MAT College Algebra

Transcription

1 MAT College Algebra Instructor: Dr. Kamal Hennayake I check my regularly. You may use the above or Course . If you have a question that would help other students you may post it in Have a question? under Discussion in Canvas. If you have questions related to the course or any of the graded deliverables, please contact your instructor. For questions and concerns related to advising, please contact Academic Advising. Course Material: Textbook: College Algebra 3 rd Corrected Edition by Carl Stitz and Jeffrey Zeager. You may buy the textbook from the Book Store or you may order it online. Note that, you do not need the textbook to enroll. It is a free open source textbook with open access to textbook and assessments. Course Description: Prerequisite: MATH 032 or an appropriate result on the placement test. 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, polynomial and rational functions; systems of equations, and appropriate applications. Student Learning Outcomes: 1. Apply the mathematical skills required in problem-solving. * Quantitative Reasoning 2. Analyze mathematical models such as formulas, graphs, and tables and draw inferences from them. * Critical Thinking, Quantitative Reasoning 3. Communicate mathematical information conceptually, symbolically, visually, and numerically using appropriate terminology. * Oral & Written Communication, Technology Literacy, Quantitative Reasoning 4. Evaluate and/or interpret mathematical information, relationships, facts, concepts, and theories. * Reading with Comprehension, Critical Thinking, Quantitative Reasoning * Meets Gen Ed Requirements

2 Course Introduction The study of mathematics is an integral part of a college education. All students need to develop critical skills in problem solving and analytical thinking. This course enables students to build a solid foundation of mathematical concepts which can be applied to a variety of fields from accounting to zoology. This fast-paced course covers an introduction to equations, inequalities, and absolute values, and a study of functions and their properties, including linear functions, quadratic functions, higher-order polynomial functions, as well as rational, exponential, and logarithmic functions. This course prepares you for pre-calculus. Problem-solving methods are mastered and applied to topics in life sciences, social sciences, physical sciences, business, and engineering. Disability Information Disability: Students with Disabilities seeking services or accommodations through Chesapeake College must disclose the need for these services or accommodations to the Office of Disability Services. Given sufficient notice and proper documentation, the College will provide reasonable accommodations, auxiliary aids, and related services required by persons with disabilities to allow access to our programs and services, if it is not an undue burden to do so. Students requiring accommodations are urged to submit requests at least 14 days in advance of the need to use them. To be eligible for academic accommodations through Chesapeake College, a student must have a documented disability as defined by the Rehabilitation Act of 1973 or the Americans with Disabilities Act (ADA) of For information on eligibility, contact: Judy Gordon Developmental Studies Case Manager/ADA Coordinator jgordon@chesapeake.edu. Phone: (410) FAX: (410) * Student Services: For help with or information about advising, registration, career planning, financial aid, or the many other aspects of your life as a student at Chesapeake College, consult the Student Success and Enrollment Services office at Grading Information and Criteria You are responsible for the following graded items: Meeting course deadlines is crucial for success in computer mediated courses. You may read at your own pace, but online participation, MyOpenMath exercises, homework problems, quizzes, midterm, and final exam must adhere to the timetable given in the course schedule. Otherwise

3 the grade will be 0. The academic schedule in this syllabus is referenced to local time (Eastern Standard Time or eastern daylight saving time, whichever is appropriate) at Wye Mills, Maryland. No late online participation, assignments, homework, or makeup for quizzes, midterm and final exam will be accepted. You are expected to submit your own work for all assignments, quizzes, and exams. No credit will be given for plagiarism. The course grade will be determined as follows: Component Weighted Percentage Canvas participation Discussions 10% MyOpenMath Assignments 25% Quizzes/project 25% One mid-term examination 15% Final examination 25% TOTAL 100% Grading Scale Letter grades will be assigned as: A % B 80 89% C 70 79% D 60 69% F 0 60%

