Synopses & Reviews
Intermediate Algebra offers a practical approach to the study of intermediate algebra concepts, consistent with the needs of today's student. The authors help students to develop a solid understanding of functions by revisiting key topics related to functions throughout the text. They put special emphasis on the worked examples in each section, treating them as the primary means of instruction, since students rely so heavily on examples to complete assignments. The applications are also uniquely designed so that students have an experience that is more true to life--students must read information as it appears in a "live" media source and extract only the relevant information needed to solve a stated problem. The unique pedagogy in the text focuses on promoting better study habits and critical thinking skills along with orienting students to think and reason mathematically. Through Intermediate Algebra, students will not only be better prepared for future math courses, they will be better prepared to solve problems and answer questions they encounter in their own lives.
About the Author
Laura Bracken is a lecturer of developmental mathematics at Lewis-Clark State College. She began her career as a secondary science teacher, graduating from Gustavus Adolphus College summa cum laude in 1978 with a double major in chemistry and natural sciences. Later, she returned to college to take more mathematics, qualified for a secondary mathematics endorsement, and continued on to a master's degree in education, concentrating on curriculum and instruction. She started the developmental mathematics program at Lewis-Clark State College in 1992. As developmental mathematics coordinator, she led her colleagues through the process of writing objectives, standardizing assessments, and convincing administrators to enforce prerequisites and placement. She developed the curriculum proposals for "stretch" courses in Elementary Algebra and Finite Mathematics in which students take a one-semester course over two semesters, which improved success rates in at-risk populations. She has worked collaboratively with science faculty to make connections between developmental math courses and introductory science courses. She participated in a Title III grant for developing distance education and regularly teaches on-line developmental courses. She has presented at numerous national and regional meetings and is currently a regional representative for the AMATYC Placement and Assessment Committee. She is a co-author of Investigating Prealgebra and Investigating Basic College Mathematics.Ed Miller is a professor of mathematics at Lewis-Clark State College. He earned his PhD in general topology at Ohio University in 1989. He teaches a wide range of courses, including elementary and intermediate algebra. Building on the gateway exams of the calculus reform movement, he began the mastery skill quiz program that is now an integral part of developmental and core mathematics courses at the college. He has developed collaborative activities and projects in finite mathematics, statistics for the natural sciences, and calculus. He has presented at national and regional meetings. Chairing the 2008 math program review, he is interested in the correlation between reading placement scores, math placement scores, and time of registration with the success rate of students in developmental and core level courses. Serving as faculty representative to the petition committee, he is familiar with the many challenges that developmental students face outside of the classroom. He has been chair of the faculty, a division chair, chair of the curriculum committee, chair of the general education committee, and active in many areas of faculty governance.
Table of Contents
1. FUNDAMENTALS OF ALGEBRA. Sets and Numerical Expressions. Algebraic Expressions. Equations and Inequalities in One Variable. Scientific Notation and Unit Analysis. Applications and Problem Solving. Linear Equations in Two Variables. Linear Inequalities in Two Variables. Summary and Review. Test. 2. POLYNOMIALS AND ABSOLUTE VALUE. Adding, Subtracting, and Multiplying Polynomial Expressions. Factoring Polynomials. Factoring Trinomials. Polynomial Equations. Absolute Value Equations. Conjunctions, Disjunctions, and Absolute Value Inequalities. Summary and Review. Test. 3. RELATIONS AND FUNCTIONS. Relations and Functions. Linear and Constant Functions. Quadratic and Cubic Functions. Polynomial Models. Operations with Functions. Absolute Value Functions. Translation of Polynomial Functions. Summary and Review. Test. Cumulative Review Chapters 1-3. 4. SYSTEM OF LINEAR EQUATIONS. Systems of Linear Equations. Algebraic Methods. Applications. Systems of Linear Equations in Three Variables. Matrix Methods. Systems of Linear Inequalities. Summary and Review. Test. 5. RATIONAL EXPRESSIONS, EQUATIONS AND FUNCTIONS. Simplifying, Multiplying, and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Rational Equations in One Variable. Rational Functions. Variation. Division of Polynomials; Synthetic Division. Rational Inequalities. Summary and Review. Test. 6. RADICAL EXPRESSIONS, EQUATIONS AND FUNCTIONS. Introduction to Radicals. Adding, Subtracting, Multiplying and Simplifying Radical Expressions. Dividing Radical Expressions and Conjugates. Rational Exponents. Radical Equations. Radical Functions. Summary and Review. Test. Cumulative Review Chapters 4-6. 7. QUADRATIC EXPRESSIONS, EQUATIONS AND FUNCTIONS. Complex Numbers. Solving Quadratic Equations. Completing the Square. Quadratic Formula. Quadratic Functions. Vertex Form of a Quadratic Function. Quadratic Inequalities. Summary and Review. Test. 8. EXPONENTIAL AND LOGARITHMIC EXPRESSIONS, EQUATIONS AND FUNCTIONS. Exponential Functions. Logarithmic Functions. Applications. Exponential Equations. Logarithmic Equations. Summary and Review. Test. 9. CONIC SECTIONS SYSTEMS OF NON-LINEAR EQUATIONS. Distance Formula, Midpoint Formula, and Circles. Ellipses. Parabolas. Hyperbolas. Systems of Non-Linear Equations in Two Variables. Summary and Review. Test. Cumulative Review Chapters 7-9. 10. SEQUENCES, SERIES AND THE BINOMIAL THEOREM. Sequences and Series. Arithmetic Sequences. Geometric Sequences. The Binomial Theorem. Summary and Review. Test. APPENDIX. A1: Solving Linear Equations in One Variable. A2: Solving Inequalities in One Variable. A3: Graphing Linear Equations. A4: Slope and Slope-Intercept Form. A5: Writing the Equation of a Line. A6: Reasonability and Problem Solving. A7: Determinants and Cramer's Rule. A8: Developing the Equations of Conic Sections.