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# Let's Review Integrated Algebra

## Paperback(Revised)

^{$}8.95

## Overview

Using many step-by-step demonstration examples, helpful diagrams, informative “Math Fact” summaries, and graphing calculator approaches, this book presents:

Answers are provided for all questions in the exercise sections and all questions on the Regents exam.

## Product Details

ISBN-13: | 9781438000176 |
---|---|

Publisher: | Barron's Educational Series, Incorporated |

Publication date: | 09/01/2012 |

Series: | Let's Review Series |

Edition description: | Revised |

Pages: | 544 |

Product dimensions: | 5.90(w) x 8.90(h) x 1.00(d) |

Age Range: | 14 - 17 Years |

## Read an Excerpt

Using many step-by-step demonstration examples, helpful diagrams, informative “Math Fact” summaries, and graphing calculator approaches, this book presents:

Answers are provided for all questions in the exercise sections and all questions on the Regents exam.

## First Chapter

Using many step-by-step demonstration examples, helpful diagrams, informative “Math Fact” summaries, and graphing calculator approaches, this book presents:

Answers are provided for all questions in the exercise sections and all questions on the Regents exam.

## Table of Contents

Preface vii

Chapter 1 Sets, Operations, and Algebraic Language 1

1.1 Numbers, Variables, and Symbols 1

1.2 Classifying Real Numbers 7

1.3 Learning More About Sets 9

1.4 Operations with Signed Numbers 17

1.5 Properties of Real Numbers 20

1.6 Exponents and Scientific Notation 24

1.7 Order of Operations 32

1.8 Translating Between English and Algebra 35

Chapter 2 Linear Equations and Inequalities 39

2.1 Solving One-Step Equations 39

2.2 Solving Multistep Equations 43

2.3 Solving Equations with Like Terms 47

2.4 Algebraic Modeling 53

2.5 Literal Equations and Formulas 59

2.6 One-Variable Linear Inequalities 66

Chapter 3 Problem Solving and Technology 72

3.1 Problem Solving Strategies 72

3.2 Using a Graphing Calculator 82

3.3 Comparing Mathematical Models 89

Chapter 4 Ratios, Rates, and Proportions 96

4.1 Ratios and Rates 96

4.2 Proportions 102

4.3 Solving Motion Problems 108

4.4 Solving Percent Problems 115

4.5 Probability Ratios 126

Chapter 5 Polynomial Arithmetic and Factoring 134

5.1 Combining Polynomials 134

5.2 Multipying and Dividing Polynomials 137

5.3 Factoring Polynomials 143

5.4 Multiplying and Factoring Special Binomial Pairs 146

5.5 Factoring Quadratic Trinomials 149

5.6 Solving Quadratic Equations by Factoring 154

5.7 Solving Word Problems with Quadratic Equations 159

Chapter 6 Rational Expressions and Equations 165

6.1 Simplifying Rational Expressions 165

6.2 Multiplying and Dividing Rational Expressions 169

6.3 Combining Rational Expressions 172

6.4 Rational Equations and Inequalities 176

Chapter 7 Radicals and Right Triangles 180

7.1 Square and Cube Roots 180

7.2 Operations with Radicals 184

7.3 Combining Radicals 189

7.4 The Pythagorean Theorem 192

7.5 General Methods for Solving Quadratic Equations 201

Chapter 8 Similar Triangles and Trigonometry 207

8.1 Trigonometric Ratios 207

8.2 Solving Problems Using Trigonometry 216

Chapter 9 Area and Volume 223

9.1 Areas of Parallelograms and Triangles 223

9.2 Area of a Trapezoid 228

9.3 Circumference and Area of a Circle 233

9.4 Areas of Overlapping Figures 239

9.5 Surface Area and Volume 245

Chapter 10 Graphing and Writing Equations of Lines 255

10.1 Slope of a Line 255

10.2 Slope-Intercept Form of a Linear Equation 264

10.3 Slopes of Parallel Lines 272

10.4 Graphing Linear Equations 277

10.5 Direct Variation 282

10.6 Point-Slope Form of a Linear Equation 285

Chapter 11 Functions, Graphs, and Models 288

11.1 Function Concepts 288

11.2 Function Graphs as Models 297

11.3 The Absolute Value Function 304

11.4 Creating a Scatter Plot 309

11.5 Finding a Line of Best Fit 313

Chapter 12 Systems of Linear Equations and Inequalities 321

12.1 Solving Linear Systems Graphically 321

12.2 Solving Linear Systems By Substitution 328

