Algebra I 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
Book 1: Starting Out with Numbers and Properties
	Chapter 1: Assembling Your Tools: Number Systems
		Identifying Numbers by Name
			Realizing real numbers
			Counting on natural numbers
			Whittling out whole numbers
			Integrating integers
			Being reasonable: Rational numbers
			Restraining irrational numbers
			Picking out primes and composites
			Zero: It’s Complicated
			Imagining imaginary numbers
			Coping with complex numbers
		Placing Numbers on the Number Line
		Speaking in Algebra
			Being precise with words
			Describing the size of an expression
			Relating operations with symbols
		Taking Aim at Algebra-Speak
			Herding numbers with grouping symbols
			Defining relationships
			Taking on algebraic tasks
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 1 Quiz
		Answers to Chapter 1 Quiz
	Chapter 2: Deciphering Signs in Expressions
		Assigning Numbers Their Place
			Using the number line
			Comparing positives and negatives with symbols
			Zeroing in on Zero
		Going in for Operations
			Sorting out types of operations
		Tackling the Basic Binary Operations
			Adding signed numbers
			Making a Difference with Signed Numbers
			Multiplying Signed Numbers
			Dividing Signed Numbers
			Working with Nothing: Zero and Signed Numbers
			Practice Questions Answers and Explanations
			Whaddya Know? Chapter 2 Quiz
			Answers to Chapter 2 Quiz
	Chapter 3: Incorporating Algebraic Properties
		Getting a Grip on Grouping Symbols
		Spreading, Grouping, and Changing the Order
			Distributing the wealth
			Making Associations Work
			Computing by Commuting
		Relating Inverses and Identities
			Investigating Inverses
			Identifying Identities
		Working with Factorial
		Applying the Greatest Integer Function
		Practice Question Answers and Explanations
		Whaddya Know? Chapter 3 Quiz
		Answers to Chapter 3 Quiz
	Chapter 4: Coordinating Fractions and Decimals
		Converting Improper Fractions and Mixed Numbers
		Finding Fraction Equivalences
			Rewriting fractions
			Determining lowest terms
		Making Proportional Statements
		Finding Common Denominators
			Creating common denominators from multiples of factors
			Using the box method
		Applying Fractional Operations
			Adding and subtracting fractions
			Multiplying and dividing fractions
		Simplifying Complex Fractions
		Performing Operations with Decimals
		Changing Fractions to Decimals and Vice Versa
			Making fractions become decimals
			Rounding decimals
			Writing decimals as equivalent fractions
		Practice Question Answers and Explanations
		Whaddya Know? Chapter 4 Quiz
		Answers to Chapter 4 Quiz
Book 2: Operating on Operations
	Chapter 5: Taming Rampaging Radicals
		Simplifying Radical Terms
		Working through Radical Expressions
			Recognizing perfect square terms
			Rewriting radical terms
		Rationalizing Fractions
		Managing Radicals as Exponential Terms
			Using Fractional Exponents
			Making the switch to fractional exponents
			Simplifying expressions with exponents
		Estimating Answers
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 5 Quiz
		Answers to Chapter 5 Quiz
	Chapter 6: Exploring Exponents
		Powering up with Exponential Notation
		Using Negative Exponents
		Multiplying and Dividing Exponentials
			Multiplying the same base
			Multiplying the same power
			Dividing with exponents
		Raising Powers to Powers
		Testing the Power of Zero
		Writing Numbers with Scientific Notation
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 6 Quiz
		Answers to Chapter 6 Quiz
Book 3: Making Things Simple by Simplifying
	Chapter 7: Simplifying Algebraic Expressions
		Addressing the Order of Operations
		Adding and Subtracting Like Terms
		Multiplying and Dividing Algebraically
			Dealing with factors
			Diving into dividing
		Gathering Terms with Grouping Symbols
		Evaluating Expressions
		Checking Your Answers
			Seeing if it makes sense
			Plugging in values
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 7 Quiz
		Answers to Chapter 7 Quiz
	Chapter 8: Working with Numbers in Their Prime
		Beginning with the Basics
		Composing Composite Numbers
		Writing Prime Factorizations
			Dividing while standing on your head
			Getting to the root of primes with a tree
			Wrapping your head around the rules of divisibility
		Making Use of a Prime Factor
			Taking primes into account
			Pulling out factors and leaving the rest
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 8 Quiz
		Answers to Chapter 8 Quiz
	Chapter 9: Specializing in Multiplication Matters
		Distributing One Factor Over Many
		Distributing Signs
		Mixing It up with Numbers and Variables
			Negative exponents yielding fractional answers
