Interactive Developmental Mathematics -- Life of Edition Standalone Access Card

by Rockswold, Gary K.; Krieger, Terry A.

• ISBN13: 9780134380001
• ISBN10: 0134380002
• Edition: 1st
• Format: Access Card
• Copyright: 2016-03-31
• Publisher: Pearson

Summary

For courses in developmental mathematics.

 

Giving Meaning to the Numbers

Gary Rockswold and Terry Krieger give meaning to the numbers that students encounter by developing concepts in context through the use of applications, multiple representations, and visualization. By seeing the concept in context before being given the mathematical abstraction, students make math part of their own experiences instead of just memorizing techniques. Research is showing that this method is essential to empowering students. Seamlessly integrated real-life connections, graphs, tables, charts, and meaningful data help students deepen understanding and prepare for future math courses—and life—by teaching them critical thinking and problem-solving skills.

 

Built in MyMathLab

Interactive Developmental Mathematics offers a completely digital experience, built by Gary Rockswold and Terry Krieger from the ground up in MyMathLab to model the way today’s students learn and interact online. MyMathLab is an online homework, tutorial, and assessment program designed to engage students and lead them to master the concepts and skills they need to succeed in math. Within its guided learning environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them master course material and understand difficult concepts.

 

Author Biography

Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over two decades. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family. Additional information about Gary Rockswold can be found atwww.garyrockswold.net.

 

Terry Krieger has taught mathematics for 20 years at the middle school, high school, vocational, community college and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University - Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry currently lives and works in Rochester, Minnesota. He has been involved with various aspects of mathematics textbook publication throughout his career in mathematics education and has joined his friend Gary Rockswold as coauthor of a developmental math series published by Pearson Education. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing. Additional information about Terry Krieger can be found at www.terrykrieger.net.

 

Table of Contents

1 Whole Numbers

1.1 Introduction to Whole Numbers

1. Reviewing Natural Numbers and Whole Numbers

2. Understanding Place Value

3. Writing Whole Numbers in Word Form

4. Writing Whole Numbers in Expanded Form

5. Graphing Whole Numbers on the Number Line

6. Reading Bar Graphs and Line Graphs

7. Reading Spider Charts

8. Reading Tables

 

1.2 Adding and Subtracting Whole Numbers; Perimeter

1. Adding Whole Numbers without Regrouping

2. Adding Whole Numbers with Regrouping

3. Using Properties of Addition

4. Recognizing Words Associated with Addition

5. Subtracting Whole Numbers without Regrouping

6. Subtracting Whole Numbers with Regrouping

7. Using Properties of Subtraction

8. Recognizing Words Associated with Subtraction

9. Solving Equations Involving Addition and Subtraction

10. Solving Perimeter and Other Applications Involving Addition and Subtraction

 

1.3 Multiplying and Dividing Whole Numbers; Area

1. Multiplying Whole Numbers

2. Using Properties of Multiplication

3. Multiplying Larger Whole Numbers

4. Recognizing Words Associated with Multiplication

5. Dividing Whole Numbers

6. Using Properties of Division

7. Performing Long Division

8. Recognizing Words Associated with Division

9. Solving Equations Involving Multiplication and Division

10. Solving Area and Other Applications Involving Multiplication and Division

 

1.4 Exponents, Variables, and Algebraic Expressions

1. Understanding Exponential Notation

2. Squaring and Cubing Numerical Expressions

3. Finding Powers of Ten

4. Using Variables

5. Recognizing Algebraic Expressions

6. Evaluating Formulas

7. Translating Words to Expressions and Formulas

8. Solving Equations

 

1.5 Rounding and Estimating; Square Roots

1. Rounding Whole Numbers

2. Estimating and Approximating

3. Solving Problems Using Estimation

4. Estimating Data Graphically

5. Finding Square Roots

 

1.6 Order of Operations

1. Applying the Order of Operations Agreement

2. Evaluating Algebraic Expressions

3. Translating Words to Symbols

 

