MATH 007
Precalculus - Fall 2014

Department of Mathematics
HOWARD UNIVERSITY
Richard E. Bayne


Table of Contents:

[ Text and Required Materials | Course Objectives | Course Content | Pre-requisites | Cooperative Learning Groups | Requirements | Administrative Policies | Office Hours ]

Text and Required Materials

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Course Content

The course will review the basic definitions and concepts of functions. In particular we shall discuss exponential, logarithmic and trigonometric functions, as well as applications involving these functions. We shall also study various methods for solving systems of equations and systems of inequalities. If time permits a few other special but useful topics in algebra will be discussed. You should view approximate pacing of the topics.

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Course Objectives

This course is a continuation of College Algebra I (MATH 006) and after completing these two courses satisfactorily, students should have a fundamental grounding in algebra and trigonometry and be prepared for calculus and other higher courses in mathematics. In particular, at the satisfactory completion of this course, in addition to having mastery of various methods for solving systems of linear equations a student will be able to recognize, sketch, and analyze graphs of exponential functions, logarithmic functions and trigonometric functions, as well as use these functions to model and solve applications. A more detailed description of the learning objectives for this course is given by the following.

At the satisfactory completion of this course, a student will be able to:

  • Determine whether a function has an inverse.
  • Given an equation describing a function, find its inverse.
  • Given the graph of a function, find the graph of its inverse.
  • Evaluate and graph exponential and logarithmic functions.
  • Solve exponential and logarithmic equations.
  • Change expressions between logarithmic and exponential form.
  • Use properties of logarithms to convert expressions involving logarithms into different forms.
  • Solve applications that involve logarithms and exponentials.
  • Be able to express angles in degree or radian measure and convert between the two forms.
  • Find the area of the sector of a circle.
  • Find the linear speed of an object traveling in circular motion.
  • Find the values of trigonometric functions of acute angles.
  • Find the remaining trigonometric functions given the value of one.
  • Understand and be able to use the fundamental trigonometric identities.
  • Know the exact values of trigonometric functions of certain acute angles.
  • Use reference angles to determine trigonometric functions of general angles.
  • Express trigonometric functions in terms of the wrapping function.
  • Be able to graph the basic graphs of the six trigonometric functions.
  • Graph transformations of the sine and cosine functions.
  • Determine the amplitude, period and phase shift of sinusoidal functions.
  • Find exact values of the inverse sine, cosine and tangent functions for particular values.
  • Find approximate values of the inverse sine, cosine and tangent functions.
  • Find exact values for expressions involving inverse sine, cosine and tangent functions.
  • Prove or disprove trigonometric identities.
  • Use sum and difference formulas to find exact values of trigonometric functions.
  • Use double-angle formulas and half-angle formulas to find exact values.
  • Solve equations involving trogonometric functions.
  • Solve right triangles.
  • Solve oblique triangles using the Law of Sines and the Law of Cosines.
  • Solve applications involving right triangles.
  • Solve applications involving oblique triangles.
  • Find the area of a triangle given two sides and the included angle.
  • Find the area of a triangle given three sides.
  • Solve a system of linear equations using substitution.
  • Solve a system of linear equations using elimination.
  • Solve a system of linear equations using row reduction of matrices.

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    Prerequisites

    It is assumed that students enrolled in this course are prepared for the course and have completed the indicated requisites. One measure of this preparedness is a mastery of the topics covered in College Algebra I (MATH 006). If you are not properly prepared or if you are not sure about your preparation, you should reconsider your enrollment in this course. Please see me if you have any questions about your readiness for this course.

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    Cooperative Learning Groups

    You may do some of the work of this course in cooperative learning groups. It seems to work best if there are three or four students in each group. You will be working with your small group in class and on certain homework assig nments

    Working well in a group is an important skill. Some of you may enjoy the group work more than others, and all of you will benefit from further developing this skill. After graduation, most of you will be working in jobs which will require you to function as a member of a project team. One objective of group work in this course is to help you to develop skills in working effectively as part of a team.

    One of the objectives of this course is to help you to learn to think about problems mathematically and to solve the problems on your own. Working with your colleagues in this class and talking about problems with your group members are strategies to help you better understand a problem situation from several points of view.

