MAT 113-101 COLLEGE ALGEBRA Room H 114 (Monday/Wednesday 10:00 11:15) Fall 2012 Kamal P. Hennayake PhD Professor of Mathematics Office: H-120 Phone: 410-822-5400 Ext. 2312 Chesapeake College Wye Mills, Maryland 21679 khennayake@chesapeake.edu http://www.chesapeake.edu/khennayake
INSTRUCTOR: Dr. Kamal P. Hennayake - Office H 120; Phone Ext. 2312 (Voice Mail) E-MAIL: khennayake@chesapeake.edu COURSE DESCRIPTION: A college level algebra course for students not majoring in mathematics, engineering, or the physical sciences. Topics included are the real number system, algebraic, exponential, logarithmic, and polynomial functions; rational polynomials, systems of equations, and appropriate applications. PREREQUISITE: Appropriate score on placement test, or MAT 032. REQUIRED COURSE MATERIALS: TEXTBOOK: College Algebra, Fifth Edition, by Robert Blitzer 2004. Prentice-Hall, Inc. ISBN 0-13-978-0-321-55983-8. Make sure to get MyMathLab (MML) student access kit with the textbook. CALCULATOR: Texas Instruments TI-83+ is recommended. INTRODUCTION: College Algebra is a prerequisite for many courses that involve mathematical applications. It provides a good background for many college level courses in a broad range of academic disciplines. The topics covered are included in the "Course Description" and computer software/graphing calculators may also be used to further illustrate specific concepts. As you begin your study of College Algebra, you may feel overwhelmed by the number of theorems, definitions, procedures, and equations that confront you. You may even wonder whether or not you can learn all of this material in the time allotted. These concerns are normal. Keep in mind that many elements of College Algebra are all around us as we go through our daily routines. Many of the concepts you will learn to express mathematically, you already know intuitively. For many of you, this may be your last math course, while for others, just the first in a series of many. Now that you have decided to take this course, remember that a positive attitude will make all the difference in the world. Your belief that you can succeed is just as important as your commitment to this course. Make sure that you are ready for this course by having the time and positive attitude that it takes to succeed. Specific suggestions for being successful in this course: Attend all classes. Students whose attendance is sporadic often do not do well because of the nature of the course, especially in the accelerated format. Most students need guidance in understanding the procedures involved in developing a new mathematical process. If you find yourself unable to keep up with the class, make an appointment immediately to see the instructor outside of class time. It is the student's responsibility to make up any work missed due to an absence for any reason. Read the book. In addition to arriving for class on time and being prepared, you will find it useful to read the section before it is covered in class. This will give you a clear idea of the new material that will be discussed. Work problems every day and check your answers. In addition to the lectures, the average student should plan to spend at least nine hours outside of class each week (3 hours for every hour spent in class). Students whose background in mathematics is below average, or who normally work at a slower than average pace, should schedule more time in order to keep up with the course material. The homework assigned represents the minimum course of study.
In order to comfortably succeed in MAT 113 you will need to be proficient in the following skills. If you need to brush up on any of these skills please ask for help immediately! o Basic equation solving o Solving application problems o Evaluating exponential expressions o Factoring all types o Simplifying rational expressions GRADES: The course grade will be determined as follows: Component Possible points Weighted Percentage 4 Tests 200 40% MyMathLab Homework (14 assignment 5 points each) 70 14% 4 Quizzes and/or projects 100 20% Final examination 130 26% TOTAL 500 100% Letter Grade Percentage A 90% - 100% B 80% - 89% C 70% - 79% D 65% - 69% F Less than 65% Tests: At the end of each module you ll take a test. You are not allowed to use notes or textbooks for tests. Don t forget to bring a pencil, and a calculator. If you missed a test for any reason, you have a zero for that test. Final exam is a comprehensive exam. Everyone must take it in class. MyMathLab assignments: You are expected to do homework problems in MML. This may help you to check whether you had understood the information from each lesson.