1.7 More with Equations and Problem Solving

1. Identifying Equations and Expressions

2. Recognizing Like Terms

3. Combining Like Terms

4. Applying Arithmetic Properties

5. Checking a Solution to an Equation

6. Applying a Problem-Solving Strategy

 

2 Integers

2.1 Integers and the Number Line

1. Introducing Signed Numbers

2. Finding Opposites

3. Working with Integers and Their Graphs

4. Comparing Integers

5. Finding Absolute Value

6. Solving Applications Involving Integers

 

2.2 Adding Integers

1. Adding Integers That Have Like Signs

2. Adding Integers That Have Unlike Signs

3. Recognizing the Addition Properties for Integers

4. Adding Integers Using a Number Line

5. Adding Integers Using Symbols

6. Solving Applications Involving Addition of Integers

 

2.3 Subtracting Integers

1. Subtracting Integers

2. Adding and Subtracting Integers

3. Subtracting Integers Using a Number Line

4. Subtracting Integers Using Symbols

5. Solving Applications Involving Subtraction of Integers

 

2.4 Multiplying and Dividing Integers

1. Multiplying Integers

2. Recognizing the Multiplication Properties for Integers

3. Multiplying More than Two Integer Factors

4. Dividing Integers

5. Finding Square Roots of Integers

6. Solving Applications Involving Multiplication and Division of Integers

 

2.5 Order of Operations; Averages

1. Using the Order of Operations Agreement with Integers

2. Evaluating Exponential Expressions

3. Evaluating Algebraic Expressions with Integers

4. Finding Averages

 

2.6 Solving Equations That Have Integer Solutions

1. Checking a Solution

2. Solving Equations Using Guess-and-Check

3. Solving Equations Using Tables of Values

4. Solving Equations That Have Integer Solutions Graphically

 

3 Algebraic Expressions and Linear Equations

3.1 Simplifying Algebraic Expressions

1. Reviewing Algebraic Expressions

2. Combining Expressions That Have Like Terms

3. Adding Expressions

4. Finding the Opposite of an Expression

5. Subtracting Expressions

6. Multiplying Expressions

7. Simplifying Expressions

 

3.2 Translating Words to Expressions and Equations

1. Translating Words to Expressions

2. Translating Words to Equations

 

3.3 Properties of Equality

1. Finding Solutions and Equivalent Equations

2. Using the Addition Property of Equality

3. Using the Multiplication Property of Equality

 

3.4 Solving Linear Equations in One Variable

1. Identifying Linear Equations in One Variable

2. Solving Linear Equations Symbolically

3. Solving Linear Equations Numerically

4. Solving Linear Equations Graphically

 

3.5 Applications and Problem Solving

1. Reviewing Steps for Problem Solving

2. Solving Applications Involving Linear Equations in One Variable

 

4 Fractions

4.1 Introduction to Fractions and Mixed Numbers

1. Reviewing Fractions and Fractional Parts

2. Introducing Rational Numbers

3. Reviewing Improper Fractions and Mixed Numbers

4. Writing Improper Fractions as Mixed Numbers

5. Writing Mixed Numbers as Improper Fractions

6. Graphing Fractions and Mixed Numbers

 

4.2 Prime Factorization and Lowest Terms

1. Using Divisibility Tests

2. Finding Prime Factorizations of Numbers

3. Identifying and Writing Equivalent Fractions

4. Simplifying Fractions to Lowest Terms

5. Comparing Fractions

6. Simplifying Rational Expressions

 

4.3 Multiplying and Dividing Fractions

1. Multiplying Fractions

2. Multiplying Rational Expressions

3. Evaluating Powers and Square Roots of Fractions

4. Dividing Fractions and Rational Expressions

5. Solving Applications Involving Fractions

 

4.4 Adding and Subtracting Fractions—Like Denominators

1. Adding Fractions—Like Denominators

2. Subtracting Fractions—Like Denominators

3. Adding and Subtracting Rational Expressions

4. Solving Applications Involving Addition and Subtraction of Fractions

4.5 Adding and Subtracting Fractions—Unlike Denominators

1. Finding the Least Common Multiple (LCM)

2. Finding the Least Common Denominator (LCD)

3. Adding and Subtracting Fractions—Unlike Denominators

4. Solving Applications Involving Addition and Subtraction of Fractions

 

