# Developmental Mathematics: Basic Mathematics, Introductory Algebra, and Intermediate Algebra, 2nd edition

Published by Pearson (April 7, 2014) © 2015

**John Squires****Karen Wyrick**

## MyLab

- Reach every student with personalized support
- Customize courses with ease
- Optimize learning with dynamic study tools

**New conceptual and application-oriented topics**provide real world context, motivating students to learn and master the material. These application topics include Multiplying and Dividing Fractions, Adding and Subtracting Fractions, Operations with Mixed Numbers, Geometric Figures, Adding and Subtracting Real Numbers, Multiplying and Dividing Real Numbers, Linear Equations and Inequalities, Graphing Linear Equations, Linear Equations and Slope, Functions, Systems of Linear Equations, Rational Equations, Variation, Quadratic Equations, Quadratic Functions, Logarithmic Equations, Balancing a Checkbook, and Determining the Best Deal when Purchasing a Vehicle.**Additional topics**have also been added to the intermediate algebra portion of the course: Solving a System in Three Variables by the Elimination Method, Factoring Trinomials by Grouping Numbers (the AC-Method,) Factoring Polynomials, Factoring the Sum and Difference of Cubes, Direct Variation, Inverse Variation, Joint and Combined Variation, Adding and Subtracting Radical Expressions, Multiplying Radical Expressions, Dividing Radical Expressions, Rationalizing the Denominator, Complex Numbers, The Discriminant in the Quadratic Formula, Solving Quadratic Equations with Real or Complex Number Solutions, Solving Equations Quadratic in Form, Solving Rational Inequalities, Introduction to Conic Sections, Composite Functions, Inverse Functions, Using a Graphing Calculator, Algebra of Functions, Transformations of Functions, Piecewise Functions, Graphing Piecewise Functions, and Systems of Non-Linear Equations.**The following topics have been added to the basic math portion of the course:**Congruent Triangles and Introduction to Probability,**Interactive****Example**animations have been added to select tutorials to provide additional student support on difficult topics.**Cumulative review tests**have been added so students can review several modules worth of material.- The
**MyMathLab Notebook**has been revised to provide "additional problems" with Guided Solutions.

