Guided Notebook with Integrated Review Worksheets for Intermediate Algebra

Description

Focuses on preparing students for their next course – often College Algebra – with a focus on STEM paths

• Heading toward College Algebra features make connections between the math students are learning, and how it will be relevant or taken further in future math courses like College Algebra or Calculus. Instructors can choose which topics they feel would most interest or engage their students. References on using Heading toward College Algebra are available in the Instructor’s Resource Manual as well.
  

• STEM-labeled material is integrated throughout the text, allowing students to know exactly why they are learning the material and how it will be applied in future classes. Instructors can choose which disciplines or topics they think would motivate their students most.
• STEM applications and exercises are integrated throughout exercise sets. These STEM-oriented exercises show that the math topics students are learning are highly relevant to future courses.
  
• STEM-driven topics focus on the mathematical skills necessary for future STEM courses, such as Chemistry. George talked to instructors across the STEM fields to land on the most necessary topics to include. In some cases, this means a special emphasis is placed on a mathematical topic, whereas in other cases, topics have actually been pulled into this course that you might not typically experience in Intermediate Algebra.
  
• STEM Spotlights at the end of each chapter highlight a particular field, ranging from Biology to Game Design. Each Spotlight includes interviews with discipline and career experts, as well as facts about the discipline to interest and motivate students, such as median salary for a career in that field. These Spotlights may motivate students who already know their major, but also can inspire future STEM students to pursue and complete their path as well.
  
• Corresponding STEM Spotlight videos and video assessment questions are assignable in MyLab Math, and build upon these Spotlights in the text.
• STEM Activities are available in the Guided Notebook student workbook, giving instructors the option to expand students’ exploration of STEM disciplines.
• A 6-step problem-solving strategy, based on Polya’s groundbreaking How to Solve It, lays the foundation for solving applied problems. 

Woodbury hallmarks bring George’s teaching philosophy to each student

• George Woodbury’s Cycles of Learning–Discover, Engage, Reflect–guide students through a three-step learning approach. Based on his own experience teaching students, George believes that discovering, engaging, and then reflecting will lead students to greater conceptual understanding when learning mathematics.
• Discover: Within each section, students “discover”each objective’s concepts through worked-out examples with detailed explanations. Students can use Example videos in MyLab Math that explain the “why” behind a particular problem solving method.
• Engage: Examples are followed by Quick Check exercises in the text, with corresponding videos in MyLab Math.  The Quick Check A exercises and corresponding videos ask students to “engage” by asking them questions and prompt them to think about the next step in solving a problem, reinforcing the problem-solving method and procedure.
• Reflect: The Quick Check B exercises and corresponding videos give students the chance to “reflect”, encouraging students to solve the problem on their own while reflecting on what they have learned.
• Designated Engage and Reflect exercises are included in the exercise sets.

• Integrated Review of necessary skills precedes each section of the text where relevant, providing examples and practice exercises on key skills needed for that section. Some review topics are revisited more than once, providing a recursive learning experience for students.
• In MyLab Math, Integrated Review is expanded upon with worksheets and videos for a quick refresher. Premade Integrated Review assignments include a Skills Check and personalized homework, so students practice only the skills they need review on.
• An “early-and-often” approach to graphing and functions builds students’ confidence with the topic. Functions are first introduced in Chapter 2, and through Chapter 7 the author aims to make students comfortable with them before more difficult material.
• Exercise sets go beyond skill and drill procedures, with unique problem types to reinforce concepts, including Vocabulary exercises, Mixed Practice, and Writing in Mathematics exercises.

Also available with MyLab Math 

MyLab™ is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. Bringing George Woodbury’s voice and approach into the MyLab course — through video support, relevant exercises, and STEM-driven resources — gives students the support to be successful on their STEM pathway.  Learn more about MyLab Math.

Reach every student with MyLab 

• A video program in MyLab Math is 100% presented by George Woodbury himself, ensuring complete consistency in approach and language.
• Objective videos cover each objective in the text, teaching the overarching concepts
  
• Example videos correspond to every objective in the text. Example videos guide students through the discovery of concepts and explaining the “why” behind a problem solving method.
  