Projects: Throughout the semester you will have at least 4 projects/writing assignments and or quizzes. Attendance and Participation: Research shows that attendance is the single most important factor in school success. Students are expected to attend each class, arrive on time, complete all assignments and learning assessments in accord with the syllabus schedule, and participate in the in-class learning process. Learning builds day by day. If you miss a day of class, you miss a day of learning. Material learned on one day is used the next day and the next day, and so forth. It is very difficult to catch up when you miss one day and fall behind. It is the student s responsibility to make up any work missed due to an absence for any reason. Classroom Etiquette: It is assumed that all students will respect each other s rights to fully participate in the discussion of the day. To that end, it is expected that students will not engage in behaviors that distract not only the instructor but also their fellow classmates. Students who engage in activities such as talking to each others, talking on cell phones or text messaging, leaving class for non-emergency needs, will be asked to leave. If you are unlucky enough to be one of these students, you will be required to meet with me in my office prior to returning to class. I expect that all of students will behave in an adult, respectful and polite manner towards both the instructor and their classmates. Students are prohibited from using, activating or displaying personal electronic devises. Learning Outcomes: Students will be able to: 1. Use appropriate algebraic problem solving tools to solve equations and/or inequalities 2. Use the rectangular coordinate system to construct graphs of given functions, and a graphing calculator to verify the graphs. 3. Algebraically and graphically analyze the characteristics of polynomial, rational, exponential, and logarithmic functions. 4. Solve systems of linear and/or non-linear equations by the methods of substitution, addition, Gaussian elimination and/or Cramer s Rule as appropriate to the problem. 5. Apply various methods of algebra to problem solving of applications and use a graphing calculator to verify the calculations and/or graphs. Review Objectives Chapter P: Prerequisites: Fundamental Concepts of Algebra - Reviewed by students Evaluate and simplify algebraic expressions. Simplify exponential expressions. Use scientific notation. Evaluate and simplify square roots. Rationalize denominators. Understand and use rational exponents. Add, subtract, and multiply polynomials. Factor polynomials. Factor the sum or difference of two cubes.
Factor algebraic expressions containing fractional and negative exponents. Specify numbers that must be excluded from the domain of a rational expression. Add, subtract, multiply, and divide rational expressions. Simplify complex rational expressions. Chapter 1 sections 1, 2, and 3: Equations and Inequalities - Reviewed by students Solve linear equations. Solve rational equations. Recognize identities, conditional equations, and inconsistent equations. Solve applied problems using mathematical models. Solve a formula for a variable. Chapter 2 sections 3 and 4: Functions and Graphs - Reviewed by students Recognize and use the forms of a line s equation. Graph equations in the rectangular coordinate system. Graph horizontal or vertical lines. Use a graph to determine intercepts. Model data with linear functions and make predictions. Find slopes and equations of parallel and perpendicular lines. Find functions average rate of change. Chapter 3.7: Modeling Using Variation - Reviewed by students Solve problems involving direct, inverse, and joint variation. Students should already understand the above objectives or should be able to review them within the first week of the semester. Course Objectives After completing each chapter the student should be able to accomplish the following: Chapter 1: Equations and Inequalities Perform operations with complex numbers and square root of negative numbers. Solve quadratic equations by factoring, by the square root property, by completing the square, by using the quadratic formula. Use the discriminant to determine the number and type of solutions. Determine the most efficient method to use when solving a quadratic equation. Solve problems modeled by quadratic equations. Solve polynomial equations by factoring, solve radical equations, solve equations with rational exponents, solve equations that are quadratic in form, and solve equations involving absolute value. Solve linear inequalities, absolute value inequalities, and graph the solution sets. Chapter 2: Functions and Graphs Determine whether a relation is a function and whether an equation represents a function. Find the domain of a function and evaluate a function. Obtain information about a function from its graph. Graph functions by plotting points, involving a transformation, or a sequence of transformations. Evaluate piecewise functions. Identify intervals on which a function increases, decreases, or is constant.