4.6 Operations on Mixed Numbers

1. Writing a Mixed Number as an Improper Fraction

2. Rounding a Mixed Number to the Nearest Integer

3. Performing Operations on Mixed Numbers

4. Adding and Subtracting Mixed Numbers—Method II

 

4.7 Complex Fractions and Order of Operations

1. Introducing Complex Fractions

2. Simplifying Complex Fractions—Method I

3. Simplifying Complex Fractions—Method II

4. Applying Order of Operations to Complex Fractions

 

4.8 Solving Equations Involving Fractions

1. Using the Addition Property of Equality with Fractions

2. Using the Multiplication Property of Equality with Fractions

3. Clearing Fractions

4. Solving Equation Involving Fractions Symbolically

5. Solving Equations Involving Fractions Numerically

6. Solving Equations Involving Fractions Graphically

7. Solving Applications Involving Equations with Fractions

 

5 Decimals

5.1 Introduction to Decimals

1. Reviewing Decimal Notation

2. Writing Decimals in Words

3. Writing Decimals as Fractions

4. Graphing Decimals on a Number Line

5. Comparing Decimals

6. Rounding Decimals

 

5.2 Adding and Subtracting Decimals

1. Estimating Decimal Sums and Differences

2. Adding and Subtracting Positive Decimals

3. Adding and Subtracting Signed Decimals

4. Evaluating and Simplifying Expressions Involving Decimal Addition and Subtraction

5. Solving Applications Involving Decimal Addition and Subtraction

5.3 Multiplying and Dividing Decimals

1. Estimating Decimal Products and Quotients

2. Multiplying a Decimal by a Decimal

3. Multiplying a Decimal by a Power of Ten

4. Dividing a Decimal by a Whole Number

5. Dividing a Decimal by a Decimal

6. Dividing a Decimal by a Power of 10

7. Writing Fractions as Decimals

8. Evaluating and Simplifying Expressions Involving Decimal Multiplication and Division

9. Solving Applications Involving Decimal Multiplication and Division

 

5.4 Real Numbers, Square Roots, and Order of Operations

1. Introducing Real Numbers

2. Approximating Square Roots

3. Applying the Order of Operations to Numerical Expressions

4. Applying the Order of Operations to Algebraic Expressions

5. Solving Applications Involving Real Numbers

 

5.5 Solving Equations Involving Decimals

1. Solving Equations Symbolically by Working Directly with Decimals

2. Solving Equations Symbolically by Clearing Decimals

3. Solving Decimal Equations Numerically

4. Solving Decimal Equations Graphically

5. Solving Applications Involving Equations with Decimals

 

5.6 Applications from Geometry and Statistics

1. Reviewing Parts of a Circle

2. Calculating the Circumference of a Circle

3. Calculating the Area of a Circle

4. Finding the Area of Composite Regions

5. Applying the Pythagorean Theorem

6. Calculating the Mean, Median, and Mode

7. Finding a Weighted Mean and GPA

 

6 Ratios, Proportions, and Measurement

6.1 Ratios and Rates

1. Writing Ratios as Fractions

2. Finding Unit Ratios

3. Writing Rates as Fractions

4. Finding Unit Rates

5. Computing Unit Pricing

 

6.2 Proportions and Similar Figures

1. Identifying Proportions

2. Solving a Proportion for an Unknown Value

3. Working with Similar Figures

4. Solving Applications Involving Proportions and Similar Figures

 

6.3 The U.S. System of Measurement

1. Converting U.S. Units of Length

2. Converting U.S. Units of Area

3. Converting U.S. Units of Capacity and Volume

4. Converting U.S. Units of Weight

 

6.4 The Metric System of Measurement

1. Understanding Metric Prefixes

2. Converting Metric Units of Length

3. Converting Metric Units of Area

4. Converting Metric Units of Capacity and Volume

5. Converting Metric Units of Mass

 