4 Participation By registering for a Web-based course, you have made a commitment to participate in your course discussion as well as other online activities. To contact your instructor, please use the discussion or links provided, which allow you to communicate with the instructor and your classmates in a virtual classroom, 24 hours a day, 7 days a week. Please plan to participate regularly. You will note in the grading policy that your online participation counts towards your final grade. You are expected to adhere to the general rules of online etiquette. To prepare to use the online discussion, you should read the notes on Online Participation and Online Etiquette in the "Introduction" module. Keep those notes handy; you may need to refer to them frequently during the semester. Communicating Mathematics Online It is important to communicate mathematics effectively when taking a mathematics class online. You may take advantage of equation editors such as those included in word processors and in Canvas s Text Editor. Or you may fall back on a plain-text format to represent mathematical symbols. However, it should be understood that it can be a learning process to become proficient in communicating about mathematics online. Your instructor will provide guidance and support as you develop the ability to communicate clearly and effectively about mathematics online. Grading Details The work you are required to do in this course consists of weekly reading assignments MyOpenMath assignments Canvas participation Quizzes one midterm examination a final examination Each of these is described below.

5 Weekly Reading Assignments Even though there is no numerical score associated with the weekly reading assignments, how well you do in the course depends heavily on how conscientiously you follow the reading assignments. Each week, there will be readings assigned from the textbook. Those readings will include a chapter or part of a chapter. You should also read the module information presented in the Course Content area of Canvas. Assignment details can be found in the schedule in this syllabus. When doing the reading for this course, you need to slow down! Reading mathematics is not like reading anything else. You need to look carefully at the numbers and formulas and spend time making sure you understand them and that they make sense. Reading any mathematical text can take three to four times longer, per page, than reading a nonmathematical text. MyOpenMath Assignments There are homework assignments each week in MyOpenMath, an interactive program that provides homework problems similar to the problems in the textbook. For each section of the textbook there will be some videos to watch to learn algebra and there will be two problem sets assigned in MyOpenMath. The first set is just simple concept questions with videos. The second set has 10 to 20 practice problems. (See the schedule for due dates.) The homework assignments give you practice in solving problems associated with each week's topics. Your aim should be mastery of all concepts, and you will be given unlimited opportunities to succeed in solving all of the problems every week. As completing the homework problems on time will help you understand and master the topics, plan your weeks according to the schedule. There will be several MyOpenMath assignments due each week; to earn credit for each MyOpenMath assignment; you must complete it on time. Canvas Participation For individual participation on an ongoing basis, there is a collection of participation topics posted in Canvas discussion. For participation credit, over the eight weeks of the term, you are expected to solve at least eight topics (from different textbook sections). You are free to choose any topic, complying with the discussion instructions, provided someone else has not already attempted it or "reserved" it. For each participation topic, you will earn up to 10 participation points for the accuracy of your solution. You may be given opportunities to attempt your solution more than one time. If you

6 make an error, you may get feedback and a chance to edit your work and resubmit it. The goal of online participation and problem solving is to help you understand the concepts and to give you an opportunity to practice solving problems and get feedback from the instructor. Online participation work is to be posted in Canvas discussion. Participation work submitted by other means will not be accepted. You may earn a total of 100 online participation points (10 topics at 10 points each is the maximum for regular participation credit). Extra credit for Canvas participation: You may solve up to three additional participation topics over the course of the term, chosen according to discussion guidelines. Each extra-credit topic is worth a maximum of 5 points. Thus, it is possible to earn 25 extra-credit points. For both your required participation topics and your extra-credit participation topics, you may receive up to 125 participation points (100 points for required participation and 25 points for extra-credit participation). You are encouraged to pursue extra credit, but your point total will be capped at 125 points overall. Quizzes and Midterm Examination Quizzes and exams are important milestones, as they provide valuable feedback for instructors and students. Quizzes are open book and will be given as indicated in the schedule. You will be given one week to work on each quiz, and the due dates of the quizzes can be found in the schedule. Each quiz will be posted in the Lessons folder under Quizzes at the beginning of the designated academic week, and each will be due at the end of that academic week. Quizzes may be submitted in plain-text format, as attached files such as Microsoft Word documents, or as handwritten and scanned documents. Quizzes and exams must be individually completed and represent your own work. Neither collaboration nor consultation with others is allowed. Midterm Examination You have to visit the Chesapeake College Testing center at Wye Mills or at Cambridge to complete the midterm exam. This is given during the 9 th week (October 11 - October 16) of the schedule. This is a closed book exam and no textbook or notes allowed. Graphing calculators are not allowed. You may use a scientific calculator.

