Algebra Essentials Practice Workbook with Answers: Linear & Quadratic Equations

Book Preface

Making the Most of this Workbook

– Mathematics is a language. You can’t hold a decent conversation in any language if you have a limited vocabulary or if you are not fluent. In order to become successful in mathematics, you need to practice until you have mastered the fundamentals and developed fluency in the subject. This Algebra Essentials Practice Workbook with Answers: Linear & Quadratic Equations, Cross Multiplying, and Systems of Equations will help you improve the fluency with which you apply fundamental techniques to solve for unknowns.
– This book is conveniently divided into 7 chapters so that you can focus on one basic skill at a time. The exercises of Chapters 1 and 2 are linear equations with a single unknown, which entail using arithmetic operations to collect and isolate the unknowns. The coefficients are all integers in Chapter 1, while Chapter 2 features fractional coefficients.

Quadratic equations are the focus of Chapters 3 thru 5. Chapter 3 is limited to quadratic equations that either do not have a constant term or do not have a term of the first power in the unknown, while Chapters 4 and 5 are focused on techniques for solving the full quadratic equation. The quadratic equations of Chapter 4 are reasonably straightforward to factor into a product of linear factors with integral coefficients, whereas the focus of Chapter 5 is how to apply the quadratic formula. Chapter 6 is dedicated to cross multiplying. Systems of linear equations with two unknowns are the subject of Chapter 7.
– Each chapter begins with a few pages of instructions describing a basic algebraic skill – such as how to factor the quadratic equation. These instructions are followed by a few examples. Use these examples as a guide until you become fluent in the technique.
– After you complete a page, check your answers with the answer key in the back of the book. Practice makes permanent, but not necessarily perfect: If you practice making mistakes, you will learn your mistakes. Check your answers and learn from your mistakes such that you practice solving the problems correctly. This way your practice will make perfect.
– Math can be fun. Make a game of your practice by recording your times and trying to improve on your times, and recording your scores and trying to improve on your scores.
Doing this will help you see how much you are improving, and this sign of improvement can give you the confidence to succeed in math, which can help you learn to enjoy this subject more

Contents
Making the Most of this Workbook 4
Chapter 1: Linear Equations with Integral Coefficients 5
Chapter 2: Linear Equations with Fractional Coefficients 28
Chapter 3: Simple Quadratic Equations 51
Chapter 4: Factoring Quadratic Equations 76
Chapter 5: Formula for the Quadratic Equation 109
Chapter 6: Cross Multiplying 132
Chapter 7: Systems of Linear Equations 158
Answer Key 193