12.3 Solving Linear Systems By Combining Equations 335

12.4 Graphing Systems of Linear Inequalities 341

Chapter 13 Quadratic and Exponential Functions 348

13.1 Graphing a Quadratic Function 348

13.2 Solving Quadratic Equations Graphically 360

13.3 Solving a Linear-Quadratic System 368

13.4 Exponential Growth and Decay 374

Chapter 14 Statistics and Visual Representations of Data 381

14.1 Measures of Central Tendency 381

14.2 Box-and-Whisker Plots 390

14.3 Histograms 399

14.4 Cumulative Frequency Histograms 407

Chapter 15 Counting and Probability of Compound Events 417

15.1 Counting Using Permutations 417

15.2 Probability of Compound Events 425

15.3 Probability Formulas for Compound Events 433

Answers and Solution Hints to Practice Exercises 442

Glossary of Integrated Algebra Terms 468

The Integrated Algebra Regents Examination 477

June 2011 Regents Examination 481

Answers 501

June 2012 Regents Examination 503

Answers 523

Index 525

## Reading Group Guide

Preface vii

Chapter 1 Sets, Operations, and Algebraic Language 1

1.1 Numbers, Variables, and Symbols 1

1.2 Classifying Real Numbers 7

1.3 Learning More About Sets 9

1.4 Operations with Signed Numbers 17

1.5 Properties of Real Numbers 20

1.6 Exponents and Scientific Notation 24

1.7 Order of Operations 32

1.8 Translating Between English and Algebra 35

Chapter 2 Linear Equations and Inequalities 39

2.1 Solving One-Step Equations 39

2.2 Solving Multistep Equations 43

2.3 Solving Equations with Like Terms 47

2.4 Algebraic Modeling 53

2.5 Literal Equations and Formulas 59

2.6 One-Variable Linear Inequalities 66

Chapter 3 Problem Solving and Technology 72

3.1 Problem Solving Strategies 72

3.2 Using a Graphing Calculator 82

3.3 Comparing Mathematical Models 89

Chapter 4 Ratios, Rates, and Proportions 96

4.1 Ratios and Rates 96

4.2 Proportions 102

4.3 Solving Motion Problems 108

4.4 Solving Percent Problems 115

4.5 Probability Ratios 126

Chapter 5 Polynomial Arithmetic and Factoring 134

5.1 Combining Polynomials 134

5.2 Multipying and Dividing Polynomials 137

5.3 Factoring Polynomials 143

5.4 Multiplying and Factoring Special Binomial Pairs 146

5.5 Factoring Quadratic Trinomials 149

5.6 Solving Quadratic Equations by Factoring 154

5.7 Solving Word Problems with Quadratic Equations 159

Chapter 6 Rational Expressions and Equations 165

6.1 Simplifying Rational Expressions 165

6.2 Multiplying and Dividing Rational Expressions 169

6.3 Combining Rational Expressions 172

6.4 Rational Equations and Inequalities 176

Chapter 7 Radicals and Right Triangles 180

7.1 Square and Cube Roots 180

7.2 Operations with Radicals 184

7.3 Combining Radicals 189

7.4 The Pythagorean Theorem 192

7.5 General Methods for Solving Quadratic Equations 201

Chapter 8 Similar Triangles and Trigonometry 207

8.1 Trigonometric Ratios 207

8.2 Solving Problems Using Trigonometry 216

Chapter 9 Area and Volume 223

9.1 Areas of Parallelograms and Triangles 223

9.2 Area of a Trapezoid 228

9.3 Circumference and Area of a Circle 233

9.4 Areas of Overlapping Figures 239

9.5 Surface Area and Volume 245

Chapter 10 Graphing and Writing Equations of Lines 255

10.1 Slope of a Line 255

10.2 Slope-Intercept Form of a Linear Equation 264

10.3 Slopes of Parallel Lines 272

10.4 Graphing Linear Equations 277

10.5 Direct Variation 282

10.6 Point-Slope Form of a Linear Equation 285

Chapter 11 Functions, Graphs, and Models 288

11.1 Function Concepts 288

11.2 Function Graphs as Models 297

11.3 The Absolute Value Function 304

11.4 Creating a Scatter Plot 309

11.5 Finding a Line of Best Fit 313

Chapter 12 Systems of Linear Equations and Inequalities 321

12.1 Solving Linear Systems Graphically 321

12.2 Solving Linear Systems By Substitution 328

12.3 Solving Linear Systems By Combining Equations 335

12.4 Graphing Systems of Linear Inequalities 341

Chapter 13 Quadratic and Exponential Functions 348

13.1 Graphing a Quadratic Function 348

13.2 Solving Quadratic Equations Graphically 360

13.3 Solving a Linear-Quadratic System 368

13.4 Exponential Growth and Decay 374