**Mini-Mod 1 Whole Numbers**

1.1 Whole Numbers

1.2 Rounding

1.3 Adding Whole Numbers; Estimation

1.4 Subtracting Whole Numbers

1.5 Basic Problem Solving

1.6 Multiplying Whole Numbers

1.7 Dividing Whole Numbers

1.8 More with Multiplying and Dividing

1.9 Exponents

1.10 Order of Operations and Whole Numbers

1.11 More Problem Solving

**Mini-Mod 2 Factors and Fractions**

2.1 Factors

2.2 Prime Factorization

2.3 Understanding Fractions

2.4 Simplifying Fractions - GCF and Factors Method

2.5 Simplifying Fractions - Prime Factors Method

2.6 Multiplying Fractions

2.7 Dividing Fractions

2.8 Applications of Multiplying and Dividing Fractions

**Mini-Mod 3 LCM and Fractions**

3.1 Finding the LCM - List Method

3.2 Finding the LCM - GCF Method

3.3 Finding the LCM - Prime Factor Method

3.4 Writing Fractions with an LCD

3.5 Adding and Subtracting Like Fractions

3.6 Adding and Subtracting Unlike Fractions

3.7 Order of Operations and Fractions

3.8 More Applications of Adding and Subtracting Fractions

**Mini-Mod 4 Mixed Numbers**

4.1 Changing a Mixed Number to an Improper Fraction

4.2 Changing an Improper Fraction to a Mixed Number

4.3 Multiplying Mixed Numbers

4.4 Dividing Mixed Numbers

4.5 Adding Mixed Numbers

4.6 Subtracting Mixed Numbers

4.7 Adding and Subtracting Mixed Numbers - Improper Fractions

4.8 Applications of Operations with Mixed Numbers

**Mini-Mod 5 Operations with Decimals**

5.1 Decimal Notation

5.2 Comparing Decimals

5.3 Rounding Decimals

5.4 Adding and Subtracting Decimals

5.5 Multiplying Decimals

5.6 Dividing Decimals

5.7 Order of Operations and Decimals

5.8 Converting Fractions to Decimals

5.9 Converting Decimals to Fractions

**Mini-Mod 6 Ratios, Rates, and Percents**

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Percent Notation

6.5 Percent and Decimal Conversions

6.6 Percent and Fraction Conversions

6.7 The Percent Equation

6.8 The Percent Proportion

6.9 Percent Applications

**Mini-Mod 7 U.S. and Metric Measurement**

7.1 U.S. Length

7.2 U.S. Weight and Capacity

7.3 Metric Length

7.4 Metric Mass and Capacity

7.5 Converting between U.S. and Metric Units

7.6 Time and Temperature

**Mini-Mod 8 Introduction to Geometry**

8.1 Lines and Angles

8.2 Figures

8.3 Perimeter - Definitions and Units

8.4 Finding Perimeter

8.5 Area - Definitions and Units

8.6 Finding Area

8.7 Understanding Circles

8.8 Finding Circumference

8.9 Finding Area — Circles

**Mini-Mod 9 More Geometry**

9.1 Volume - Definitions and Units

9.2 Finding Volume

9.3 Square Roots

9.4 The Pythagorean Theorem

9.5 Similar Figures

9.6 Finding Missing Lengths

9.7 Congruent Triangles

9.8 Applications of Geometric Figures

**Mini-Mod 10 Statistics**

10.1 Bar Graphs and Histograms

10.2 Line Graphs

10.3 Circle Graphs

10.4 Mean

10.5 Median

10.6 Mode

10.7 Introduction to Probability

**Mini-Mod 11 Real Numbers and Variables**

11.1 Introduction to Real Numbers

11.2 Graphing Rational Numbers Using a Number Line

11.3 Translating Phrases into Algebraic Inequalities

11.4 Finding the Absolute Value of a Real Number

**Mini-Mod 12 Adding and Subtracting with Real Numbers**

12.1 Adding Real Numbers with the Same Sign

12.2 Adding Real Numbers with Different Signs

12.3 Finding the Opposite of a Real Number

12.4 Subtracting Real Numbers

12.5 Addition Properties of Real Numbers

12.6 Applications of Adding and Subtracting Real Numbers

**Mini-Mod 13 Multiplying and Dividing with Real Numbers**

13.1 Multiplying Real Numbers

13.2 Finding the Reciprocal of a Real Number

13.3 Dividing Real Numbers

13.4 Exponents and the Order of Operations

13.5 The Distributive Property

13.6 Multiplication Properties of Real Numbers

13.7 Applications of Multiplying and Dividing Real Numbers

**Mini-Mod 14 Variables and Expressions**

14.1 Introduction to Expressions