6.5 U.S.–Metric Conversions; Temperature

1. Completing Conversions of Length

2. Completing Conversions of Capacity and Volume

3. Completing Conversions of Mass (Weight)

4. Converting Temperatures Symbolically

5. Converting Temperatures Numerically

6. Converting Temperatures Graphically

 

6.6 Time and Speed

1. Converting Units of Time

2. Converting Units of Speed

3. Solving an Application Involving Speed

 

7 Percent and Probability

7.1 Introduction to Percent; Circle Graphs

1. Understanding Percent Notation

2. Writing Percents as Fractions or Decimals

3. Writing Fractions or Decimals as Percents

4. Reading Circle Graphs

5. Solving Percent Applications

 

7.2 Using Equations to Solve Percent Problems

1. Understanding Basic Percent Statements

2. Translating Percent Statements to Equations

3. Introducing Percent Problems

4. Translating Percent Problems to Equations

5. Finding an Unknown Part in a Percent Equation

6. Finding an Unknown Whole in a Percent Equation

7. Finding an Unknown Percent in a Percent Equation

 

7.3 Using Proportions to Solve Percent Problems

1. Reviewing Proportions

2. Translating Percent Statements to Proportions

3. Translating Percent Problems to Proportions

4. Finding an Unknown Part in a Percent Proportion

5. Finding an Unknown Whole in a Percent Proportion

6. Finding an Unknown Percent in a Percent Proportion

 

7.4 Applications: Sales Tax, Discounts, and Net Pay

1. Finding a Missing Part in a Percent Application

2. Finding a Missing Whole in a Percent Application

3. Finding a Missing Percent in a Percent Application

4. Finding Sales Tax and Total Amount Paid

5. Finding Discounts and Sale Price

6. Calculating Commission

7. Calculating Net Pay

8. Finding Percent Change

 

7.5 Applications: Simple and Compound Interest

1. Introducing Principal, Interest, and Interest Rates

2. Calculating Simple Interest

3. Finding the Total Value of an Investment or Loan

4. Calculating Compound Interest

 

7.6 Probability and Percent Chance

1. Understanding Experiments, Outcomes, and Events

2. Finding Probability and Percent Chance

3. Finding the Complement of an Even

 

8 Geometry

8.1 Plane Geometry; Points, Lines, and Angles

1. Reviewing Geometric Terms and Concepts

2. Classifying Acute, Right, Obtuse, and Straight Angles

3. Recognizing Congruent, Supplementary, and Complementary Angles

4. Recognizing Parallel, Intersecting, and Perpendicular Lines

5. Using Properties of Parallel Lines Cut by a Transversal

 

8.2 Triangles

1. Classifying Triangles

2. Applying the Sum of the Angle Measures

3. Using Congruent Triangle Properties

 

8.3 Polygons and Circles

1. Understanding Properties of Polygons

2. Finding Angles in Regular Polygons

3. Understanding Properties of Quadrilaterals

4. Finding the Radius and Diameter of a Circle

 

8.4 Perimeter and Circumference

1. Finding the Perimeter of a Polygon

2. Finding the Circumference of a Circle

3. Finding the Perimeter of Composite Figures

 

8.5 Area, Volume, and Surface Area

1. Finding the Area of Common Polygons

2. Finding the Area of a Circle

3. Finding the Volume and Surface Area of Geometric Solids

 

9 Linear Equations and Inequalities in One Variable

9.1 Review of Linear Equations in One Variable

1. Identifying Linear Equations in One Variable

2. Solving Linear Equations Numerically

3. Solving Linear Equations Symbolically

4. Applying the Distributive Property

5. Clearing Fractions and Decimals

6. Solving Equations That Have No Solutions or Infinitely Many Solutions

7. Solving Equations for a Variable

 

9.2 Further Problem Solving

1. Reviewing Steps for Solving a Problem

2. Translating Words into Equations

3. Solving Distance Problems

4. Solving Mixture Problems

 

9.3 Linear Inequalities in One Variable

1. Introducing Linear Inequalities

2. Graphing Linear Inequalities on a Number Line

3. Checking Solutions to Linear Inequalities

4. Solving Linear Inequalities with Tables

5. Writing Solution Sets Using Interval Notation

6. Applying the Addition Property of Inequalities

7. Applying the Multiplication Property of Inequalities

8. Writing Solution Sets Using Set-Builder Notation

9. Translating Words to Inequalites

10. Solving Applications Involving Linear Inequalities

 