Chapter 14 Statistics and Visual Representations of Data 381

14.1 Measures of Central Tendency 381

14.2 Box-and-Whisker Plots 390

14.3 Histograms 399

14.4 Cumulative Frequency Histograms 407

Chapter 15 Counting and Probability of Compound Events 417

15.1 Counting Using Permutations 417

15.2 Probability of Compound Events 425

15.3 Probability Formulas for Compound Events 433

Answers and Solution Hints to Practice Exercises 442

Glossary of Integrated Algebra Terms 468

The Integrated Algebra Regents Examination 477

June 2011 Regents Examination 481

Answers 501

June 2012 Regents Examination 503

Answers 523

Index 525

## Interviews

Preface vii

Chapter 1 Sets, Operations, and Algebraic Language 1

1.1 Numbers, Variables, and Symbols 1

1.2 Classifying Real Numbers 7

1.3 Learning More About Sets 9

1.4 Operations with Signed Numbers 17

1.5 Properties of Real Numbers 20

1.6 Exponents and Scientific Notation 24

1.7 Order of Operations 32

1.8 Translating Between English and Algebra 35

Chapter 2 Linear Equations and Inequalities 39

2.1 Solving One-Step Equations 39

2.2 Solving Multistep Equations 43

2.3 Solving Equations with Like Terms 47

2.4 Algebraic Modeling 53

2.5 Literal Equations and Formulas 59

2.6 One-Variable Linear Inequalities 66

Chapter 3 Problem Solving and Technology 72

3.1 Problem Solving Strategies 72

3.2 Using a Graphing Calculator 82

3.3 Comparing Mathematical Models 89

Chapter 4 Ratios, Rates, and Proportions 96

4.1 Ratios and Rates 96

4.2 Proportions 102

4.3 Solving Motion Problems 108

4.4 Solving Percent Problems 115

4.5 Probability Ratios 126

Chapter 5 Polynomial Arithmetic and Factoring 134

5.1 Combining Polynomials 134

5.2 Multipying and Dividing Polynomials 137

5.3 Factoring Polynomials 143

5.4 Multiplying and Factoring Special Binomial Pairs 146

5.5 Factoring Quadratic Trinomials 149

5.6 Solving Quadratic Equations by Factoring 154

5.7 Solving Word Problems with Quadratic Equations 159

Chapter 6 Rational Expressions and Equations 165

6.1 Simplifying Rational Expressions 165

6.2 Multiplying and Dividing Rational Expressions 169

6.3 Combining Rational Expressions 172

6.4 Rational Equations and Inequalities 176

Chapter 7 Radicals and Right Triangles 180

7.1 Square and Cube Roots 180

7.2 Operations with Radicals 184

7.3 Combining Radicals 189

7.4 The Pythagorean Theorem 192

7.5 General Methods for Solving Quadratic Equations 201

Chapter 8 Similar Triangles and Trigonometry 207

8.1 Trigonometric Ratios 207

8.2 Solving Problems Using Trigonometry 216

Chapter 9 Area and Volume 223

9.1 Areas of Parallelograms and Triangles 223

9.2 Area of a Trapezoid 228

9.3 Circumference and Area of a Circle 233

9.4 Areas of Overlapping Figures 239

9.5 Surface Area and Volume 245

Chapter 10 Graphing and Writing Equations of Lines 255

10.1 Slope of a Line 255

10.2 Slope-Intercept Form of a Linear Equation 264

10.3 Slopes of Parallel Lines 272

10.4 Graphing Linear Equations 277

10.5 Direct Variation 282

10.6 Point-Slope Form of a Linear Equation 285

Chapter 11 Functions, Graphs, and Models 288

11.1 Function Concepts 288

11.2 Function Graphs as Models 297

11.3 The Absolute Value Function 304

11.4 Creating a Scatter Plot 309

11.5 Finding a Line of Best Fit 313

Chapter 12 Systems of Linear Equations and Inequalities 321

12.1 Solving Linear Systems Graphically 321

12.2 Solving Linear Systems By Substitution 328

12.3 Solving Linear Systems By Combining Equations 335

12.4 Graphing Systems of Linear Inequalities 341

Chapter 13 Quadratic and Exponential Functions 348

13.1 Graphing a Quadratic Function 348

13.2 Solving Quadratic Equations Graphically 360

13.3 Solving a Linear-Quadratic System 368

13.4 Exponential Growth and Decay 374

Chapter 14 Statistics and Visual Representations of Data 381

14.1 Measures of Central Tendency 381

14.2 Box-and-Whisker Plots 390

14.3 Histograms 399

14.4 Cumulative Frequency Histograms 407

Chapter 15 Counting and Probability of Compound Events 417

15.1 Counting Using Permutations 417