14.2 Evaluating Algebraic Expressions

14.3 Simplifying Expressions

14.4 Simplifying Expressions with Parentheses

14.5 Translating Words into Symbols

**Mini-Mod 15 Introduction to Solving Linear Equations**

15.1 Translating Words into Equations

15.2 Linear Equations and Solutions

15.3 Using the Addition Property of Equality

15.4 Using the Multiplication Property of Equality

15.5 Using the Addition and Multiplication Properties Together

**Mini-Mod 16 Solving More Linear Equations and Inequalities**

16.1 Solving Equations with Variables on Both Sides

16.2 Solving Equations with Parentheses

16.3 Solving Equations with Fractions

16.4 Solving a Variety of Equations

16.5 Solving Equations and Formulas for a Variable

16.6 Solving and Graphing Linear Inequalities

16.7 Applications of Linear Equations and Inequalities

**Mini-Mod 17 Introduction to Graphing Linear Equations**

17.1 The Rectangular Coordinate System

17.2 Graphing Linear Equations by Plotting Points

17.3 Graphing Linear Equations Using Intercepts

17.4 Graphing Linear Equations of the Form *x*=*a*, *y*=*b*, and *y*=*mx*

17.5 Applications of Graphing Linear Equations

**Mini-Mod 18 Slope and the Equation of a Line**

18.1 The Slope of a Line

18.2 Slope-Intercept Form

18.3 Graphing Lines Using the Slope and y-Intercept

18.4 Writing Equations of Lines Using a Point and Slope

18.5 Writing Equations of Lines Using Two Points

18.6 Writing Equations of Parallel and Perpendicular Lines

18.7 Graphing Linear Inequalities in Two Variables

18.8 Applications of Linear Equations and Slope

**Mini-Mod 19 Introduction to Functions **

19.1 Relations and Functions

19.2 The Vertical Line Test

19.3 Function Notation

19.4 Evaluating Functions

19.5 Applications of Functions

**Mini-Mod 20 Solving Systems of Linear Equations **

20.1 Introduction to Systems of Linear Equations

20.2 Solving by the Graphing Method

20.3 Solving by the Substitution Method

20.4 Solving by the Elimination Method

20.5 Solving a System in Three Variables by the Elimination Method

20.6 Applications of Systems of Linear Equations

**Mini-Mod 21 Introduction to Polynomials and Exponent Rules**

21.1 Introduction to Polynomials

21.2 Addition of Polynomials

21.3 Subtraction of Polynomials

21.4 Product Rule for Exponents

21.5 Power Rule for Exponents

**Mini-Mod 22 Multiplying Polynomials**

22.1 Multiplying by a Monomial

22.2 Multiplying Binomials

22.3 Multiplying Polynomials

22.4 Multiplying the Sum and Difference of Two Terms

22.5 Squaring Binomials

**Mini-Mod 23 Dividing Polynomials and More Exponent Rules**

23.1 The Quotient Rule

23.2 Integer Exponents

23.3 Scientific Notation

23.4 Dividing a Polynomial by a Monomial

23.5 Dividing a Polynomial by a Binomial

**Mini-Mod 24 Factoring Polynomials**

24.1 Greatest Common Factor

24.2 Factoring by Grouping

24.3 Factoring Trinomials of the Form *x*^{2}+*bx*+*c*

24.4 Factoring Trinomials of the Form *ax*^{2}+*bx*+*c*

24.5 More Factoring of Trinomials by the Reverse FOIL Method

24.6 Factoring Trinomials by Grouping Numbers (the *ac*-Method)

**Mini-Mod 25 More Factoring and Quadratic Equations**

25.1 Special Cases of Factoring

25.2 Factoring Polynomials

25.3 Factor the Sum and Difference of Cubes

25.4 Solving Quadratic Equations by Factoring

25.5 Applications of Quadratic Equations

**Mini-Mod 26 Introduction to Rational Expressions**

26.1 Undefined Rational Expressions

26.2 Simplifying Rational Expressions

26.3 Multiplying Rational Expressions

26.4 Dividing Rational Expressions

**Mini-Mod 27 Adding and Subtracting Rational Expressions**

27.1 Adding Like Rational Expressions

27.2 Subtracting Like Rational Expressions

27.3 Finding the Least Common Denominator for Rational Expressions

27.4 Adding and Subtracting Unlike Rational Expressions