10 Graphing Equations

10.1 Introduction to Graphing

1. Introducing Tables and Graphs

2. Understanding the Rectangular Coordinate System

3. Reading and Plotting Ordered Pairs

4. Reading and Making Scatterplots

5. Choosing a Scale for a Graph

6. Reading and Making Line Graphs

 

10.2 Equations in Two Variables

1. Introducing Equations in Two Variables

2. Recognizing Ordered Pairs as Solutions

3. Making a Table of Solutions

4. Graphing Linear Equations in Two Variables

5. Writing the Standard Form for a Linear Equation

6. Solving an Equation in Standard Form for a Variable

7. Graphing Nonlinear Equations in Two Variables

 

10.3 Intercepts, Horizontal Lines, and Vertical Lines

1. Finding Intercepts

2. Using Intercepts to Graph Lines

3. Recognizing Horizontal Lines and Their Equations

4. Recognizing Vertical Lines and Their Equations

5. Writing the Equation of Any Line in Standard Form

 

10.4 Slope and Rates of Change

1. Introducing Slope

2. Recognizing Positive, Negative, Zero, and Undefined Slope

3. Finding Slopes of Lines

4. Using Slope to Sketch a Line
5. Using Slope to Complete a Table

6. Understanding Slope as a Rate of Change

 

10.5 Slope–Intercept Form

1. Determining a Line

2. Finding Slope–Intercept Form

3. Working with Parallel Lines and Their Slopes

4. Working with Perpendicular Lines and Their Slopes

 

10.6 Point–Slope Form

1. Deriving the Point–Slope Form for the Equation of a Line

2. Finding Point–Slope Form

3. Solving Applications Involving Equations of Lines

 

10.7 Introduction to Modeling

1. Introducing Linear Models

2. Modeling Linear Data

 

11 Systems of Linear Equations in Two Variables

11.1 Solving Systems of Linear Equations Graphically and Numerically

1. Solving Equations Graphically

2. Solving Equations Numerically with a Table of Values

3. Introducing Systems of Linear Equations

4. Recognizing Types of Equations and Number of Solutions

5. Checking a Solution to a System of Equations

6. Solving Systems Graphically and Numerically

7. Solving Applications Involving Systems of Equations

 

11.2 Solving Systems of Linear Equations by Substitution

1. Using the Method of Substitution

2. Solving for a Variable Before Using Substitution

3. Recognizing Systems That Have No Solutions or Infinitely Many Solutions

4. Solving Applications Involving the Method of Substitution

 

11.3 Solving Systems of Linear Equations by Elimination

1. Using the Method of Elimination

2. Multiplying Before Applying Elimination

3. Solving a System Symbolically, Graphically, and Numerically

4. Recognizing Systems That Have No Solutions or Infinitely Many Solutions

5. Solving Applications Involving the Method of Elimination

 

11.4 Systems of Linear Inequalities

1. Finding Solutions to a Linear Inequality in Two Variables

2. Writing and Graphing a Linear Inequality in Two Variables

3. Finding Solutions to Systems of Linear Inequalities

4. Solving Applications Involving Systems of Linear Inequalities

 

12 Polynomials and Exponents

12.1 Rules for Exponents

1. Reviewing Bases and Exponents

2. Computing Zero Exponents

3. Applying the Product Rule

4. Applying the Power Rules

 

12.2 Addition and Subtraction of Polynomials

1. Introducing Nonlinear Data and Polynomials

2. Recognizing Monomials and Polynomials

3. Adding Polynomials

4. Subtracting Polynomials

5. Evaluating Polynomial Expressions

 

12.3 Multiplication of Polynomials

1. Multiplying Monomials

2. Reviewing the Distributive Properties

3. Multiplying Monomials and Polynomials

4. Multiplying Polynomials

 

12.4 Special Products

1. Finding the Product of a Sum and Difference

2. Squaring Binomials

3. Cubing Binomials

 

