Preliminary Edition of Beginning and Intermediate Algebra

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 1 Summary Chapter 1 Review Chapter 1 Test 2 Variables and Exponents 2.1 Simplifying Expressions 2.2 a) The Product Rule and Power Rules for Exponents b) Combining the Rules 2.3 a) Integer Exponents With Real-Number Bases 2.3 b) Integer Exponents With Variable Bases 2.4 The Quotient Rule SUMMARY EXERCISES: Putting All the Rules Together 2.5 Scientific Notation Chapter 2 Summary Chapter 2 Review Chapter 2 Test Cumulative Review Ch. 1 & 2 3 Linear Equations and Inequalities 3.1 Solving Linear Equations Part I 3.2 Solving Linear Equations Part II SUMMARY EXERCISES 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 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 3 Summary Chapter 3 Review Chapter 3 Test Cumulative Review Ch. 1 3 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 Chapter 4 Summary Chapter 4 Review Chapter 4 Test Cumulative Review Ch. 1 4 5 Solving Systems of Linear Equations 5.1 Solving Systems by Graphing 5.2 Solving Systems by Substitution 5.3 Solving Systems by the Addition Method SUMMARY EXERCISES 5.4 Applications of Systems of Two Equations Chapter 5 Summary Chapter 5 Review Chapter 5 Test Cumulative Review Ch. 1 5 6 Polynomials 6.1 Review of Rules of Exponents 6.2 Addition and Subtraction of Polynomials 6.3 Multiplication of Polynomials SUMMARY EXERCISES 6.4 Division of Polynomials Chapter 6 Summary Chapter 6 Review Chapter 6 Test Cumulative Review Ch. 1 6 7 Factoring Polynomials 7.1 The Greatest Common Factor and Factoring by Grouping 7.2 Factoring Trinomials of the Form x2 + bx + c 7.3 Factoring Trinomials of the Form ax2 + bx + c (x 1) 7.4 Factoring Binomials and Perfect Square Trinomials SUMMARY EXERCISES 7.5 Solving Quadratic Equations by Factoring 7.6 Applications of Quadratic Equations Chapter 7 Summary Chapter 7 Review Chapter 7 Test Cumulative Review Ch. 1 7 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 SUMMARY EXERCISES 8.5 Simplifying Complex Fractions 8.6 Solving Equations Containing Rational Expressions SUMMARY EXERCISES 8.7 Applications Chapter 8 Summary Chapter 8 Review Chapter 8 Test Cumulative Review Ch. 1 8 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 Systems of Linear Equations in Three Variables 9.5 Solving Systems Using Gaussian Reduction Chapter 9 Summary Chapter 9 Review Chapter 9 Test Cumulative Review Ch. 1 9 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 Chapter 10 Summary Chapter 10 Review Chapter 10 Test Cumulative Review Ch. 1 10 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 Quadratic Equations Using the Quadratic Formula SUMMARY EXERCISES 11.6 Equations in Quadratic Form 11.7 Formulas and Applications Chapter 11 Summary Chapter 11 Review Chapter 11 Test Cumulative Review Ch. 1 11 12 Functions and their Graphs 12.1 Relations and Functions 12.2 Function Notation and Linear Functions 12.3 Graphs of Other Functions 12.4 Transformations of Graphs 12.5 Quadratic Functions and their Graphs 12.6 Applications of Quadratic Functions and Graphing Other Parabolas SUMMARY EXERCISES 12.7 The Algebra of Functions 12.8 Variation Chapter 12 Summary Chapter 12 Review Chapter 12 Test Cumulative Review Ch. 1 12 13 Inverse, Exponential, and Logarithmic Functions 13.1 Inverse Functions 13.2 Exponential Functions 13.3 Logarithmic Functions SUMMARY EXERCISES 13.4 Properties of Logarithms 13.5 Common and Natural Logarithms and Change of Base 13.6 Solving Exponential and Logarithmic Equations Chapter 13 Summary Chapter 13 Review Chapter 13 Test Cumulative Review Ch. 1 13 14 Conic Sections, Nonlinear Inequalities, and Nonlinear Systems 14.1 Review of Parabolas 14.2 The Circle 14.3 The Ellipse and the Hyperbola SUMMARY EXERCISES 14.4 Nonlinear Systems of Equations 14.5 Quadratic and Rational Inequalities 14.6 Second Degree Inequalities and Systems of Inequalities Chapter 14 Summary Chapter 14 Review Chapter 14 Test Cumulative Review Ch. 1 14 15 Sequences and Series 15.1 Sequences and Series 15.2 Arithmetic Sequences and Series 15.3 Geometric Sequences and Series 15.4 The Binomial Theorem Chapter 15 Summary Chapter 15 Review Chapter 15 Test Cumulative Review Ch. 1 15 APPENDIXES A. Beginning Algebra Review B. Synthetic Division C. Determinants and Cramer's RuleMessersmith, Sherri is the author of 'Preliminary Edition of Beginning and Intermediate Algebra ', published 2006 under ISBN 9780073406152 and ISBN 0073406155.