Practical Algebra: A Self-Teaching Guide

Description

The most practical, complete, and accessible guide for understanding algebra If you want to make sense of algebra, check out Practical Algebra: A Self-Teaching Guide. Written by two experienced classroom teachers, this Third Edition is completely revised to align with the Common Core Algebra I math standards used in many states. You’ll get an overview of solving linear and quadratic equations, using ratios and proportions, decoding word problems, graphing and interpreting functions, modeling the real world with statistics, and other concepts found in today’s algebra courses. This book also contains a brief review of pre-algebra topics, including arithmetic and fractions. It has concrete strategies that help diverse students to succeed, such as: over 500 images and tables that illustrate important concepts over 200 model examples with complete solutions almost 1,500 exercises with answers so you can monitor your progress Practical Algebra emphasizes making connections to what you already know and what you’ll learn in the future. You’ll learn to see algebra as a logical and consistent system of ideas and see how it connects to other mathematical topics. This book makes math more accessible by treating it as a language. It has tips for pronouncing and using mathematical notation, a glossary of commonly used terms in algebra, and a glossary of symbols. Along the way, you’ll discover how different cultures around the world over thousands of years developed many of the mathematical ideas we use today. Since students nowadays can use a variety of tools to handle complex modeling tasks, this book contains technology tips that apply no matter what device you’re using. It also describes strategies for avoiding common mistakes that students make. By working through Practical Algebra, you’ll learn straightforward techniques for solving problems, and understand why these techniques work so you’ll retain what you’ve learned. You (or your students) will come away with better scores on algebra tests and a greater confidence in your ability to do math. Cover Title Page Copyright Page Contents Acknowledgments Introduction Chapter 1 Basic Concepts 1.1 Addition, Subtraction, Multiplication, Division Exercises Questions to Think About 1.2 Order of Operations Exercises Questions to Think About 1.3 Sets and Properties of Numbers Exercises Questions to Think About Chapter 1 Test Chapter 1 Solutions Chapter 1 Test Solutions Chapter 2 Fractions 2.1 Basic Operations Exercises Questions to Think About 2.2 Simplifying Fractions Exercises Questions to Think About Chapter 2 Test Chapter 2 Solutions Chapter 2 Test Solutions Chapter 3 Linear Equations 3.1 Solving One‐Step Equations Exercises Questions to Think About 3.2 Solving Two‐Step Equations Exercises 3.3 Translating Between Words and Symbols Exercises Questions to Think About 3.4 Solving Word Problems Exercises 3.5 Equations with Like Terms Exercises Questions to Think About 3.6 Equations with Variables on Both Sides Exercises Questions to Think About 3.7 Equations with Parentheses Exercises Questions to Think About 3.8 Using Tables to Solve Word Problems Involving Values Exercises 3.9 Transforming Formulas Exercises Chapter 3 Test Chapter 3 Solutions Chapter 3 Test Solutions Chapter 4 Ratios and Proportions 4.1 Expressing Ratios in Simplest Form Exercises 4.2 Using Ratios in the Real World Exercises 4.3 Proportions and Equations with Fractions Exercises Questions to Think About 4.4 Converting Units Exercises 4.5 Percents Exercises Chapter 4 Test Chapter 4 Solutions Chapter 4 Test Solutions Chapter 5 Linear Inequalities 5.1 Basic Principles of Solving Inequalities Exercises 5.2 Representing Inequalities Exercises Questions to Think About 5.3 Solving Linear Inequalities Exercises 5.4 Compound Inequalities Exercises Questions to Think About 5.5 Word Problems with Inequalities Exercises Chapter 5 Test Chapter 5 Solutions Chapter 5 Test Solutions Chapter 6 Functions