle on this subject and solve even the trickiest algebra problems. This friendly guide shows you how to get up to speed on exponential functions, laws of logarithms, conic sections, matrices, and other advanced algebra concepts. In no time you'll have the tools you need to: Interpret quadratic functions Find the roots of a polynomial Reason with rational functions Expose exponential and logarithmic functions Cut up conic sections Solve linear and non linear systems of equations Equate inequalities Simplifyy complex numbers Make moves with matrices Sort out sequences and sets This straightforward guide offers plenty of multiplication tricks that only math teachers know. It also profiles special types of numbers, making it easy for you to categorize them and solve any problems without breaking a sweat. When it comes to understanding and working out algebraic equations, Algebra II For Dummies is all you need to succeed!

Introduction
About This Book
Conventions Used in This Book
Foolish Assumptions
How This Book Is Organized
Icons Used in This Book
Where to Go from Here
Homing in on Basic Solutions
Going Beyond Beginning Algebra
Outlining Algebra Properties
Keeping order with the commutative property
Maintaining group harmony with the associative property
Distributing a wealth of values
Checking out an algebraic ID
Singing along in-verses
Ordering Your Operations
Equipping Yourself with the Multiplication Property of Zero
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
Implementing Factoring Techniques
Factoring two terms
Taking on three terms
Factoring four or more terms by grouping
Toeing the Straight Line: Linear Equations
Linear Equations: Handling the First Degree
Tackling basic linear equations
Clearing out fractions
Isolating different unknowns
Linear Inequalities: Algebraic Relationship Therapy
Solving basic inequalities
Introducing interval notation
Compounding inequality issues
Absolute Value: Keeping Everything in Line
Solving absolute-value equations
Seeing through absolute-value inequality
Cracking Quadratic Equations
Solving Simple Quadratics with the Square Root Rule
Finding simple square-root solutions
Dealing with radical square-root solutions
Dismantling Quadratic Equations into Factors
Factoring binomials
Factoring trinomials
Factoring by grouping
Resorting to the Quadratic Formula
Finding rational solutions
Straightening out irrational solutions
Formulating huge quadratic results
Completing the Square: Warming Up for Conics
Squaring up to solve a quadratic equation
Completing the square twice over
Getting Promoted to High-Powered Quadratics (without the Raise)
Handling the sum or difference of cubes
Tackling quadratic-like trinomials
Solving Quadratic Inequalities
Keeping it strictly quadratic
Signing up for fractions
Increasing the number of factors
Rooting Out the Rational, Radical, and Negative
Acting Rationally with Fraction-Filled Equations
Solving rational equations by tuning in your LCD
Solving rational equations with proportions
Ridding Yourself of a Radical
Squaring both sides of a radical equation
Calming two radicals
Changing Negative Attitudes about Exponents
Flipping negative exponents out of the picture
Factoring out negatives to solve equations
Fooling Around with Fractional Exponents
Combining terms with fractional exponents
Factoring fractional exponents
Solving equations by working with fractional exponents
Graphing Your Way to the Good Life
Coordinating Your Graphing Efforts
Identifying the parts of the coordinate plane
Plotting from dot to dot
Streamlining the Graphing Process with Intercepts and Symmetry
Finding x- and y-intercepts
Reflecting on a graph's symmetry
Graphing Lines
Finding the slope of a line
Facing two types of equations for lines
Identifying parallel and perpendicular lines
Looking at 10 Basic Forms
Lines and quadratics
Cubics and quartics
Radicals and rationals
Exponential and logarithmic curves
Absolute values and circles
Solving Problems with a Graphing Calculator
Entering equations into graphing calculators correctly
Looking through the graphing window
Facing Off with Functions
Formulating Function Facts
Defining Functions
Introducing function notation
Evaluating functions
Homing In on Domain and Range
Determining a function's domain
Describing a function's range
Betting on Even or Odd Functions
Recognizing even and odd functions
Applying even and odd functions to graphs
Facing One-to-One Confrontations
Defining one-to-one functions
Eliminating one-to-one violators
Going to Pieces with Piecewise Functions
Doing piecework
Applying piecewise functions
Composing Yourself and Functions
Performing compositions
Simplifying the difference quotient
Singing Along with Inverse Functions
Determining if functions are inverses
Solving for the inverse of a function
Sketching and Interpreting Quadratic Functions
Interpreting the Standard Form of Quadratics
Starting with "a" in the standard form
Following up with "b" and "c"
Investigating Intercepts in Quadratics
Finding the one and only y-intercept
Finding the x-intercepts