15.2 Probability of Compound Events 425

15.3 Probability Formulas for Compound Events 433

Answers and Solution Hints to Practice Exercises 442

Glossary of Integrated Algebra Terms 468

The Integrated Algebra Regents Examination 477

June 2011 Regents Examination 481

Answers 501

June 2012 Regents Examination 503

Answers 523

Index 525

## Recipe

Preface vii

Chapter 1 Sets, Operations, and Algebraic Language 1

1.1 Numbers, Variables, and Symbols 1

1.2 Classifying Real Numbers 7

1.3 Learning More About Sets 9

1.4 Operations with Signed Numbers 17

1.5 Properties of Real Numbers 20

1.6 Exponents and Scientific Notation 24

1.7 Order of Operations 32

1.8 Translating Between English and Algebra 35

Chapter 2 Linear Equations and Inequalities 39

2.1 Solving One-Step Equations 39

2.2 Solving Multistep Equations 43

2.3 Solving Equations with Like Terms 47

2.4 Algebraic Modeling 53

2.5 Literal Equations and Formulas 59

2.6 One-Variable Linear Inequalities 66

Chapter 3 Problem Solving and Technology 72

3.1 Problem Solving Strategies 72

3.2 Using a Graphing Calculator 82

3.3 Comparing Mathematical Models 89

Chapter 4 Ratios, Rates, and Proportions 96

4.1 Ratios and Rates 96

4.2 Proportions 102

4.3 Solving Motion Problems 108

4.4 Solving Percent Problems 115

4.5 Probability Ratios 126

Chapter 5 Polynomial Arithmetic and Factoring 134

5.1 Combining Polynomials 134

5.2 Multipying and Dividing Polynomials 137

5.3 Factoring Polynomials 143

5.4 Multiplying and Factoring Special Binomial Pairs 146

5.5 Factoring Quadratic Trinomials 149

5.6 Solving Quadratic Equations by Factoring 154

5.7 Solving Word Problems with Quadratic Equations 159

Chapter 6 Rational Expressions and Equations 165

6.1 Simplifying Rational Expressions 165

6.2 Multiplying and Dividing Rational Expressions 169

6.3 Combining Rational Expressions 172

6.4 Rational Equations and Inequalities 176

Chapter 7 Radicals and Right Triangles 180

7.1 Square and Cube Roots 180

7.2 Operations with Radicals 184

7.3 Combining Radicals 189

7.4 The Pythagorean Theorem 192

7.5 General Methods for Solving Quadratic Equations 201

Chapter 8 Similar Triangles and Trigonometry 207

8.1 Trigonometric Ratios 207

8.2 Solving Problems Using Trigonometry 216

Chapter 9 Area and Volume 223

9.1 Areas of Parallelograms and Triangles 223

9.2 Area of a Trapezoid 228

9.3 Circumference and Area of a Circle 233

9.4 Areas of Overlapping Figures 239

9.5 Surface Area and Volume 245

Chapter 10 Graphing and Writing Equations of Lines 255

10.1 Slope of a Line 255

10.2 Slope-Intercept Form of a Linear Equation 264

10.3 Slopes of Parallel Lines 272

10.4 Graphing Linear Equations 277

10.5 Direct Variation 282

10.6 Point-Slope Form of a Linear Equation 285

Chapter 11 Functions, Graphs, and Models 288

11.1 Function Concepts 288

11.2 Function Graphs as Models 297

11.3 The Absolute Value Function 304

11.4 Creating a Scatter Plot 309

11.5 Finding a Line of Best Fit 313

Chapter 12 Systems of Linear Equations and Inequalities 321

12.1 Solving Linear Systems Graphically 321

12.2 Solving Linear Systems By Substitution 328

12.3 Solving Linear Systems By Combining Equations 335

12.4 Graphing Systems of Linear Inequalities 341

Chapter 13 Quadratic and Exponential Functions 348

13.1 Graphing a Quadratic Function 348

13.2 Solving Quadratic Equations Graphically 360

13.3 Solving a Linear-Quadratic System 368

13.4 Exponential Growth and Decay 374

Chapter 14 Statistics and Visual Representations of Data 381

14.1 Measures of Central Tendency 381

14.2 Box-and-Whisker Plots 390

14.3 Histograms 399

14.4 Cumulative Frequency Histograms 407

Chapter 15 Counting and Probability of Compound Events 417

15.1 Counting Using Permutations 417

15.2 Probability of Compound Events 425

15.3 Probability Formulas for Compound Events 433

Answers and Solution Hints to Practice Exercises 442

Glossary of Integrated Algebra Terms 468

The Integrated Algebra Regents Examination 477

June 2011 Regents Examination 481

Answers 501

June 2012 Regents Examination 503

Answers 523

Index 525