12.5 Integer Exponents and the Quotient Rule

1. Using Negative Integers as Exponents

2. Applying the Quotient Rule

3. Applying Other Rules for Exponents

4. Reading and Writing Scientific Notation

 

12.6 Division of Polynomials

1. Dividing by a Monomial

2. Dividing by a Polynomial

 

13 Factoring Polynomials and Solving Equations

13.1 Introduction to Factoring

1. Introducing Factoring

2. Finding Common Factors

3. Finding the Greatest Common Factor

4. Factoring by Grouping

 

13.2 Factoring Trinomials I (x ² + bx + c)

1. Reviewing Binomial Multiplication

2. Factoring Trinomials with Leading Coefficient 1

3. Identifying Prime Polynomials

4. Relating Geometry and Visual Factoring

 

13.3 Factoring Trinomials II (ax ² + bx + c)

1. Factoring Trinomials by Grouping

2. Factoring with FOIL in Reverse

 

13.4 Special Types of Factoring

1. Factoring the Difference of Two Squares

2. Factoring Perfect Square Trinomials

3. Factoring the Sum and Difference of Two Cubes

4. Using Special Methods in General Factoring

 

13.5 Summary of Factoring

1. Summarizing General Guidelines for Factoring Polynomials

2. Factoring Polynomials

 

13.6 Solving Equations by Factoring I (Quadratics)

1. Applying the Zero-Product Property

2. Solving Quadratic Equations by Factoring

3. Solving Applications Involving Quadratic Equations

 

13.7 Solving Equations by Factoring II (Higher Degree)

1. Recognizing Nonlinear Data and Polynomial Models

2. Factoring Higher-Degree Polynomials

3. Solving Polynomial Equations

4. Solving Applications Involving Polynomial Equations

 

14 Rational Expressions

14.1 Introduction to Rational Expressions

1. Evaluating Rational Expressions

2. Recognizing Undefined Expressions

3. Simplifying Rational Expressions

4. Solving Applications Involving Rational Expressions

5. Solving Applications Involving Probability

 

14.2 Multiplication and Division of Rational Expressions

1. Reviewing Multiplication and Division of Fractions

2. Multiplying Rational Expressions

3. Dividing Rational Expressions

 

14.3 Addition and Subtraction of Rational Expressions—Like Denominators

1. Reviewing Addition and Subtraction of Fractions That Have Like Denominators

2. Adding and Subtracting Rational Expressions That Have Like Denominators

 

14.4 Addition and Subtraction of Rational Expressions—Unlike Denominators

1. Finding Least Common Multiples

2. Using a Step Diagram to Find the LCM

3. Reviewing Addition and Subtraction of Fractions—Unlike Denominators

4. Adding and Subtracting Rational Expressions That Have Unlike Denominators

5. Solving Applications Involving Addition and Subtraction of Rational Expressions

 

14.5 Complex Fractions

1. Reviewing Complex Fractions

2. Simplifying the Numerator and Denominator (Method I)

3. Simplifying by Multiplying by the LCD (Method II)

 

14.6 Rational Equations and Formulas

1. Solving Rational Equations

2. Recognizing Rational Expressions and Equations

3. Finding Graphical and Numerical Solutions

4. Solving a Rational Equation or Formula for a Variable

5. Solving Applications Involving Rational Equations

 

14.7 Proportions and Variation

1. Solving Proportions

2. Using Proportions with Similar Figures

3. Solving Direct Variation Problems

4. Solving Inverse Variation Problems

5. Analyzing Data

6. Solving Joint Variation Problems

 

15 Introduction to Functions

15.1 Functions and Their Representations

1. Introducing Functions

2. Recognizing Representations of Functions

3. Evaluating Different Representations

4. Defining a Function

5. Finding Domain and Range

6. Identifying a Function

7. Applying the Vertical Line Test

 

15.2 Linear Functions

1. Recognizing Representations of Linear Functions

2. Identifying Linear Functions

3. Recognizing Graphs of Linear Functions

4. Modeling Data with Linear Functions

5. Applying the Midpoint Formula

 

