"Beginning and Intermediate Algebra, 2e", by Messersmith is the first text in a series of future offerings in developmental mathematics. The author presents the content in bite-size pieces, focusing not only on learning mathematical concepts, but also explaining the why behind those concepts. For students, learning mathematics is not just about the memorization of concepts and formulas, but it is also about the journey of learning how to problem solve. By breaking the sections down into manageable chunks, the author has identified the core places where students traditionally struggle, and then assists them in understanding that material to be successful moving forward. Proven pedagogical features, such as You Try problems after each example, reinforce a student's mastery of a concept.While teaching in the classroom, Messersmith has created worksheets for each section that fall into three categories: review worksheets/basic skills, worksheets to teach new content, and worksheets to reinforce/pull together different concepts. These worksheets are a great way to both enhance instruction and to give the students more tools to be successful in studying a given topic.
The author is also an extremely popular lecturer, and finds it important to be in the video series that accompany her texts. Finally, the author finds it important to not only provide quality, but also an abundant quantity of exercises and applications. The book is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone. Messersmith - mapping the journey to mathematical success!
Table of Contents
Chapter 1: The Real Number System and Geometry 1.1 Review of Fractions 1.2 Exponents and Order of Operations 1.3 Geometry Review 1.4 Sets of Numbers and Absolute Value 1.5 Addition and Subtraction of Real Numbers 1.6 Multiplication and Division of Real Numbers 1.7 Algebraic Expressions and Properties of Real Numbers Chapter 2: Variables and Exponents 2.1 Simplifying Expressions 2.2a The Product Rule and Power Rules of Exponents 2.2b Combining the Rules 2.3a Integer Exponents with Real Number Bases 2.3b Integer Exponents with Variable Bases 2.4 The Quotient Rule Mid-Chapter Summary: Putting the Rules Together 2.5 Scientific Notation Chapter 3: Linear Equations and Inequalities 3.1 Solving Linear Equations Part I 3.2 Solving Linear Equations Part II 3.3 Applications of Linear Equations to General Problems, Consecutive Integers, and Fixed and Variable Cost 3.4 Applications of Linear Equations to Percent Increase/Decrease and Investment Problems Section 3.5 Geometry Applications and Solving Formulas for a Specific Variable 3.6 Applications of Linear Equations to Proportions, d=rt, and Mixture Problems 3.7 Solving Linear Inequalities in One Variable 3.8 Solving Compound Inequalities Chapter 4: Linear Equations in Two Variables 4.1 Introduction to Linear Equations in Two Variables 4.2 Graphing by Plotting Points and Finding Intercepts 4.3 The Slope of a Line 4.4 The Slope-Intercept Form of a Line 4.5 Writing an Equation of a Line 4.6 Parallel and Perpendicular Lines 4.7 Introduction to Functions 4.8 Function Notation and Linear Functions Chapter 5: Solving Systems of Linear Equations 5.1 Solving Systems of Linear Equations by Graphing 5.2 Solving Systems of Linear Equations by Substitution 5.3 Solving Systems of Linear Equations by the Elimination Method Mid-Chapter Summary 5.4 Applications of Systems of Two Equations 5.5 Systems of Linear Equations in Three Variables 6: Polynomials 6.1 Review of Rules of Exponents 6.2 Addition and Subtraction of Polynomials 6.3 Multiplication of Polynomials 6.4 Division of Polynomials Chapter 7: Factoring Polynomials 7.1 The Greatest Common Factor and Factoring by Grouping 7.2 Factoring Trinomials of the Form x^2 + bx + c 7.3 Factoring Trinomials of the Form ax^2 + bx + c (a not equal to 1) 7.4 Factoring Binomials and Perfect Square Trinomials Mid-Chapter Summary 7.5 Solving Quadratic Equations by Factoring 7.6 Applications of Quadratic Equations Chapter 8: Rational Expressions 8.1 Simplifying Rational Expressions 8.2 Multiplying and Dividing Rational Expressions 8.3 Finding the Least Common Denominator 8.4 Adding and Subtracting Rational Expressions Mid-Chapter Summary 8.5 Simplifying Complex Fractions 8.6 Solving Rational Equations 8.7 Applications of Equations Containing Rational Expressions 9: Absolute Value Equations and Inequalities and More on Solving Systems 9.1 Solving Absolute Value Equations 9.2 Solving Absolute Value Inequalities 9.3 Linear Inequalities in Two Variables 9.4 Solving Systems of Equations Using Matrices Chapter 10: Radicals and Rational Exponents 10.1 Finding Roots 10.2 Rational Exponents 10.3 Simplifying Expressions Containing Square Roots 10.4 Simplifying Expressions Containing Higher Roots 10.5 Adding and Subtracting Radicals 10.6 Combining Multiplication, Addition, and Subtraction of Radicals 10.7 Dividing Radicals 10.8 Solving Radical Equations 11: Quadratic Equations 11.1 Review of Solving Equations by Factoring 11.2 Solving Quadratic Equations Using the Square Root Property 11.3 Complex Numbers 11.4 Solving Quadratic Equations by Completing the Square 11.5 Solving Equations Using the Quadratic Formula Mid-Chapter Summary 11.6 Equations in Quadratic Form 11.7 Formulas and Applications Chapter 12: Functions and their Graphs 12.1 Relations and Functions 12.2 Graphs of Functions and Transformations 12.3 Quadratic Functions and their Graphs 12.4 Applications of Quadratic Functions and Graphing Other Parabolas 12.5 The Algebra of Functions 12.6 Variation Chapter 13: Inverse, Exponential, and Logarithmic Functions 13.1 Inverse Functions 13.2 Exponential Functions 13.3 Logarithmic Functions 13.4 Properties of Logarithms 13.5 Common and Natural Logarithms and Change of Base 13.6 Solving Exponential and Logarithmic Equations 14: Conic Sections, Nonlinear Inequalities, and Nonlinear Systems 14.1 The Circle 14.2 The Ellipse and the Hyperbola Mid-Chapter Summary 14.3 Nonlinear Systems of Equations 14.4 Quadratic and Rational Inequalities Chapter 15: Sequences and Series **Available online** 15.1 Sequences and Series 15.2 Arithmetic Sequences and Series 15.3 Geometric Sequences and Series 15.4 The Binomial Theorem Appendix: Beginning Algebra Review A1 The Real Number System and Geometry A2 Variables and Exponents A3 Linear Equations and Inequalities A4 Linear Equations in Two Variables and Functions A5 Solving Systems of Linear Equations A6 Polynomials A7 Factoring Polynomials A8 Rational Expressions