• Quick Check videos correspond to every Quick Check exercise in the text. Quick Check A videos engage students by asking questions and prompting them to think about the next step in solving a problem. Quick Check B videos encourage students to solve a problem on their own and reflect on what they have learned.
• STEM videos give background about STEM topics that are introduced in the text, and includes strategies for working with problems related to the topic.
• Heading toward College Algebra videos give background about math topics that I have included that go beyond what is typically covered in intermediate algebra, including ideas from college algebra, trigonometry, statistics, and calculus. Strategies for working with problems related to these topics is also provided.
• Modeling videos will walk through how to model functions (linear, quadratic, square root, exponential) from data, showing how to use Desmos as well as how to interpret/use the results.
• Calculator Videos show how to use the TI-84 calculator for new or difficult calculations in an associated example.
• Integrated Review exercises and examples from the text are expanded upon in MyLab Math, with pre-assigned Skills Check and Personalized Homework assignments, as well as videos and worksheets to help students review topics.
• Bring STEM fields to life with STEM-driven MyLab resources, such as exercises and videos.
• STEM Spotlight videos, in the MyLab Math course, expand upon the in-text feature, and provide more insight into the disciplines and careers featured in the book, as well as captivate students’ interest with fun and interesting facts displayed in a dynamic way. Follow-up STEM Video Assessment Questions are available in MyLab Math so that instructors can easily assign a follow-up homework assignment to assess students completion and comprehension of the material and video.
• Exercises with a STEM focus, which are labeled with a STEM icon in the text, are easy to find in the Assignment Manager with a “STEM” callout.
• For instructors using this text for the first time, implementation resources help to make set-up a cinch.
• Enhanced Sample Assignments make course set-up easier by giving instructors a starting point for each section. Each assignment, hand-picked by George Woodbury to align with the text, includes a thoughtful mix of question types – including STEM exercises, Writing in Math exercises, and Mixed Practice.
• George Woodbury’s Guide to MyLab Math is included in the Instructor’s Resource Manual. In this resource, George includes his tips for setting up homework, incorporating videos, using the Cycles of Learning, and much more!
• The Guided Notebook complements the work students do in their text and MyLab.
• This student workbook is available for each section of the text, pointing students to useful videos for each objective, providing practice problems, and giving students a place to take notes and stay organized.
• STEM Activities in the workbook can be used in conjunction with the STEM topics in each section, and each chapter’s STEM Spotlight videos.
• Integrated Review is expanded upon in the workbook, giving students more practice on the prerequisite skills included in the Integrated Review feature in the text.
• The Guided Notebook is available for download in MyLab Math, or as a printed loose-leaf workbook that can be packaged with the text or a MyLab Math access code.
• Mathematicians in History is an additional resource available to students in the MyLab Math course that gives students the context of past STEM experts who made a difference in the math field.  Instructor implementation resources are also available in George Woodbury’s Guide to MyLab Math.

For each section of the text the Guided Notebook is available to point students to useful videos associated with the section objectives, to provide extra practice problems, and to give students a place to take notes and stay organized throughout the course. Additionally, there are STEM activities that can be used in conjunction with the STEM Discipline & Career Spotlight videos and text, and additional review practice problems to expound on the integrated review that is incorporated in the text.

George Woodbury earned a bachelor’s degree in Mathematics from the University of California—Santa Barbara and a master’s degree in Mathematics from California State University—Northridge. He currently teaches at College of the Sequoias in Visalia, CA, just outside of Fresno. George has been honored as an instructor by both his students and his colleagues. Aside from teaching and writing, George served as the department chair of the math/engineering division from 1999 through 2004. He has been a user of MyLabTM Math and Statistics since their inception, continually coming up with creative ways to integrate his teaching methods with technology. He actively blogs on georgewoodbury.com about thoughts on math, statistics, teaching, and study skills.