15.3 Compound Inequalities

1. Introducing Compound Inequalities

2. Finding Symbolic Solutions and Graphing Them on a Number Line

3. Finding Numerical and Graphical Solutions

4. Writing Solutions in Interval Notation

 

15.4 Other Functions and Their Properties

1. Introducing Nonlinear Functions

2. Expressing Domain and Range in Interval Notation

3. Recognizing Absolute Value Functions and Their Properties

4. Recognizing Polynomial Functions and Their Properties

5. Recognizing Rational Functions and Their Properties

6. Performing Operations on Functions

 

15.5 Absolute Value Equations and Inequalities

1. Solving x = k

2. Solving ax + b = k

3. Solving an Equation That Has Two Absolute Values

4. Solving Absolute Value Inequalities Numerically and Graphically

5. Finding Symbolic Solutions Based on Visualization (Method I)

6. Finding Symbolic Solutions (Method II)

 

16 Systems of Linear Equations, Matrix Solutions, Determinants

16.1 Systems of Linear Equations in Three Variables

1. Writing Systems of Linear Equations and Recognizing Solutions

2. Solving Linear Systems with Substitution and Elimination

3. Modeling with Linear Systems

4. Recognizing Linear Systems That Have No Solutions

5. Recognizing Linear Systems That Have Infinitely Many Solutions

 

16.2 Matrix Solutions of Linear Systems

1. Representing Systems of Linear Equations with Matrices

2. Relating Matrices and Social Networks

3. Applying Gauss–Jordan Elimination

4. Using Technology to Solve Systems of Linear Equations

 

16.3 Determinants

1. Calculating Determinants

2. Finding Areas of Regions

3. Applying Cramer’s Rule

 

17 Radical Expressions and Functions

17.1 Radical Expressions and Functions

1. Introducing Radical Expressions

2. Relating Absolute Value and Square Roots

3. Recognizing Square Root Functions and Their Properties

4. Recognizing Cube Root Functions and Their Properties

 

17.2 Rational Exponents

1. Using Rational Numbers as Exponents

2. Applying Properties of Rational Exponents

 

17.3 Simplifying Radical Expressions

1. Applying the Product Rule for Radical Expressions

2. Applying the Quotient Rule for Radical Expressions

 

17.4 Operations on Radical Expressions

1. Adding Like Radicals

2. Finding Like Radicals and Then Adding

3. Subtracting Like Radicals

4. Multiplying Radical Expressions

5. Rationalizing the Denominator

 

17.5 More Radical Functions

1. Recognizing Root Functions and Their Properties

2. Recognizing Power Functions and Their Properties

3. Modeling with Power Functions

 

17.6 Equations Involving Radical Expressions

1. Solving Radical Equations Using the Power Rule

2. Identifying Extraneous Solutions

3. Solving Radical Equations by Squaring Twice

4. Solving Radical Equations Involving Cube Roots

5. Reviewing the Pythagorean Theorem

6. Deriving and Applying the Distance Formula

7. Solving Equations of the Form xⁿ = k

 

17.7 Complex Numbers

1. Introducing the Imaginary Unit and Standard Form

2. Adding and Subtracting Complex Numbers

3. Multiplying Complex Numbers

4. Computing Powers of i

5. Finding Complex Conjugates

6. Dividing Complex Numbers

 

18 Quadratic Functions and Equations

18.1 Quadratic Functions and Their Graphs

1. Working with Graphs of Quadratic Functions—Parabolas

2. Using the Vertex Formula

3. Graphing Quadratic Functions by Hand

4. Recognizing When Functions Are Increasing or Decreasing

5. Solving Min–Max Applications

 

18.2 Parabolas and Modeling

1. Graphing y = ax ², a > 0

2. Graphing y = ax ², a < 0

3. Performing Vertical and Horizontal Translations

4. Finding Vertex Form

5. Completing the Square to Find the Vertex

6. Modeling with Quadratic Functions

 

