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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 studentï¿½s 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-Hillï¿½s online homework management system, MathZone.
Messersmith ï¿½ mapping the journey to mathematical success!
Table of Contents
Chapter 1: The Real Number System and Geometry Section 1.1 Review of Fractions Section 1.2 Exponents and Order of Operations Section 1.3 Geometry Review Section 1.4 Sets of Numbers and Absolute Value Section 1.5 Addition and Subtraction of Real Numbers Section 1.6 Multiplication and Division of Real Numbers Section 1.7 Algebraic Expressions and Properties of Real Numbers Chapter 2: Variables and Exponents Section 2.1 Simplifying Expressions Section 2.2a The Product Rule and Power Rules of Exponents Section 2.2b Combining the Rules Section 2.3a Integer Exponents with Real Number Bases Section 2.3b Integer Exponents with Variable Bases Section 2.4 The Quotient Rule Mid-Chapter Summary: Putting the Rules Together Section 2.5 Scientific Notation Chapter 3: Linear Equations and Inequalities Section 3.1 Solving Linear Equations Part I Section 3.2 Solving Linear Equations Part II Section 3.3 Applications of Linear Equations to General Problems, Consecutive Integers, and Fixed and Variable Cost Section 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 Section 3.6 Applications of Linear Equations to Proportions,d=rt, and Mixture Problems Section 3.7 Solving Linear Inequalities in One Variable Section 3.8 Solving Compound Inequalities Chapter 4: Linear Equations in Two Variables Section 4.1 Introduction to Linear Equations in Two Variables Section 4.2 Graphing by Plotting Points and Finding Intercepts Section 4.3 The Slope of a Line Section 4.4 The Slope-Intercept Form of a Line Section 4.5 Writing an Equation of a Line Section 4.6 Parallel and Perpendicular Lines Section 4.7 Introduction to Functions Section 4.8 Function Notation and Linear Functions Chapter 5: Solving Systems of Linear Equations Section 5.1 Solving Systems of Linear Equations by Graphing Section 5.2 Solving Systems of Linear Equations by Substitution Section 5.3 Solving Systems of Linear Equations by the Elimination Method Mid-Chapter Summary Section 5.4 Applications of Systems of Two Equations Section 5.5 Systems of Linear Equations in Three Variables Chapter 6: Polynomials Section 6.1 Review of Rules of Exponents Section 6.2 Addition and Subtraction of Polynomials Section 6.3 Multiplication of Polynomials Section 6.4 Division of Polynomials Chapter 7: Factoring Polynomials Section 7.1 The Greatest Common Factor and Factoring by Grouping Section 7.2 Factoring Trinomials of the Form x^2 + bx + c Section 7.3 Factoring Trinomials of the Form ax^2 + bx + c (a not equal to 1) Section 7.4 Factoring Binomials and Perfect Square Trinomials Mid-Chapter Summary Section 7.5 Solving Quadratic Equations by Factoring Section 7.6 Applications of Quadratic Equations Chapter 8: Rational Expressions Section 8.1 Simplifying Rational Expressions Section 8.2 Multiplying and Dividing Rational Expressions Section 8.3 Finding the Least Common Denominator Section 8.4 Adding and Subtracting Rational Expressions Mid-Chapter Summary Section 8.5 Simplifying Complex Fractions Section 8.6 Solving Rational Equations Section 8.7 Applications of Equations Containing Rational Expressions Chapter 9: Absolute Value Equations and Inequalities and More on Solving Systems Section 9.1 Solving Absolute Value Equations Section 9.2 Solving Absolute Value Inequalities Section 9.3 Linear Inequalities in Two Variables Section 9.4 Solving Systems of Equations Using Matrices Chapter 10: Radicals and Rational Exponents Section 10.1 Finding Roots Section 10.2 Rational Exponents Section 10.3 Simplifying Expressions Containing Square Roots Section 10.4 Simplifying Expressions Containing Higher Roots Section 10.5 Adding and Subtracting Radicals Section 10.6 Combining Multiplication, Addition, and Subtraction of Radicals Section 10.7 Dividing Radicals Section 10.8 Solving Radical Equations Chapter 11: Quadratic Equations Section 11.1 Review of Solving Equations by Factoring Section 11.2 Solving Quadratic Equations Using the Square Root Property Section 11.3 Complex Numbers Section 11.4 Solving Quadratic Equations by Completing the Square Section 11.5 Solving Equations Using the Quadratic Formula Mid-Chapter Summary Section 11.6 Equations in Quadratic Form Section 11.7 Formulas and Applications Chapter 12: Functions and their Graphs Section 12.1 Relations and Functions Section 12.2 Graphs of Functions and Transformations Section 12.3 Quadratic Functions and their Graphs Section 12.4 Applications of Quadratic Functions and Graphing Other Parabolas Section 12.5 The Algebra of Functions Section 12.6 Variation Chapter 13: Inverse, Exponential, and Logarithmic Functions Section 13.1 Inverse Functions Section 13.2 Exponential Functions Section 13.3 Logarithmic Functions Section 13.4 Properties of Logarithms Section 13.5 Common and Natural Logarithms and Change of Base Section 13.6 Solving Exponential and Logarithmic Equations Chapter 14: Conic Sections, Nonlinear Inequalities, and Nonlinear Systems Section 14.1 The Circle Section 14.2 The Ellipse and the Hyperbola Mid-Chapter Summary Section 14.3 Nonlinear Systems of Equations Section 14.4 Quadratic and Rational Inequalities Chapter 15: Sequences and Series **Available online** Section 15.1 Sequences and Series Section 15.2 Arithmetic Sequences and Series Section 15.3 Geometric Sequences and Series Section 15.4 The Binomial Theorem Appendix: Beginning Algebra Review Section A1 The Real Number System and Geometry Section A2 Variables and Exponents Section A3 Linear Equations and Inequalities Section A4 Linear Equations in Two Variables and Functions Section A5 Solving Systems of Linear Equations Section A6 Polynomials Section A7 Factoring Polynomials Section A8 Rational Expressions