Identify even or odd functions and recognize their symmetries. Use transformations to graph functions and graph functions involving sequence of transformations. Combine functions using the algebra of functions. Form composite functions and determine domains for composite functions. Write functions as compositions. Verify inverse functions. Find the inverse of a function and graph both functions on the same axes. Use the horizontal line test to determine if a function has an inverse function. Use the graph of a one-to-one function to graph its inverse function. Find the distance between two points and the midpoint of a line segment. Use the general form and standard form of a circle s equation. Chapter 3: Polynomial and Rational Functions Recognize characteristics of parabolas and graph parabolas. Use factoring to find zeros of polynomial functions and identify the multiplicity of a zero. Understand the relationship between degree and turning points. Use long division and synthetic division to divide polynomials. Use the Rational Zero Theorem to find possible rational zeros. Find polynomials with given zeros. Identify vertical and horizontal asymptotes. Solve problems modeled by polynomial or rational inequalities. Chapter 4: Exponential and Logarithmic Functions Evaluate and graph exponential functions and logarithmic functions. Change from logarithmic to exponential form and exponential to logarithmic form. Find the domain of a logarithmic function. Use properties of logarithms. Solve exponential and logarithmic equations. Solve applied problems involving exponential and logarithmic equations. Model data with exponential and logarithmic functions. Chapter 5: Systems of Equations and Inequalities - (Optional as time permits) Solve linear systems and nonlinear systems by substitution and by addition. Solve systems of linear equations in three variables. Find partial fraction decomposition of a rational expression. Graph system of inequalities. Solve problems involving systems of inequalities. Chapter 6: Matrices and Determinants (Optional as time permits) Use matrices and Gaussian elimination and Gauss-Jordan elimination to solve systems. Apply Gaussian elimination to systems without unique solutions and with differing numbers of variables and equations.
MAT 113-101 College Algebra Fall 2012 Day Date Activity Extra Practice Problems (Not for grading) P.1: Algebraic Expressions and Real numbers Pg 15: 15, 27, 29, 33, 49, 59, 65, 73, 83, 95, 101 P.2: Exponents and Scientific Notation Pg 31: 21, 63, 75, 85, 89, 105 1 Aug 22 P.3: Radicals and Rational Exponents Pg 46: 11, 21, 31, 43, 53, 65, 73, 81, 89, 99 P.4: Polynomials Pg 58: 3, 7, 11, 17, 33, 57, 65, 69, 81 P.5: Factoring Polynomials Pg 71: 9, 13, 37, 47, 55, 63, 91, 95, 101 P.6: Rational Expressions Pg 82: 9, 17, 31, 35, 53, 57, 63 1.1 Graphs and Graphing Utilities Pg 97: 3, 15, 31, 43 1.2 Linear Equations and Rational Equations Pg 112: 