			Working with Fractional Powers
		Distributing More Than One Term
			Distributing binomials
			Distributing trinomials
		Curses, Foiled Again — Or Not
		Squaring Binomials
		Multiplying the Sum and Difference of the Same Two Terms
		Powering Up Binomials
			Cubing binomials
			Raising Binomials to Higher Powers
		Creating the Sum and Difference of Cubes
		Multiplying Conjugates
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 9 Quiz
		Answers to Chapter 9 Quiz
	Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions
		Dividing by a Monomial
		Dividing by a Binomial
		Dividing by Polynomials with More Terms
		Simplifying Division Synthetically
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 10 Quiz
		Answers to Chapter 10 Quiz
Book 4: Factoring
	Chapter 11: Figuring on Factoring
		Factoring out the Greatest Common Factor
			Factoring out numbers
			Factoring out variables
			Unlocking combinations of numbers and variables
		Using the Box Method
		Changing Factoring into a Division Problem
		Reducing Algebraic Fractions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 11 Quiz
		Answers to Chapter 11 Quiz
	Chapter 12: Taking the Bite out of Binomial Factoring
		Reining in Big and Tiny Numbers
		Factoring the Difference of Squares
		Factoring Differences and Sums of Cubes
		Making Factoring a Multiple Mission
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 12 Quiz
		Answers to Chapter 12 Quiz
	Chapter 13: Factoring Trinomials and Special Polynomials
		Recognizing the Standard Quadratic Expression
		Focusing First on the Greatest Common Factor
			Unwrapping the FOILing Package
			The opening to unFOIL
			Coming to the end of the FOIL roll
		Factoring Quadratic-Like Trinomials
		Factoring Trinomials Using More Than One Method
		Factoring by Grouping
		Putting All the Factoring Together and Making Factoring Choices
			Combining unFOIL and the GCF
			Grouping and unFOILing in the same package
		Incorporating the Remainder Theorem
			Synthesizing with synthetic division
			Choosing numbers for synthetic division
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 13 Quiz
		Answers to Chapter 13 Quiz
Book 5: Solving Linear and Polynomial Equations
	Chapter 14: Establishing Ground Rules for Solving Equations
		Creating the Correct Setup for Solving Equations
			Setting up equations for further action
			Making plans for solving equations
		Keeping Equations Balanced
			Balancing with binary operations
			Squaring both sides and suffering the consequences
			Taking a root of both sides
		Solving with Reciprocals
		Making a List and Checking It Twice
			Doing a reality check
			Thinking like a car mechanic when checking your work
		Practice Problems Answers and Explanations
		Whaddya Know? Chapter 14 Quiz
		Answers to Chapter 14 Quiz
	Chapter 15: Lining Up Linear Equations
		Playing by the Rules
		Using the Addition/Subtraction Property
		Using the Multiplication/Division Property
			Devising a method using division
			Making the most of multiplication
			Reciprocating the invitation
		Putting Several Operations Together
		Solving Linear Equations with Grouping Symbols
			Nesting isn’t for the birds
			Distributing first
			Multiplying or dividing before distributing
		Working with Proportions
			Using the rules for proportions
			Transforming fractional equations into proportions
		Solving for Variables in Formulas
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 15 Quiz
		Answers to Chapter 15 Quiz
	Chapter 16: Muscling Up to Quadratic Equations
		Using the Square-Root Rule
		Factoring for a Solution
			Zeroing in on the multiplication property of zero
			Assigning the greatest common factor and multiplication property of zero to solving quadratics
		Solving Quadratics with Three Terms
		Using the Quadratic Formula
		Completing the Square
		Imagining the Worst with Imaginary Numbers
		Practice Problems Answers and Explanations
		Whaddya Know? Chapter 16 Quiz
		Answers to Chapter 16 Quiz
Book 6: Dealing with Non-Polynomial Equations and Inequalities
	Chapter 17: Yielding to Higher Powers
		Queuing Up to Cubic Equations
			Solving perfectly cubed equations
			Working with the not-so-perfectly cubed
			Going for the greatest common factor
			Grouping cubes
			Solving cubics with integers
		Determining How Many Possible Roots
		Applying the Rational Root Theorem
		Using the Factor/Root Theorem
		Solving by Factoring
		Solving Powers That Are Quadratic-Like
		Solving Synthetically
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 17 Quiz
		Answers to Chapter 17 Quiz
	Chapter 18: Reeling in Radical and Absolute Value Equations
		Raising Both Sides to Solve Radical Equations
			Powering up by squaring both sides