1. Review of Real Numbers
   • R.1 Integers, Opposites, and Absolute Value
   • R.2 Exponents and Order of Operations
2. Linear and Absolute Value Equations and Inequalities
   • 1.1 Introduction to Algebra
   • 1.2 Linear Equations
   • 1.3 Problem Solving: Applications of Linear Equations
   • 1.4 Proportions and Dimensional Analysis
   • 1.5 Absolute Value Equations
   • 1.6 Linear Inequalities
   • 1.7 Absolute Value Inequalities
3. Graphing Linear Equations
   • 2.1 The Rectangular Coordinate System; Equations in Two Variables
   • 2.2 Slope of a Line
   • 2.3 Equations of Lines
   • 2.4 Linear Inequalities
   • 2.5 Linear Functions
   • 2.6 Absolute Value Functions
4. Systems of Equations
   • 3.1 Systems of Two Equations in Two Unknowns
   • 3.2 Applications of Systems of Equations
   • 3.3 Systems of Linear Inequalities
   • 3.4 Systems of Three Equations in Three Unknowns
   • 3.5 Using Matrices to Solve Systems of Equations
   • 3.6 Determinants and Cramer’s Rule
5. Exponents, Polynomials, and Factoring Polynomials
   • 4.1 Exponents
   • 4.2 Negative Exponents; Scientific Notation
   • 4.3 Polynomials; Addition, Subtraction, and Multiplication of Polynomials
   • 4.4 Polynomial Division
   • 4.5 An Introduction to Factoring; The Greatest Common Factor; Factoring by Grouping
   • 4.6 Factoring Trinomials of Degree 2
   • 4.7 Factoring Special Binomials
   • 4.8 Factoring Polynomials: A General Strategy
   • 4.9 Solving Quadratic Equations By Factoring

• Chapters 1—4 Cumulative Review

1. Rational Expressions and Equations
   • 5.1 Rational Expressions and Functions
   • 5.2 Multiplication and Division of Rational Expressions
   • 5.3 Addition and Subtraction of Rational Expressions
   • 5.4 Complex Fractions
   • 5.5 Rational Equations
   • 5.6 Applications of Rational Equations
2. Radical Expressions and Equations
   • 6.1 Square Roots; Radical Notation
   • 6.2 Rational Exponents
   • 6.3 Simplifying, Adding, and Subtracting Radical Expressions
   • 6.4 Multiplying and Dividing Radical Expressions
   • 6.5 Radical Equations and Applications of Radical Equations
   • 6.6 The Complex Numbers
3. Quadratic Equations
   • 7.1 Solving Quadratic Equations by Extracting Square Roots; Completing the Square
   • 7.2 The Quadratic Formula
   • 7.3 Equations That Are Quadratic in Form
   • 7.4 Graphing Quadratic Equations and Quadratic Functions
   • 7.5 Applications Using Quadratic Equations
   • 7.6 Quadratic and Rational Inequalities
   • 7.7 Other Functions and Their Graphs

• Chapters 5—7 Cumulative Review

1. Logarithmic and Exponential Functions
   • 8.1 The Algebra of Functions
   • 8.2 Inverse Functions
   • 8.3 Exponential Functions
   • 8.4 Logarithmic Functions
   • 8.5 Properties of Logarithms
   • 8.6 Exponential and Logarithmic Equations
   • 8.7 Applications of Exponential and Logarithmic Functions
   • 8.8 Graphing Exponential and Logarithmic Functions
2. Conic Sections
   • 9.1 Parabolas
   • 9.2 Circles
   • 9.3 Ellipses
   • 9.4 Hyperbolas
   • 9.5 Nonlinear Systems of Equations
3. Sequences, Series, and the Binomial Theorem
   • 10.1 Sequences and Series
   • 10.2 Arithmetic Sequences and Series
   • 10.3 Geometric Sequences and Series
   • 10.4 The Binomial Theorem

• Chapters 8—10 Cumulative Review

Answers to Selected Exercises*

*Additional Instructor’s Answers are given in the Annotated Instructor’s Edition.

Integrated Review Topics:

• Chapter 1
  • Build variable expressions – sections 1.3, 1.6
  • Evaluate variable expressions – 1.2
  • Find the absolute value of an integer – 1.5, 1.7
  • Find the least common multiple (LCM) of two natural numbers – 1.2
  • Graph integers on a number line – 1.6
  • Identify linear equations with no solution – 1.5
  • Multiply fractions – 1.4
  • Perform arithmetic operations with integers – 1.2
  • Present the solutions of an inequality on a number line and using interval notation – 1.7
  • Simplify a fraction to lowest terms – 1.2, 1.4
  • Simplify variable expressions – 1.2
  • Solve compound linear inequalities – 1.7
  • Solve linear equations using the five-step general strategy – 1.3, 1.5, 1.6
  • Solve linear equations using the multiplication property of equality – 1.4
  • Solve linear inequalities – 1.7
• Chapter 2
  • Determine whether a value is a solution of an equation – 2.1
  • Determine whether an ordered pair is a solution of an equation in two variables – 2.4
  • Determine whether two lines are parallel – 2.3
  • Determine whether two lines are perpendicular – 2.3
  • Evaluate variable expressions – 2.5
  • Find the absolute value of an integer – 2.6
  • Find the slope of a line passing through two points using the slope formula – 2.3
  • Graph a line using its slope and y-intercept – 2.4, 2.5
  • Graph horizontal lines and vertical lines – 2.4
  • Graph integers on a number line – 2.1
  • Graph linear equations using their intercepts – 2.4
  • Graph linear functions – 2.6
  • Interpret the slope and y-intercept in real-world applications – 2.5
  • Plot ordered pairs on a rectangular coordinate plane – 2.2
  • Simplify a fraction to lowest terms – 2.2
  • Solve linear equations using the five-step general strategy – 2.1
  • Solve literal equations for a specified variable – 2.2, 2.3
  • Subtract integers – 2.2
• Chapter 3
  • Build variable expressions – 3.2
  • Complete ordered pairs for a linear equation in two variables – 3.1, 3.5
  • Create an augmented matrix for a system of three equations in three unknowns – 3.6
  • Create an augmented matrix for a system of two equations in two unknowns – 3.6
  • Determine if an ordered pair is a solution of an equation – 3.1
  • Determine if an ordered pair is a solution to a system of equations – 3.4
  • Graph a line using its slope and y-intercept – 3.3
  • Graph a line using the most efficient strategy – 3.1
  • Graph a linear inequality in two variables – 3.3
  • Graph linear equations using their intercepts 3.3
  • Identify linear equations that are contradictions or identities – 3.1
  • Solve linear equations containing fractions – 3.1
  • Solve linear equations using the five-step general strategy – 3.1
  • Solve systems of linear equations by using the addition method – 3.2
  • Solve systems of linear equations by using the substitution method – 3.2
  • Solve systems of linear equations using the addition method – 3.4, 3.5
  • Solve systems of three linear equations in three unknowns – 3.5
• Chapter 4
  • Evaluate functions – 4.1
  • Factor a difference of squares – 4.8
  • Factor a difference or sum of cubes – 4.8
  • Factor a polynomial by grouping – 4.6, 4.8
  • Factor a trinomial of the form ax² + bx + c – 4.8
  • Factor a trinomial of the form x² + bx + c – 4.8
  • Factor the GCF out of each term of a polynomial – 4.6, 4.7, 4.8
  • Find special products – 4.7
  • Find the prime factorization of a natural number – 4.5
  • Multiply a monomial by a polynomial – 4.4, 4.5
  • Multiply polynomials – 4.4, 4.5, 4.6
  • Perform arithmetic operations with decimals – 4.2
  • Simplify a fraction to lowest terms – 4.1
  • Simplify exponents – 4.1
  • Simplify variable expressions – 4.3
  • Solve linear equations containing fractions – 4.9
  • Solve linear equations using the five-step general strategy – 4.9
  • Solve problems involving consecutive integers – 4.9
  • Subtract integers – 4.2
  • Understand the strategy for factoring a general polynomial – 4.9
  • Use the distributive property of real numbers – 4.3
  • Use the product rule for exponents – 4.3
  • Use the quotient rule for exponents – 4.2, 4.4
  • Use unit factors for dimensional analysis – 4.2
• Chapter 5
  • Add and subtract fractions with the same denominator – 5.3
  • Add and subtract fractions with unlike denominators – 5.3
  • Add and subtract polynomials – 5.3
  • Divide fractions – 5.2
  • Evaluate algebraic expressions – 5.1
  • Evaluate functions – 5.1
  • Factor polynomials – 5.1
  • Find the least common denominator (LCD) of two or more rational expressions – 5.4