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    Requirements

    Regular attendance, participation, lab activities, homework:

    This class meets four times per week and begins at 9:10 am. Each student is expected to attend every session and to arrive before the class begins. Students are responsible for all class work and assignments whether or not they are in attendance. Some material will be presented in class from a different perspective than that given in the text. "Getting someone's notes" is a poor substitute for being present and involved in class discussion. However, if you must miss a class, it is your responsibility to find out what you missed. Make a friend! NOTE: experience has shown that there is a high correlation between class attendance and success.

    Mathematics is not a spectator sport. During most class periods there will be time for large and/or small group discussions about selected problems. It is important to learn to ask helpful questions and to listen constructively to each other. Constructive participation sometimes means allowing others time and space to think about the problem.

    Homework assignments will be assigned continuously and will count for 100 total points. These points will be determined based on work assigned directly from the text as well as work done using WeBWorK, an online system that allows you to work problems accessible on the World Wide Web. Students are expected to do every homework assignment.
    NO HOMEWORK WILL BE ACCEPTED LATE.

      Each student will be expected to do the following:
                    1. Attend every class.
                    2. Devote a minimum of 12 hours of study per week to the course.
                    3. Come to each class on time and ready to participate.
                    4. Be willing to help your classmates.
                    5. Be able to explain concepts to the instructor or to other students.
                    6. Meet with group members at least twice each week to
                       review and discuss course material.
                    7. Do all class activities and homework assignments.             
    
    Tests:
    There will be four hour exams each worth 100 points. The material to be covered on each test will be announced in advance of the scheduled test date. Tests are tentatively scheduled for the following dates:

    • Test 1: week 4
    • Test 2: week 7
    • Test 3: week 10
    • Test 4: week 13

      Please note that these dates may change depending on class progress and unforseen circumstances. ALL EXAMS COUNT; -- NO SCORES WILL BE DISCARDED.

    Ordinarily, there are no make-up tests; exceptions to this policy will be considered on a case-by-case basis. You must determine BEFORE the exam date whether your excuse will be acceptable.

    Final Exam: 200 points
    The final exam will be comprehensive and is scheduled for Tuesday, Dec 9 at 4:00 pm.

    Generally, incomplete grades will not be given. If there is an emergency which causes a student to be unable to finish course requirements, the emergency must be documented by the student's advisor or by the advisory center.

    WeBWorK:
    In addition to homework problems that will be assigned from the text, there will be continuing assignments of problems on line using WeBWorK. WeBWorK is an online system that allows you to work homework problems on the web. You will have the opportunity to work the problems more than once and generally will be able to work them until you get the correct answer. You should read through the Introduction to WeBWorK before the end of the first week of classes.

    Homework
    Homework will count for 100 points. These points will be determined by work done from the textbook and work done on WeBWorK, as described above. The percentage from each is generally weighted in the student's favor, usually 55% of the greater and 45% of the lesser. Back to TOC

    Administrative Policies

    GRADES

    Total points attainable will be determined as follows:
            homework                        100 pts
            hour exams                      100 pts each
            final exam                      200 pts
    
    Grades for the course will be computed as follows:

            85% - 100% of total points available    A
            75% - 84% of total points available     B
            60% - 74% of total points available     C
            50% - 59% of total points available     D
            0% - 49% of total points available      F
    
    In borderline situations, final exam results may be given the greater consideration.

    Academic Integrity Policy

    Students who cheat violate their own integrity and the integrity of the university by claiming credit for work they have not done and knowledge they do not possess. All students are expected to recognize and to abide by the policy on academic integrity found in the Student Handbook. Because you will be asked to do a lot of work in collaboration with your group members, I will ask you to sign all homework assignments attesting to the fact that you have actively participated in the work.

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    Office Hours

    Your tuition entitles you to see your instructor in conference about problems, personal and academic. Take advantage of the conference hours. Although the Mathematics Department office and department mail boxes are located on the second floor of Academic Support Building B (behind Locke Hall), my office is located in 236 Annex III, on the corner of 4th and College Streets, and can be reached easily from either of the two south-facing doors which are accessible from the driveway between Annex III and the C. B. Powell building. As a rule, I am available for students on most days other than Tuesdays. My scheduled office hours for fall 2014 are