7 Final Examination The final exam constitutes 25 percent of the final course grade. The final exam is close book and includes multiple-choice and short answer questions. However, you are required to show your work and calculations, where requested, in order to receive full credit. The chapters to be covered on the final exam are Chapters 1-6. The final exam must be individually completed and represent your own personal work. Neither collaboration nor consultation with others is allowed. The solutions for the final examination will not be posted. The final exam will be given during the final exam week, and you are expected to visit the testing center to take the exam as scheduled (December 6 to 10). In the event of illness or extraordinary circumstances, you must contact the instructor and provide documentation to request an exception and approval to take a makeup exam. If the request is not approved, the exam grade will be recorded as a zero. Tips for Success in Online Courses: Log in to class regularly. Study at least one section daily. Complete the MyOpenMath homework at least one section per day. Do not wait till Sunday evening to complete all the assignments for the week. You will find yourself very stressed if you do not work on a section or two every day. Learning takes time, focus, repetition and practice. Pay attention. Read all the information given in Canvas and MyOpenMath. Take notes. When you are reading the textbook, doing MyOpenMath activities, or completing homework take notes. Keep up with readings and assignments. Reading math is no like reading anything else! You need to look very carefully at the numbers and formulas and spend some time making sure that you understand them and that they make sense. Ask questions when you do not understand something. I will try to respond within 24 hours during the week. Adhere to the deadlines posted in the course outline. There are absolutely no extensions for weekly discussions, MyOpenMath homework, quizzes, midterm exam, and final exam.

8 Additional Information Late Policy Meeting course deadlines is crucial for success in computer-mediated courses. You may read at your own pace, but homework in MyOpenMath, Canvas participation, quizzes, and projects must adhere to the timetable given in the schedule. Otherwise the grade will be zero. No late MyOpenMath homework, Canvas participation, quizzes, or exams will be accepted. Originality of Work You are expected to submit your own work for all assignments and quizzes. Assignments which are highly similar in content and presentation will be considered suspect and will be questioned. No credit will be given for plagiarism. Refer to the Chesapeake College Policy on Academic Dishonesty and Plagiarism. Tutoring - Wye Mills and Cambridge If you live in the vicinity of the Wye Mills or Cambridge, Maryland, you may take advantage of free, walk-in tutoring. Guideline for Receiving Tutoring Services We appreciate that many students may seek tutoring services to supplement our instructional program. However, tutors may not be used to complete any portion of assignments, projects, quizzes, and exams on behalf of students. Students are expected to submit their own work. Students who are suspected of submitting the work of their tutors will be reported to the dean's office for potential investigation in accordance to Chesapeake College s Policy on Academic Dishonesty and Plagiarism. If you are to receive tutoring services, inform your tutor of this expectation and clarify your tutor's role and responsibility to your academic endeavors at Chesapeake College. Project Descriptions You may find project information in Canvas Class under project. Academic Policies Academic Integrity Chesapeake College is an academic community that honors integrity and respect for others; and it is expected that as a member of this community, you will maintain a high level of personal integrity in your academic work at all times.

9 Academic dishonesty is the failure to maintain academic integrity and includes the intentional or unintentional presentation of another person's idea or product as one's own (plagiarism) and/or the use or attempt to use unauthorized materials, information, or study aids in any academic exercise and/or doing work for another student (cheating). All academic work you submit during your time at Chesapeake College should be original work for each of your courses. Course Expectations For a fourteen-week course, students should expect to spend about five hours per week in class discussion and activities (online or on-site) and two times that number of hours outside the class in study, assigned reading, and preparation of assignments. Students are expected to achieve the same intended learning outcomes and do the same amount of work in an online course as they would in an on-site course. Active participation is required in all online courses, and students should expect to log in to their online courses several times a week. Students are expected to do a minimum of two hours of work outside of class for every hour in class. Some assignments may require more time. The syllabus is my opportunity to tell you how I manage this class and give you notice of what is expected of you as a student. Please remember that I will do everything I can to help you and I expect you to be motivated and responsible for your own learning and course grade. If you have any questions about the syllabus please let me know soon. This is an online class. Therefore, you the student have the burden of making sure you stay on pace and meet the deadlines. The course outline provides the deadlines that you are responsible for. I hope we all will have a good semester.