**Mini-Mod 28 Complex Rational Expressions and Rational Equations **

28.1 Simplifying Complex Rational Expressions by Adding and Subtracting

28.2 Simplifying Complex Rational Expressions by Multiplying by the LCD

28.3 Solving Rational Equations

28.4 Applications of Rational Equations: Solving Formulas for a Variable

28.5 Applications of Rational Equations: Work Problems

28.6 Applications of Rational Equations: *D* = *RT*

**Mini-Mod 29 Variation**

29.1 Direct Variation

29.2 Inverse Variation

29.3 Joint and Combined Variation

29.4 Applications of Variation

**Mini-Mod 30 Roots and Radicals**

30.1 Square Roots

30.2 Higher-Order Roots

30.3 Simplifying Radical Expressions

30.4 Rational Exponents

30.5 More on The Pythagorean Theorem

30.6 The Distance Formula

**Mini-Mod 31 Operations of Radical Expressions**

31.1 Introduction to Radical Functions

31.2 Adding and Subtracting Radical Expressions

31.3 Multiplying Radical Expressions

31.4 Dividing Radical Expressions

31.5 Rationalizing the Denominator

31.6 Solving Radical Equations

**Mini-Mod 32 Solving Quadratic Equations**

32.1 Introduction to Solving Quadratic Equations

32.2 Solving Quadratic Equations by Factoring

32.3 Solving Quadratic Equations using the Square Root Property

32.4 Solving Quadratic Equations by Completing the Square

32.5 Solving Quadratic Equations using the Quadratic Formula

32.6 Applications with Quadratic Equations

**Mini-Mod 33 Complex Numbers and More Quadratic Equations**

33.1 Complex Numbers

33.2 The Discriminant in the Quadratic Formula

33.3 Solving Quadratic Equations with Real or Complex Number Solutions

33.4 Solving Equations Quadratic in Form

33.5 Complex and Quadratic Applications

**Mini-Mod 34 Graphing Quadratic Functions**

34.1 Introduction to Graphing Quadratic Functions

34.2 Finding the Vertex of a Quadratic Function

34.3 Finding the Intercepts of a Quadratic Function

34.4 Graphing Quadratic Functions Summary

34.5 Applications with Quadratic Functions

**Mini-Mod 35 Compound and Non-Linear Inequalities**

35.1 Interval Notation

35.2 Graphing Compound Inequalities

35.3 Solving Compound Inequalities

35.4 Solving Quadratic Inequalities

35.5 Solving Rational Inequalities

**Mini-Mod 36 Absolute Value Equations and Inequalities**

36.1 Introduction to Absolute Value Equations

36.2 Solving Basic Absolute Value Equations

36.3 Solving Multiple Absolute Value Equations

36.4 Solving Absolute Value Inequalities

**Mini-Mod 37 Conic Sections**

37.1 Introduction to Conic Sections

37.2 The Circle

37.3 The Parabola

37.4 The Ellipse

37.5 The Hyperbola

**Mini-Mod 38 Logarithmic and Exponential Functions**

38.1 Composite Functions

38.2 Inverse Functions

38.3 Evaluating Exponential and Logarithmic Expressions

38.4 Graphing Exponential Functions

38.5 Converting Between Exponential and Logarithmic Forms

38.6 Graphing Logarithmic Functions

**Mini-Mod 39 Solving Logarithmic and Exponential Equations**

39.1 Properties of Logarithms

39.2 Common and Natural Logarithms

39.3 Change of Base of Logarithms

39.4 Solving Simple Exponential Equations and Applications

39.5 Solving Exponential Equations and Applications

39.6 Solving Simple Logarithmic Equations

39.7 Solving Logarithmic Equations and Applications

**Appendix A: More on Functions**

A.1 Using a Graphing Calculator

A.2 Algebra of Functions

A.3 Transformations of Functions

A.4 Piecewise Functions

A.5 Graphing Piecewise Functions

**Appendix B: More on Systems**

B.1 Systems of Linear Inequalities

B.2 Systems of Non-Linear Equations

B.3 Matrices and Determinants

B.4 Solving Systems of Linear Equations Using Matrices

B.5 Cramer’s Rule

**Appendix C: Additional Topics **

C.1 Sets

C.2 The Midpoint Formula

C.3 Surface Area

C.4 Synthetic Division

C.5 Balancing a Checking Account

C.6 Determining the Best Deal when Purchasing a VehicleNeed help? Get in touch