18.3 Quadratic Equations

1. Recognizing Quadratic Equations

2. Solving Quadratic Equations (Three Methods)

3. Applying the Square Root Property

4. Completing the Square

5. Solving an Equation for a Variable

6. Solving Applications Involving Quadratic Equations

 

18.4 The Quadratic Formula

1. Deriving the Quadratic Formula

2. Solving Equations Using the Quadratic Formula

3. Finding the Discriminant

4. Using Intercepts to Graph Quadratic Functions

5. Solving Quadratic Equations That Have Complex Solutions

 

18.5 Quadratic Inequalities

1. Recognizing Quadratic Inequalities

2. Finding Graphical and Numerical Solutions

3. Finding Symbolic Solutions

 

18.6 Equations in Quadratic Form

1. Solving Higher Degree Polynomial Equations

2. Solving Equations That Have Rational Exponents

3. Solving Equations That Have Complex Solutions

 

19 Exponential and Logarithmic Functions

19.1 Composite and Inverse Functions

1. Introducing Composition of Functions

2. Evaluating Composite Functions Symbolically

3. Evaluating Composite Functions Numerically and Graphically

4. Recognizing One-to-One Functions

5. Applying the Horizontal Line Test

6. Finding Inverse Functions

7. Using Tables to Express Inverse Functions

8. Using Graphs to Express Inverse Functions

 

19.2 Exponential Functions

1. Introducing Exponential Functions

2. Recognizing Graphs of Exponential Functions and Their Properties

3. Comparing Exponential and Linear Growth

4. Relating Percent Change and Exponential Functions

5. Computing Compound Interest

6. Computing Compound Interest Paid More than Once a Year

7. Modeling with Exponential Functions

8. Recognizing the Natural Exponential Function and its Properties

 

19.3 Logarithmic Functions

1. Introducing the Common Logarithmic Function

2. Recognizing the Graph of the Common Logarithmic Function and its Properties

3. Finding the Inverse of the Common Logarithmic Function

4. Working with Base 2 Logarithms

5. Working with Base e (The Natural Logarithm)

6. Working with Base a Logarithms

7. Finding Inverses of Base a Logarithms

 

19.4 Properties of Logarithms

1. Applying the Product Rule

2. Applying the Quotient Rule

3. Applying the Power Rule

4. Applying More than One Property

5. Using the Change of Base Formula

 

19.5 Exponential and Logarithmic Equations

1. Recognizing Exponential Equations and Models

2. Solving Applications Involving Exponential Equations

3. Recognizing Logarithmic Equations and Models

4. Solving Applications Involving Logarithmic Equations

 

20 Conic Sections

20.1 Parabolas and Circles

1. Recognizing Types of Conic Sections

2. Graphing Parabolas with Horizontal Axes of Symmetry and Writing Their Equations

3. Graphing Circles and Writing Their Equations

4. Completing the Square to Find the Center and Radius

 

20.2 Ellipses and Hyperbolas

1. Graphing Ellipses and Writing Their Equations

2. Graphing Hyperbolas and Writing Their Equations

 

20.3 Nonlinear Systems of Equations and Inequalities

1. Recognizing Solutions to Nonlinear Systems of Equations

2. Solving Nonlinear Systems Using the Method of Substitution

3. Solving Nonlinear Systems Graphically and Symbolically

4. Solving Nonlinear Systems of Inequalities

 

21 Sequences and Series

21.1 Sequences

1. Finding Terms of a Sequence

2. Recognizing Representations of Sequences

3. Modeling Population Growth with a Sequence

 

21.2 Arithmetic and Geometric Sequences

1. Recognizing Arithmetic Sequences

2. Writing Arithmetic Sequences

3. Recognizing Geometric Sequences

4. Writing Geometric Sequences

5. Solving Applications Involving Sequences

 

21.3 Series

1. Introducing Series

2. Working with Arithmetic Series

3. Working with Geometric Series

4. Using Summation Notation

 

21.4 The Binomial Theorem

1. Introducing Pascal’s Triangle

2. Writing Factorial Notation and Binomial Coefficients

3. Computing Binomial Coefficients

4. Expanding a Binomial Using the Binomial Theorem

5. Finding a Particular Term of (a + b) ⁿ