10 MATH : 14-Week Course Schedule - Fall, 2015 (Starts 8/24/15) Module Assignments Relations and Functions (August 24 September 6) Textbook sections MyOpenMath Section 1.1: due 8/30/15 MyOpenMath Section 1.2: due 9/06/15 MyOpenMath Section 1.3: due 9/06/1 Canvas Participation Discussion 1: due 8/31/15 Make corrections if any by 9/06/15 1 Objectives Identify sets Describe sets using the verbal, roster, and set-builder methods Recognize the different sets of numbers Write sets in interval notation Write sets as inequalities Find the intersection and union of sets Find points symmetric or reflected about the x-axis, y-axis, and origin Determine the distance of a line segment Determine the midpoint of a line segment Recognize relations Graph relations Find x- and y-intercepts of an equation Test the graph of an equation for symmetry Determine whether a relation is a function Use the vertical line test to determine if a graph represents that of a function Find the domain and range of a function from a set of points Find the domain and range of a function from a graph Determine whether an equation is a function.

11 Module Assignments Continuation of Relations and Functions (September 7 - September 13) Textbook sections MyOpenMath Section 1.4: due 9/13/15 MyOpenMath Section 1.5: due 9/13/15 Canvas Participation Discussion 2: due 9/13/15 Make corrections if any by 9/15/15 Outcomes Evaluate a function at a given value or expression Find the domain of a function Use function evaluation to solve application problems Evaluate piecewise functions Find the sum, difference, product, or quotient of two (or more) functions Find the domain of a function formed by function arithmetic Find the difference quotient of a function Use function arithmetic to solve application problems. Continuation of Relations and Functions (September 14 - September 20) Textbook sections MyOpenMath Section 1.6: due 9/20/15 MyOpenMath Section 1.7: due 9/20/15 Canvas Participation Discussion 3: due 9/20/15 Make corrections if any by 9/22/15 Outcomes Graph functions Find the zeros of a function Determine analytically if a function is even, odd, or neither Find the intervals on which a function is increasing, decreasing, and/or constant Find the local and/or absolute extrema of a function Find various characteristics of a graph Given a point, find the corresponding transformed point for a transformed function Graph transformations Find a formula for a transformed function given the sequence of transformations Find a formula for a transformed function given the transformed graph Identify the transformations occurring in a function.

12 Module Assignments Linear and Quadratic Functions (September 21 October 4) Textbook sections MyOpenMath Section 2.2: due 09/27/15 MyOpenMath Section 2.3: due 10/04/15 MyOpenMath Section 2.4: due 10/04/15 Canvas Participation Discussion 4: due 09/27/15 Make corrections if any by 10/04/15 Quiz 1 on : due 9/27/15 4 Outcomes Solve absolute value functions Graph absolute value functions Graph absolute value functions using transformations Find requested characteristics of an absolute value function Graph quadratic functions Convert quadratic functions from general form ( ) to standard form ( ) ( ) Find the vertex of a quadratic function in general form using Find the zeros of a quadratic function using the quadratic formula Use the discriminant to find the type and number of solutions of a quadratic function Use quadratic functions to solve application problems Find the solution(s) for absolute value inequalities analytically Find the solution(s) for absolute value inequalities graphically Find the solution(s) for quadratic inequalities analytically Find the solution(s) for quadratic inequalities graphically.