Going to the Extreme: Finding the Vertex
Lining Up along the Axis of Symmetry
Sketching a Graph from the Available Information
Applying Quadratics to the Real World
Selling candles
Shooting basketballs
Launching a water balloon
Staying Ahead of the Curves: Polynomials
Taking a Look at the Standard Polynomial Form
Exploring Polynomial Intercepts and Turning Points
Interpreting relative value and absolute value
Counting intercepts and turning points
Solving for polynomial intercepts
Determining Positive and Negative Intervals
Using a sign-line
Interpreting the rule
Finding the Roots of a Polynomial
Factoring for polynomial roots
Saving your sanity: The Rational Root Theorem
Letting Descartes make a ruling on signs
Synthesizing Root Findings
Using synthetic division to test for roots
Synthetically dividing by a binomial
Wringing out the Remainder (Theorem)
Relying on Reason: Rational Functions
Exploring Rational Functions
Sizing up domain
Introducing intercepts
Adding Asymptotes to the Rational Pot
Determining the equations of vertical asymptotes
Determining the equations of horizontal asymptotes
Graphing vertical and horizontal asymptotes
Crunching the numbers and graphing oblique asymptotes
Accounting for Removable Discontinuities
Removal by factoring
Evaluating the removal restrictions
Showing removable discontinuities on a graph
Pushing the Limits of Rational Functions
Evaluating limits at discontinuities
Going to infinity
Catching rational limits at infinity
Putting It All Together: Sketching Rational Graphs from Clues
Exposing Exponential and Logarithmic Functions
Evaluating Exponential Expressions
Exponential Functions: It's All About the Base, Baby
Observing the trends in bases
Meeting the most frequently used bases: 10 and e
Solving Exponential Equations
Making bases match
Recognizing and using quadratic patterns
Showing an "Interest" in Exponential Functions
Applying the compound interest formula
Looking at continuous compounding
Logging On to Logarithmic Functions
Meeting the properties of logarithms
Putting your logs to work
Solving Logarithmic Equations
Setting log equal to log
Rewriting log equations as exponentials
Graphing Exponential and Logarithmic Functions
Expounding on the exponential
Not seeing the logs for the trees
Conquering Conics and Systems of Equations
Cutting Up Conic Sections
Cutting Up a Cone
Opening Every Which Way with Parabolas
Looking at parabolas with vertices at the origin
Observing the general form of parabola equations
Sketching the graphs of parabolas
Converting parabolic equations to the standard form
Going Round and Round in Conic Circles
Standardizing the circle
Specializing in circles
Preparing Your Eyes for Solar Ellipses
Raising the standards of an ellipse
Sketching an elliptical path
Feeling Hyper about Hyperbolas
Including the asymptotes
Graphing hyperbolas
Identifying Conics from Their Equations, Standard or Not
Solving Systems of Linear Equations
Looking at the Standard Linear-Systems Form and Its Possible Solutions
Graphing Solutions of Linear Systems
Pinpointing the intersection
Toeing the same line twice
Dealing with parallel lines
Eliminating Systems of Two Linear Equations with Addition
Getting to an elimination point
Recognizing solutions for parallel and coexisting lines
Solving Systems of Two Linear Equations with Substitution
Variable substituting made easy
Identifying parallel and coexisting lines
Using Cramer's Rule to Defeat Unwieldy Fractions
Setting up the linear system for Cramer
Applying Cramer's Rule to a linear system
Raising Linear Systems to Three Linear Equations
Solving three-equation systems with algebra
Settling for a generalized solution for linear combinations
Upping the Ante with Increased Equations
Applying Linear Systems to Our 3-D World
Using Systems to Decompose Fractions
Solving Systems of Nonlinear Equations and Inequalities
Crossing Parabolas with Lines
Determining the point(s) 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
Playing Fair with Inequalities
Drawing and quartering inequalities
Graphing areas with curves and lines
Shifting into High Gear with Advanced Concepts
Simplifying Complex Numbers in a Complex World
Using Your Imagination to Simplify 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
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
Applying matrices and operations
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
Making a List: 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
Applying Sums of Sequences to the Real World
Cleaning up an amphitheater
Negotiating your allowance
Bouncing a ball
Highlighting Special Formulas
Everything You Wanted to Know about Sets
Revealing Set Notation
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
Using Venn diagrams with set operations
Adding a set to a Venn diagram
Focusing on Factorials
Making factorial 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
The Part of Tens
Ten Multiplication Tricks
Ten Special Types of Numbers
Index

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