15, 29, 49, 53, 57, 63, 67, 79, 105 2 Aug 27 1.3 Models and Applications Pg 126: 9, 17, 21, 39, 51, 63 2.3 Linear Functions and Slope Pg 239: 5, 13, 19, 29, 37, 43, 55, 59, 63, 69, 87 2.4 More on Slope Pg 250: 1, 3, 5, 7, 9, 11, 13, 15, 17, 25, 27 3.7 Modeling Using Variation Pg 401: 3, 7, 9, 11, 19, 21, 23, 25, 27 Baseline Quiz: Due Sep 5 Pg 82: 1, 5, 9, 15, 18, 23; Pg 183: 3; Pg 295: 25 3 Aug 29 1.4 Complex Numbers Pg 135: 3, 11, 21, 25, 33, 43, 46 4 Sep 5 1.5 Quadratic Equations Pg 152: 13, 31, 45, 61, 69, 77, 107, 149, 151 5 Sep 10 1.6 Other Types of Equations Pg 168: 3, 9, 13, 17, 33, 39, 55, 59, 71, 75, 79 6 Sep 12 1.7 Linear and Absolute Value Inequalities Pg 185: 13, 17, 23, 31, 49, 57, 67, 93, 97, 123 7 Sep 17 Test 1 Pg 195: 11, 15, 16, 17, 20, 21, 33, 34, 44 8 Sep 19 2.1 Basics of Functions and Their Graphs Pg 210: 9, 25, 37, 43, 49, 53, 65, 67, 69, 71, 73, 75, 77, 81, 87, 89, 91 9 Sep 24 2.2 More on Functions and Their Graphs Pg 223: 9, 23, 29, 35, 41, 47, 51, 55, 57, 59, 61 10 Sep 26 2.5 Transformations of Functions Pg 266: 17, 19, 21, 23, 25, 27, 29, 31, 53, 55, 57, 59, 61, 63, 65, 81, 83, 85, 87, 89, 91, 93 11 Oct 1 2.6 Combinations; Composite Functions Pg 279: 13, 19, 27, 35, 37, 59, 63, 65, 67, 69 12 Oct 3 Review for test 2 Pg 304: 9, 17, 19, 22, 27, 49, 51, 53, 55, 57, 74, 77, 81 13 Oct 8 Test 2 Pg 309: 2, 3, 16, 17, 18, 19, 20, 29, 32 14 Oct 10 2.7 Inverse Functions Pg 290: 5, 11, 23, 35, 37, 39, 41, 49, 53 15 Oct 15 2.8 Distance and Midpoint; Circles Pg 300: 7, 21, 29, 31, 35, 41, 45, 49, 55, 59 16 Oct 17 3.1 Quadratic Functions Pg 324: 9, 13, 15, 17, 25, 37, 39, 41, 43, 65, 67 17 Oct 22 3.2 Polynomial Functions and Their Graphs Pg 338: 5, 21, 23, 25, 29, 35, 41, 49, 55, 61, 63 Oct 22 Mid-term Grades Due 18 Oct 24 Review for Test 3 Pg 307: 87, 94, 96, 97, 99, 105; Pg 406: 3, 8, 18, 25 19 Oct 29 Test 3 20 Oct 31 3.3 Dividing Polynomials: Pg 350: 5, 9, 15, 23, 31, 39, 41, 43, 45 21 Nov 5 3.4 Zeros of Polynomial Functions Pg 361: 5, 15, 19, 25, 27, 33, 35, 37, 41, 49, 51 Nov 1 Last Day to drop a course with a W grade 22 Nov 7 3.5 Rational Functions and Their Graphs Pg 380: 5, 9, 11, 13, 15, 17, 19, 21, 27, 29, 31, 33, 37, 41, 51, 57, 71, 75 23 Nov 12 3.6 Polynomial and Rational Inequalities Pg 391: 9, 19, 39, 43, 47, 55, 79 24 Nov 14 Review for Test 4 Pg 407: 27, 31, 35, 37, 47, 49, 57, 69,
Day Date Activity Homework 25 Nov 19 Test 4 Pg 410: 9, 10, 11, 14, 18, 23 4.1 Exponential Functions Pg 420: 7, 15, 25, 27, 29, 31, 33, 53, 55 26 Nov 26 4.2 Logarithmic Functions Pg 434: 5, 13, 17, 29, 41, 43, 53, 55, 57, 75, 77, 79, 81, 89, 97 27 Nov 28 4.3 Properties of Logarithms Pg 445: 7, 19, 31, 49, 57, 65, 77, 79, 81 28 Dec 3 4.4 Exponential and Logarithmic Equations Pg 456: 1, 7, 19, 23, 31, 49, 57, 65, 77, 79, 81, 89, 91 29 Dec 10 Final Examination (130 points) 9:30 11:30 This is a tentative schedule. It is subject to change.
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