13 Module Assignments Polynomial Functions (October 5 October 11) Textbook sections MyOpenMath Section 3.1 and 3.2: due 10/11/15 Canvas Participation Discussion 5: due 10/11/15 Make corrections if any by 10/13/15 Quiz 2 on due 10/11/ Outcomes Determine if a function is a polynomial Identify the degree, leading term, leading coefficient, and constant term of a polynomial Solve application problems involving polynomials Determine the end behavior of polynomials Use the Intermediate Value Theorem to locate a zero of a polynomial Use a sign diagram for a polynomial function Determine the multiplicity of a zero Using zero s multiplicity, determine the behavior of a polynomial at its zeros Divide polynomials using long division Write the quotient of a polynomial in the form ( ) ( ) ( ) ( ) Find a function value using the Remainder Theorem Find the factor(s) of a polynomial using the Factor Theorem Divide polynomials using synthetic division Determine the maximum number of zeros of a polynomial Make connections between the zeros, factors, and graph of polynomial functions. Polynomial Functions (October 12 October 18) Textbook sections MyOpenMath Section 3.3: due 10/18/15 MyOpenMath Section 3.4: due 10/18/15 Canvas Participation Discussion 6: due 10/18/15 Make corrections if any by 10/20/15 Midterm (Ch 1 and Ch 2): Due 10/16/15 Visit the testing center to take the Midterm (October 11 16) Outcomes Use Descartes s Rule of Signs to determine the number of positive and negative real zeros of a polynomial Solve application problems using the zeros of a polynomial Add, subtract, multiply, and/or divide complex numbers Find a polynomial using the Fundamental Theorem of Algebra and Complex Factorization Theorem Find all the zeros of a polynomial function.

14 Module Assignments Rational Functions (October 19 November 2) Textbook sections MyOpenMath Section 4.1 and 4.2: due 11/01/15 MyOpenMath Section 4.3: due 11/01/15 Canvas Participation Discussion 7: due 10/25/15 Make corrections if any by 10/31/15 Quiz 3 on : Due 10/25/15 Outcomes Find the domain of a rational function Find the vertical asymptote(s) and hole(s) of a rational function Find the horizontal asymptote of a rational function Solve application problems involving rational functions Find the slant asymptote of a rational function Graph rational functions Solve rational inequalities Solve application problems involving rational inequalities.

15 Module Assignments Further Topics in Functions (November 2 November 15) Textbook sections MyOpenMath Section 5.1: due 11/08/15 MyOpenMath Section 5.2: due 11/15/15 MyOpenMath Section 5.3: due 11/15/15 Canvas Participation Discussion 8: due 11/08/15 Make corrections if any by 11/14/15 Quiz 4 on Sections : due 11/08/15 8 Outcomes Find a composition of functions Find a function value of a composition of functions Find the domain of a composition of functions Given a composition of functions, find two functions that were composed to make the composition Determine if a function is one-to-one analytically Determine if a function is one-to-one graphically Find the inverse of a function Determine if a two functions are inverses of one another analytically Determine if a two functions are inverses of one another graphically Graph a function and its inverse Find the domain of a function s inverse Solve application problems involving inverses Solve equations involving radicals Solve equations involving rational exponents.

16 Module Assignments Exponential and logarithmic functions (November 16 November 29) Textbook sections MyOpenMath Section 6.1: due 11/22/15 MyOpenMath Section 6.2: due 11/29/15 MyOpenMath Section 6.3: due 11/29/15 Canvas Participation Discussion 9: due 11/22/15 Make corrections if any by 11/28/15 Quiz 5 on Sections : due 11/22/15 9 Outcomes Solve application problems involving exponential or logarithmic functions Convert equations from exponential to logarithmic and from logarithmic to exponential Evaluate logarithms Find the domain of logarithmic functions Graph exponential or logarithmic functions Graph exponential or logarithmic functions using transformations Verify that the given exponential and logarithmic functions are inverses of one another Find the inverse of an exponential or logarithmic function Expand logarithms using logarithmic properties Use the properties of logarithms to write a logarithmic expression as a single logarithm Use the change of base formula to convert an expression with the indicated base Use the change of base formula to approximate a logarithm Solve exponential equations. Continuation of Exponential and Logarithmic Functions (November 30 December 6) Textbook sections MyOpenMath Section 6.4: due 12/06/15 MyOpenMath Section 6.5: due 12/06/15 Canvas Participation Discussion 10: due 12/05/15 Make corrections if any by 12/07/15

17 Final Exam (December 6 December 10) Review for the final exam Final exam (cumulative): due 12/10/15 Visit the testing center to take the Final Exam (December 6 10)