			Raising to higher powers
		Doubling the Fun with Radical Equations
		Solving Absolute Value Equations
			Making linear absolute value equations absolutely wonderful
			Factoring absolute value equations for solutions
		Checking for Absolute Value Extraneous Roots
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 18 Quiz
		Answers to Chapter 18 Quiz
	Chapter 19: Getting Even with Inequalities
		Defining the Inequality Notation
			Pointing in the right direction
			Grappling with graphing inequalities
		Using the Rules to Work on Inequality Statements
		Rewriting Inequalities Using Interval Notation
		Solving Linear Inequalities
		Solving Quadratic Inequalities
		Dealing with Polynomial and Rational Inequalities
		Solving Absolute-Value Inequalities
		Solving Complex Inequalities
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 19 Quiz
		Answers to Chapter 19 Quiz
Book 7: Evaluating Formulas and Story Problems
	Chapter 20: Facing Up to Formulas
		Working with Formulas
		Measuring Up
			Finding out how long: Units of length
			Putting the Pythagorean Theorem to work
		Deciphering Perimeter, Area, and Volume
			Using perimeter formulas to get around
			Squaring off with area formulas
			Soaring with Heron’s formula
			Working with volume formulas
		Getting Interested in Using Percent
			Compounding interest formulas
			Gauging taxes and discounts
		Working out the Combinations and Permutations
			Counting down to factorials
			Counting on combinations
			Ordering up permutations
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 20 Quiz
		Answers to Chapter 20 Quiz
	Chapter 21: Making Formulas Work in Basic Story Problems
		Setting Up to Solve Story Problems
		Applying the Pythagorean Theorem
		Using Geometry to Solve Story Problems
		Working around Perimeter, Area, and Volume
			Parading out perimeter and arranging area
			Adjusting the area
			Pumping up the volume
		Going ’Round in Circles
		Putting Distance, Rate, and Time in a Formula
			Going the distance with the distance-rate-time formula
			Figuring distance plus distance
			Equating distances
			Figuring distance and fuel
		Counting on Interest and Percent
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 21 Quiz
		Answers to Chapter 21 Quiz
	Chapter 22: Relating Values in Story Problems
		Tackling Age Problems
		Tackling Consecutive Integer Problems
		Working Together on Work Problems
		Throwing an Object into the Air
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 22 Quiz
		Answers to Chapter 22 Quiz
	Chapter 23: Measuring Up with Quality and Quantity Story Problems
		Achieving the Right Blend with Mixture Problems
		Concocting the Correct Solution 100% of the Time
		Dealing with Money Problems
			Investigating investments and interest
			Going for the green: Money
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 23 Quiz
		Answers to Chapter 23 Quiz
Book 8: Getting a Grip on Graphing
	Chapter 24: Getting a Handle on Graphing
		Thickening the Plot with Points
			Interpreting ordered pairs
			Actually Graphing Points
			Sectioning Off by Quadrants
		Graphing Lines
			Using points to lay out lines
			Going with the horizontal and vertical
			Graphing Lines Using Intercepts
		Computing Slopes of Lines
			Sighting the slope
			Formulating slope
			Graphing with the Slope-Intercept Form
			Changing to the Slope-Intercept Form
		Writing Equations of Lines
			Given a point and a slope
			Given two points
		Picking on Parallel and Perpendicular Lines
		Finding Distances between Points
		Finding Midpoints of Segments
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 24 Quiz
		Answers to Chapter 24 Quiz
	Chapter 25: Extending the Graphing Horizon
		Finding the Intersections of Lines
			Graphing for intersections
			Substituting to find intersections
		Graphing Parabolas and Circles
		Curling Up with Parabolas
			Trying out the basic parabola
			Putting the vertex on an axis
			Going around in circles with a circular graph
		Plotting and Plugging in Polynomial Graphs
		Investigating Graphs of Inequality Functions
		Taking on Absolute-Value Function Graphs
		Graphing with Transformations
			Sliding and multiplying
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 25 Quiz
		Answers to Chapter 25 Quiz
	Chapter 26: Coordinating Systems of Equations and Graphing
		Defining Solutions of Systems of Equations
		Solving Systems of Linear Equations
			Using elimination
			Using substitution
			Introducing intersections of lines
		Solving Systems Involving Non-Linear Equations
		Taking on Systems of Three Linear Equations
		Practice Problems Answers and Explanations
		Whaddya Know? Chapter 26 Quiz
		Answers to Chapter 26 Quiz
Index
EULA