and Graphs with Two Variables 6.1 Functions and Function Notation Exercises Questions to Think About 6.2 Introduction to Graphing Exercises 6.3 Characteristics of Graphs Exercises Questions to Think About 6.4 Evaluating Functions from Equations and Graphs Exercises Chapter 6 Test Chapter 6 Solutions Chapter 6 Test Solutions Chapter 7 Linear Functions and Their Graphs 7.1 Introduction to Linear Functions Exercises Questions to Think About 7.2 Slope Formula Exercises Questions to Think About 7.3 Determining If an Ordered Pair Is a Solution to an Equation Exercises Questions to Think About 7.4 Writing the Equation of a Line Exercises Questions to Think About 7.5 Solving Systems of Linear Equations by Graphing Exercises Questions to Think About 7.6 Solving Systems of Linear Equations by Substitution Exercises 7.7 Solving Systems of Linear Equations by Elimination Exercises Questions to Think About 7.8 Solving Systems of Linear Inequalities Exercises Questions to Think About 7.9 Word Problems with Systems of Linear Equations and Inequalities Exercises Chapter 7 Test Review Test 1: Chapters 1–7 Chapter 7 Solutions Chapter 7 Test Solutions Review Test 1 Solutions Chapter 8 Operations with Polynomials 8.1 Adding and Subtracting Polynomials Exercises Questions to Think About 8.2 Multiplying Monomials: Rules of Exponents Exercises 8.3 Dividing Monomials: Rules of Exponents Exercises 8.4 Multiplying Polynomials Exercises Questions to Think About 8.5 Dividing Polynomials Exercises Questions to Think About Chapter 8 Test Chapter 8 Solutions Chapter 8 Test Solutions Chapter 9 Quadratic Functions 9.1 Factoring a Monomial from a Polynomial Exercises Questions to Think About 9.2 Factoring by Grouping Exercises Questions to Think About 9.3 Factoring Trinomials Exercises Questions to Think About 9.4 Special Cases of Factoring Exercises Questions to Think About 9.5 Solving Quadratic Equations by Factoring Exercises Questions to Think About 9.6 Radical Expressions Exercises Questions to Think About 9.7 Solving Quadratic Equations by Completing the Square Exercises Questions to Think About 9.8 Solving Quadratic Equations Using the Quadratic Formula Exercises Questions to Think About 9.9 Graphing Quadratic Functions Exercises Questions to Think About 9.10 Solving Quadratic Equations by Graphing Exercises Questions to Think About 9.11 Solving Quadratic Equations by the Mean‐Product Method Exercises Questions to Think About 9.12 Solving Quadratic‐Linear Systems Exercises Questions to Think About 9.13 Using Quadratic Equations to Solve Word Problems Exercises Chapter 9 Test Chapter 9 Solutions Chapter 9 Test Solutions Chapter 10 Exponential Functions 10.1 Graphing Exponential Functions Exercises Questions to Think About 10.2 Using Exponential Functions to Solve Word Problems Exercises Chapter 10 Test Chapter 10 Solutions Chapter 10 Test Solutions Chapter 11 Sequences 11.1 Writing Recursive Formulas for Sequences Exercises Questions to Think About 11.2 Writing Explicit Formulas for Arithmetic and Geometric Sequences Exercises Questions to Think About 11.3 Modeling with Sequences Exercises Chapter 11 Test Chapter 11 Solutions Chapter 11 Test Solutions Chapter 12 Summary of Functions 12.1 Cubic, Square Root, and Cube Root Functions Exercises Questions to Think About 12.2 Piecewise Functions Exercises 12.3 Transformations of Functions Exercises Questions to Think About 12.4 Average Rate of Change of Functions Exercises 12.5 Comparing Functions Exercises Chapter 12 Test Chapter 12 Solutions Chapter 12 Test Solutions Chapter 13 Statistics 13.1 Two‐Way Tables Exercises 13.2 Dotplots and Histograms Exercises Questions to Think About 13.3 Shape, Center, and Spread Exercises Questions to Think About 13.4 Scatterplots and Regression Exercises Questions to Think About Chapter 13 Test Review Test 2: Chapters 8–13 Chapter 13 Solutions Chapter 13 Test Solutions Review Test 2 Solutions Formulas Glossary of Mathematical Symbols Glossary of Mathematical Terms About the Authors Index EULA