Оглавление
Mary Jane Sterling. Algebra I All-in-One For Dummies
Algebra I All-In-One For Dummies® To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Algebra I All-In-One For Dummies Cheat Sheet” in the Search box. Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Starting Out with Numbers and Properties. Contents at a Glance
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
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
Breaking into binary operations
Introducing nonbinary operations
Getting it absolutely right with absolute value
Getting the facts straight with factorial
Getting the most for your math with the greatest integer
Tackling the Basic Binary Operations
Adding signed numbers
Adding like to like: Same-signed numbers
Adding different signs
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
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
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
Getting terminal results with terminating decimals
Repeating yourself with repeating decimals
Practice Question Answers and Explanations
Whaddya Know? Chapter 4 Quiz
Answers to Chapter 4 Quiz
Operating on Operations. Contents at a Glance
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
Exploring Exponents
Powering up with Exponential Notation
PAYING OFF A ROYAL DEBT EXPONENTIALLY
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
Making Things Simple by Simplifying. Contents at a Glance
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
Working with Numbers in Their Prime
Beginning with the Basics
WHY ISN’T THE NUMBER 1 PRIME?
MERSENNE PRIMES
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
Specializing in Multiplication Matters
Distributing One Factor Over Many
Distributing Signs
Mixing It up with Numbers and Variables
Negative exponents yielding fractional answers
PALINDROMES
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
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
Factoring. Contents at a Glance
Figuring on Factoring
Factoring out the Greatest Common Factor
REVIEWING THE TERMS AND RULES
Factoring out numbers
Writing factoring as division
Outlining the factoring method
FACTORING IN THE REAL WORLD
Factoring out variables
Unlocking combinations of numbers and variables
DIOPHANTUS
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
Taking the Bite out of Binomial Factoring
Reining in Big and Tiny Numbers
Factoring the Difference of Squares
Factoring Differences and Sums of Cubes
GREAT LEADERS MAKE GREAT MATHEMATICIANS
Making Factoring a Multiple Mission
Practice Questions Answers and Explanations
Whaddya Know? Chapter 12 Quiz
Answers to Chapter 12 Quiz
Factoring Trinomials and Special Polynomials
Recognizing the Standard Quadratic Expression
Focusing First on the Greatest Common Factor
CARL FRIEDRICH GAUSS, CHILD PRODIGY
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
Solving Linear and Polynomial Equations. Contents at a Glance
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
Adding to each side or subtracting from each side
Multiplying each side by the same number
Dividing each side of the equation by the same number
Squaring both sides and suffering the consequences
USING A BALANCE SCALE TO FIND THE COUNTERFEIT COIN
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
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
ARCHIMEDES: MOVER AND BATHER
Practice Questions Answers and Explanations
Whaddya Know? Chapter 15 Quiz
Answers to Chapter 15 Quiz
Muscling Up to Quadratic Equations
Using the Square-Root Rule
Factoring for a Solution
Zeroing in on the multiplication property of zero
GETTING THE QUADRATIC SECOND-DEGREE
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
Dealing with Non-Polynomial Equations and Inequalities. Contents at a Glance
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
Factoring out a first-degree variable GCF
Factoring out a second-degree 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
PHYSICAL CHALLENGES
Solving Synthetically
Practice Questions Answers and Explanations
Whaddya Know? Chapter 17 Quiz
Answers to Chapter 17 Quiz
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
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
Evaluating Formulas and Story Problems. Contents at a Glance
Facing Up to Formulas
Working with Formulas
Measuring Up
Finding out how long: Units of length
Putting the Pythagorean Theorem to work
PUZZLING PYTHAGORAS
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
Figuring simple interest
Tallying compound interest
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
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
Building a pyramid
Circling Jupiter
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
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
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
Getting a Grip on Graphing. Contents at a Glance
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
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
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. Symbol
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
About the Author
Dedication
Author’s Acknowledgments
WILEY END USER LICENSE AGREEMENT
