ALGEBRA in WORDS · A Guide of Hints, Strategies and Simple Explanations by Bullock, Gregory -- Read -- Imperial Library of Trantor

Index

INTRODUCTION

What Is This Book? Why Do You Need Algebra?

REVIEW OF THE BASICS

The Real Order of Operations: GEMA The Truth about PEMDAS The Unwritten 1 Property Crises of Zeros, Ones & Negatives Integers & Whole Numbers Prime Numbers Is 51 a Prime Number? What is a Term? What is a “Like-Term”? What is a Factor? Factoring The Procedure for Prime Factoring The Prime Number Multiples Table The Greatest Common Factor (GCF) The Least Common Denominator (LCD) GCF vs. LCD

FRACTIONS

Procedure for Adding & Subtracting Fractions Multiplying Fractions Dividing Fractions

OPERATIONS OF BASES WITH EXPONENTS

Multiplying Bases With Exponents Dividing Bases With Exponents Exponents of Exponents (a.k.a. Powers of Powers)

SOLVING SIMPLE ALGEBRAIC EQUATIONS

Solving a Simple Algebraic Equation with One Variable (First Degree) Arrangement: Descending Order Expressions vs. Equations

LINEAR EQUATIONS

A Diagonal Line: A Horizontal Line: A Vertical Line: What Does “Undefined” Mean? How to Graph a Linear Equation The Slope Equation The 4 Important Equations for Lines When x1=x2: When y1=y2: Parallel & Perpendicular Lines on a Graph

SOLVING A SYSTEM OF (TWO) LINEAR EQUATIONS

What Does “Solving In Terms Of” Mean? Graph & Check The Substitution Method The Addition/Elimination Method

Examples for Choosing the Method

Interpreting the “Solutions”

One Solution - Consistent No Solution - Inconsistent, Parallel Infinite Solutions - Dependent

TRINOMIALS & QUADRATICS

What Are “Solutions” to Quadratic Equations? Solving Quadratic Equations

Factor & Solve Trial & Error/Reverse FOIL Method The ac/Grouping Method Complete the Square The Quadratic Formula The Part Everyone Forgets (The Last Step of the Quadratic Equation) Graph & Check

Quadratics with Zero When c is 0: ax2 + bx = 0 When Both b & c are 0: ax2 = 0 When b is 0: ax2 + c = 0 “The Difference of Two Squares” Conjugate Pair Binomials Taking the Square Root of Both Sides The Sum of Two Squares Special Words for Special Cases

Perfect Square Trinomial The Difference of Two Squares

Prime vs. No Solution Clarification: When the Solution is 0

RATIONAL EXPRESSIONS

Procedure for Simplifying Rational Expressions Procedure for Adding & Subtracting Rational Expressions Simplifying a Complex Rational Expression

The Wrong Way to Simplify a Rational Expression Extraneous Solutions Procedure for Solving Equations with Rational Expressions & Extraneous Solutions Cross Multiplication Cross-Multiplication vs. Cross Cancelling

RADICALS, ROOTS & POWERS

Perfect Squares & Associated Square Roots List of Perfect Squares & Associated Square Roots Common Perfect Cubes & Associated Cube Roots Other Powers & Relationships of 2, 3, 4 & 5 Manipulating & Simplifying Radicals List of Common Radical Fingerprints Extraneous Roots in Radical Equations

FMMs (FREQUENTLY MADE MISTAKES)

The Two Meanings of “Cancelling Out” Checking Your Answers Miscellaneous Mistakes Scientific Notation on Your Calculator What Does “Error” on a Calculator Mean?

CLOSING