  • Find the least common multiple (LCM) of two natural numbers – 5.4
  • Identify factors that are opposites of each other – 5.2
  • Multiply fractions – 5.2
  • Simplify a fraction to lowest terms – 5.1
  • Simplify rational expressions to lowest terms – 5.2, 5.3, 5.4
  • Solve a quadratic equation by factoring – 5.1, 5.5
  • Solve linear equations containing fractions – 5.5
  • Solve literal equations for a specified variable – 5.5
  • Solve linear equations using the five-step general strategy – 5.1, 5.5
  • Solve problems involving motion – 5.6
  • Solve rational equations – 5.6
  • Understand the six steps for solving applied problems – 5.6
• Chapter 6
  • Evaluate functions – 6.1
  • Find nth roots – 6.2, 6.3
  • Find the prime factorization of a number – 6.1, 6.3
  • Find the square root of a number – 6.2, 6.3, 6.6
  • Multiply polynomials – 6.4, 6.5, 6.6
  • Multiply radical expressions – 6.4
  • Rationalize a denominator with one term – 6.6
  • Rationalize a denominator with two terms – 6.6
  • Simplify variable expressions – 6.3, 6.4, 6.6
  • Simplify expressions using the rules of exponents – 6.2
  • Solve a quadratic equation by factoring – 6.5
  • Solve linear equations – 6.5
  • Solve linear inequalities – 6.1
  • Use the power rule for exponents – 6.1
• Chapter 7
  • Determine the domain and range of a function from its graph – 7.7
  • Factor trinomials of degree 2 – 7.1
  • Find the square root of a number – 7.1, 7.2, 7.5
  • Find the x- and y-intercepts of a line from its equation – 7.4
  • Graph absolute value functions by shifting – 7.4, 7.7
  • Graph quadratic functions of the form f(x) = a(x – h)² + k by shifting – 7.7
  • Present the solutions of an inequality on a number line and using interval notation – 7.6
  • Solve a quadratic equation by factoring – 7.1, 7.2
  • Solve applied geometry problems – 7.5
  • Solve applied work-rate problems – 7.3
  • Solve radical equations – 7.3
  • Solve rational equations – 7.3
  • Solve quadratic equations by completing the square – 7.2, 7.4
  • Solve quadratic equations by factoring or by using the quadratic formula – 7.4, 7.5, 7.6
  • Solve quadratic equations by using the quadratic formula – 7.3
• Chapter 8
  • Add and subtract polynomials – 8.1
  • Convert an equation from logarithmic form to exponential form – 8.6
  • Evaluate exponential functions – 8.4
  • Evaluate functions – 8.1, 8.3
  • Evaluate logarithms and logarithmic functions – 8.5
  • Find the composite function of two functions f(x) and g(x) – 8.2
  • Find the inverse of a one-to-one function – 8.6
  • Graph exponential functions – 8.4, 8.8
  • Graph linear functions – 8.3
  • Graph logarithmic functions – 8.8
  • Interpret graphs of functions – 8.3
  • Multiply polynomials – 8.1
  • Simplify expressions with exponents – 8.4
  • Simplify rational expressions to lowest terms – 8.1
  • Solve a logarithmic equation by converting it to exponential form – 8.7
  • Solve an exponential equation by using logarithms – 8.7
  • Solve linear equations – 8.6
  • Solve literal equations for a specified variable – 8.2
  • Solve quadratic equations by factoring – 8.6
  • Use the product and quotient rules for logarithms – 8.6
  • Use the product rule for exponents – 8.5
  • Use the quotient rule for exponents – 8.5
• Chapter 9
  • Find a vertex by completing the square – 9.2
  • Find the center of a circle and its radius by completing the square – 9.3
  • Find the center of an ellipse and the lengths of its axes by completing the square – 9.4
  • Find the square root of a number – 9.2, 9.3
  • Graph circles centered at a point (h, k) – 9.3
  • Graph ellipses centered at a point (h, k) – 9.4
  • Graph equations of the form y = a(x – h)² + k – 9.2
  • Graph quadratic equations in standard form – 9.1
  • Graph quadratic functions of the form f1×2 = 1x – h22 + k by shifting – 9.1
  • Solve a quadratic equation by factoring – 9.1
  • Solve quadratic equations by completing the square – 9.1
  • Solve quadratic equations by extracting square roots – 9.1
  • Solve quadratic equations by using the quadratic formula – 9.1
  • Solve systems of linear equations by using the addition method – 9.5
  • Solve systems of linear equations by using the substitution method – 9.5
• Chapter 10
  • Add, subtract, multiply, and divide integers – 10.1
  • Evaluate functions – 10.1
  • Find partial sums of a sequence – 10.2
  • Find partial sums of an arithmetic sequence – 10.3
  • Find special products – 10.4
  • Find the general term of a sequence – 10.2
  • Find the general term of an arithmetic sequence – 10.3
  • Multiply polynomials – 10.4