Synopses & Reviews
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 students 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-Hills online homework management system, MathZone.
Messersmith – mapping the journey to mathematical success!
Table of Contents
1 The Real Number System and Geometry1.1 Review of Fractions1.2 Exponents and Order of Operations1.3 Geometry Review1.4 Sets of Numbers and Absolute Value1.5 Addition and Subtraction of Real Numbers1.6 Multiplication and Division of Real Numbers1.7 Algebraic Expressions and Properties of Real NumbersChapter 1 SummaryChapter 1 ReviewChapter 1 Test2 Variables and Exponents2.1 Simplifying Expressions2.2 a) The Product Rule and Power Rules for Exponents b) Combining the Rules 2.3 a) Integer Exponents With Real-Number Bases2.3 b) Integer Exponents With Variable Bases 2.4 The Quotient RuleSUMMARY EXERCISES: Putting All the Rules Together2.5 Scientific NotationChapter 2 SummaryChapter 2 ReviewChapter 2 TestCumulative Review – Ch. 1and2 3 Linear Equations and Inequalities3.1 Solving Linear Equations – Part I3.2 Solving Linear Equations – Part II SUMMARY EXERCISES3.3 Applications of Linear Equations to General Problems, Consecutive Integers, and Fixed and Variable Cost3.4 Applications of Linear Equations to Percent Increase/Decrease and Investment Problems3.5 Geometry Applications and Solving Formulas for a Specific Variable3.6 Applications of Linear Equations to Proportions, d=rt, and Mixture Problems3.7 Solving Linear Inequalities in One Variable3.8 Solving Compound InequalitiesChapter 3 SummaryChapter 3 ReviewChapter 3 TestCumulative Review – Ch. 1 – 34 Linear Equations in Two Variables4.1 Introduction to Linear Equations in Two Variables4.2 Graphing by Plotting Points and Finding Intercepts4.3 The Slope of a Line4.4 The Slope-Intercept Form of a Line4.5 Writing an Equation of a Line4.6 Parallel and Perpendicular LinesChapter 4 SummaryChapter 4 ReviewChapter 4 TestCumulative Review – Ch. 1 – 45 Solving Systems of Linear Equations5.1 Solving Systems by Graphing5.2 Solving Systems by Substitution5.3 Solving Systems by the Addition MethodSUMMARY EXERCISES 5.4 Applications of Systems of Two EquationsChapter 5 SummaryChapter 5 ReviewChapter 5 TestCumulative Review – Ch. 1 – 56 Polynomials6.1 Review of Rules of Exponents6.2 Addition and Subtraction of Polynomials6.3 Multiplication of PolynomialsSUMMARY EXERCISES6.4 Division of PolynomialsChapter 6 SummaryChapter 6 ReviewChapter 6 TestCumulative Review – Ch. 1 – 67 Factoring Polynomials7.1 The Greatest Common Factor and Factoring by Grouping7.2 Factoring Trinomials of the Form x2 + bx + c7.3 Factoring Trinomials of the Form ax2 + bx + c (x ¿ 1) 7.4 Factoring Binomials and Perfect Square TrinomialsSUMMARY EXERCISES7.5 Solving Quadratic Equations by Factoring7.6 Applications of Quadratic EquationsChapter 7 SummaryChapter 7 ReviewChapter 7 TestCumulative Review – Ch. 1 – 78 Rational Expressions8.1 Simplifying Rational Expressions8.2 Multiplying and Dividing Rational Expressions8.3 Finding the Least Common Denominator8.4 Adding and Subtracting Rational ExpressionsSUMMARY EXERCISES8.5 Simplifying Complex Fractions8.6 Solving Equations Containing Rational ExpressionsSUMMARY EXERCISES8.7 Applications Chapter 8 SummaryChapter 8 ReviewChapter 8 TestCumulative Review – Ch. 1 – 89 Absolute Value Equations and Inequalities and More on Solving Systems9.1 Solving Absolute Value Equations9.2 Solving Absolute Value Inequalities9.3 Linear Inequalities in Two Variables9.4 Systems of Linear Equations in Three Variables9.5 Solving Systems Using Gaussian ReductionChapter 9 SummaryChapter 9 ReviewChapter 9 TestCumulative Review – Ch. 1 – 910 Radicals and Rational Exponents10.1 Finding Roots10.2 Rational Exponents10.3 Simplifying Expressions Containing Square Roots10.4 Simplifying Expressions Containing Higher Roots10.5 Adding and Subtracting Radicals10.6 Combining Multiplication, Addition, and Subtraction of Radicals10.7 Dividing Radicals10.8 Solving Radical Equations Chapter 10 SummaryChapter 10 ReviewChapter 10 TestCumulative Review – Ch. 1 – 1011 Quadratic Equations11.1 Review of Solving Equations by Factoring11.2 Solving Quadratic Equations Using the Square Root Property11.3 Complex Numbers11.4 Solving Quadratic Equations by Completing the Square11.5 Solving Quadratic Equations Using the Quadratic FormulaSUMMARY EXERCISES 11.6 Equations in Quadratic Form 11.7 Formulas and Applications Chapter 11 SummaryChapter 11 ReviewChapter 11 TestCumulative Review Ch. 1 – 1112 Functions and their Graphs12.1 Relations and Functions 12.2 Function Notation and Linear Functions12.3 Graphs of Other Functions12.4 Transformations of Graphs 12.5 Quadratic Functions and their Graphs12.6 Applications of Quadratic Functions and Graphing Other ParabolasSUMMARY EXERCISES 12.7 The Algebra of Functions12.8 VariationChapter 12 SummaryChapter 12 ReviewChapter 12 TestCumulative Review – Ch. 1 – 1213 Inverse, Exponential, and Logarithmic Functions13.1 Inverse Functions13.2 Exponential Functions13.3 Logarithmic FunctionsSUMMARY EXERCISES13.4 Properties of Logarithms13.5 Common and Natural Logarithms and Change of Base13.6 Solving Exponential and Logarithmic Equations Chapter 13 SummaryChapter 13 ReviewChapter 13 TestCumulative Review – Ch. 1 – 1314 Conic Sections, Nonlinear Inequalities, and Nonlinear Systems14.1 Review of Parabolas14.2 The Circle14.3 The Ellipse and the HyperbolaSUMMARY EXERCISES14.4 Nonlinear Systems of Equations14.5 Quadratic and Rational Inequalities14.6 Second – Degree Inequalities and Systems of InequalitiesChapter 14 SummaryChapter 14 ReviewChapter 14 TestCumulative Review – Ch. 1 – 1415 Sequences and Series15.1 Sequences and Series15.2 Arithmetic Sequences and Series15.3 Geometric Sequences and Series15.4 The Binomial TheoremChapter 15 SummaryChapter 15 ReviewChapter 15 TestCumulative Review – Ch. 1 – 15 APPENDIXES
A. Beginning Algebra Review B. Synthetic Division C. Determinants and Cramers Rule