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INTERMEDIATE ALGEBRA employs a proven, three-step problem-solving approach—learn a skill, use the skill to solve equations, and then use the equations to solve application problems—to keep students focused on building skills and reinforcing them through practice. This simple and straightforward approach, in an easy-to-read format, has helped many students grasp and apply fundamental problem-solving skills. The carefully structured pedagogy includes learning objectives, detailed examples to develop concepts, practice exercises, an extensive selection of problem-set exercises, and well-organized end-of-chapter reviews and assessments. The clean and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad array of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. Also, as recommended by the American Mathematical Association of Two-Year Colleges, many basic geometric concepts are integrated in problem-solving scenarios. The text's resource package—anchored by Enhanced WebAssign, an online homework management tool—saves instructors time while also providing additional help and skill-building practice for students outside of class.
- Clear-cut, three-step problem-solving approach—The authors keep students focused on problem-solving by helping them understand and apply three easy steps: learn a skill (in which algebraic skills are demonstrated in worked out problems), use the skill to solve equations and inequalities, and then apply the skill by using equations and inequalities as problem-solving tools in word problems.
- Examples comprise the "learning" portion of the three-step approach. Practice Your Skills problems within the examples are the "using" portion. Apply Your Skill examples are the "apply" portion. Many examples contain annotations, remarks, or check steps that verify that an answer is correct and encourage students to check their work.
- Focus on learning objectives and outcomes—Learning objectives begin each section and are repeated within the sections as subheads to organize the material. Exercises in the problem sets and chapter review problem sets are grouped by learning objectives, allowing instructors to see which concepts a student has mastered when their assignments are completed.
- Plentiful problem-solving opportunities are offered in Concept Quizzes before each section (primarily true/false), problem sets, review problems, chapter tests, and cumulative review problem sets—all with answers provided. Thoughts into Words problems encourage students to express in written form their thoughts about mathematical ideas. Further Investigations are slightly more complex.
- Easy-to-use, information-rich, chapter summaries—Presented in a grid format and organized by learning objective, these recaps organize the chapter content for easy accessibility. For each learning objective, the grid includes a summary of the relevant mathematical technique or concept in simple language, an example to illustrate it, and (to reinforce the need to practice) the appropriate Chapter Review Problems for the objective.
Sets, Real Numbers, and Numerical Expressions. Operations with Real Numbers. Properties or Real Numbers and the Use of Exponents. Algebraic Expressions.
2. EQUATIONS, INEQUALITIES AND PROBLEM SOLVING.
Solving First-Degree Equations. Equations Involving Fractional Forms. Equations Involving Decimals and Problem Solving. Formulas. Inequalities. More on Inequalities and Problem Solving. Equations and Inequalities Involving Absolute Values.
3. LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES.
Rectangular Coordinate System and Linear Equations. Linear Inequalities in Two Variables. Distance and Slope. Determining the Equation of a Line.
4. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations and Linear Inequalities in Two Variables. Substitution Method. Elimination-by-Addition Method. Systems of Three Linear Equations in Three Variables.
Polynomials: Sums and Differences. Products and Quotients of Monomials. Multiplying Polynomials. Factoring: Use of the Distributive Property. Factoring: Difference of two Squares and Sums or Difference in Two Cubes. Factoring Trinomials. Equations and Problem Solving.
6. RATIONAL EXPRESSIONS.
Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. More on Rational Expressions and Complex Fractions. Dividing Polynomials. Fractional Equations. More Rational Equations and Applications.
7. EXPONENTS AND RADICALS.
Using Integers as Exponents. Roots and Radicals. Combining Radicals and Simplifying Radicals That Contain Variables. Products and Quotients Involving Radicals. Merging Exponents and Roots. Scientific Notation.
8. QUADRATIC EQUATIONS AND INEQUALITIES.
Complex Numbers. Quadratic Equations. Completing the Square. Quadratic Formula. More Quadratic Equations and Applications. Quadratic and Other Nonlinear Inequalities.
9. CONIC SECTIONS.
Graphing Nonlinear Equations. Graphing Parabolas. More Parabolas and Some Circles. Graphing Ellipses. Graphing Hyperbolas. Systems Involving Nonlinear Equations.
Relations and Functions. Functions: Their Graphs and Applications. Graphing Made Easy Via Transformations. Composition of Functions. Inverse Functions. Direct and Inverse Variations.
11. EXPONENTIAL AND LOGARITHMIC FUCNTIONS.
Exponents and Exponential Functions. Applications of Exponential Functions. Logarithms. Logarithmic Functions. Exponential Equations, Logarithmic Equations, and Problem Solving.
APPENDIX A: PRIME NUMBERS AND OPERATIONS WITH FRACTIONS.
APPENDIX B1: MATRIX APPROACH TO PROBLEM SOLVING.
APPENDIX B2: DETERMINANTS.
APPENDIX B3: 3 X 3 DETERMINANTS AND SYSTEMS OF THREE LINEAR EQUATIONS IN THREE VARIABLES.
APPENDIX B4: SYSTEMS INVOLVING NONLINEAR EQUATIONS AND SYSTEMS OF INEQUALITIES.
Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.
Online Solution Builder
Complete Solutions Manual
The Complete Solutions Manual provides worked-out solutions to all of the problems in the text.
Annotated Instructor's Edition
In the Annotated Instructor's Edition, answers are printed next to all respective exercises. Graphs, tables, and other answers appear in an answer section at the back of the text. Problems that are available in electronic form in Enhanced WebAssign are identified by a highlighted problem number. To create an assessment, whether a quiz, homework assignment, or test, the instructor can select the problems by problem number from the identified problems in the text.