Math 74

Precalculus

Spring, 2003

Instructor:Dr. Orin Chein

Office:612 Computer Building

Phone: 204-7846

Office hours (subject to change):M 1:00-2:00, T 11:30-12:30, W 8:30-9:15, F 10:40-11:30 or by appointment.

E-mail: orin@math.temple.edu

Web site: http://www.math.temple.edu/~orin/courses/S03/courses.htm

 

Teaching Assistant:

            To be announced.

 

Text: College Algebra and Trigonometry: (Basics Through Precalculus),

            by John Schiller and Marie Wurster (Third edition).

 

Prerequisite:  Math 73, with a grade of C or better, or placement into Math 74 based on the Temple University placement examination.

 

Blackboard:

            It is essential that all students have a Blackboard account, as this will be used for testing as well as for various forms of communication.

 

Course description:

            This course covers most of the background topics needed for success in Calculus.  It assumes that the student has previous experience with algebra and is familiar with such topics as the real number system, signed numbers, order, absolute value, powers and roots, negative and fractional exponents, operations with radicals, operations with polynomials and rational functions, factoring polynomials, linear equations and inequalities, the coordinate plane and algebraic and geometric solutions of systems of linear equations.  Although the course will begin with a very brief review

of these topics, students who have not had this previous exposure are advised to take Math 45 or Math 73, depending on the gaps in the student’s background.  Students must successfully complete a diagnostic examination on the review material by the end of the second week of the semester in order to remain in the class.

            The course will be divided into four units: Review (Chapters P,1 and 2), quadratic expressions (Chapter 3), polynomial, rational, algebraic, exponential and logarithmic functions (Chapters 4 and 5), and trigonometry (Chapters 6 and 7).

            The syllabus calls for us to cover the following sections of “new material” in the text: 3.1-3.3, 3.5, 3.6, 4.1-4.5, 5.1-5.4, 6.1-6.5, 7.1-7.3, 7.5-7.8.I also believe that some of the material in section 10.1 is very important, and I will try to work it in at some time during the semester.  (Sections that are omitted from the syllabus are not omitted because they are not important; rather, they are omitted because there is not enough time to do everything so that choices have to be made.  Although I will not ask questions about them on any examinations in this course, I would urge all serious students to read the omitted sections and to even peruse the remaining chapters of the book when time permits.)

             

The approach:

            This section of the course is being taught using an experimental “mastery learning” approach.

There is a great deal of evidence to indicate that students who complete Precalculus with a grade of C or lower have a very difficult time and generally do not do well in subsequent courses such as Calculus.  Knowing 70%, or even 80% of the material in one course does not adequately prepare you for a subsequent course that builds on the previous one.  As a result, in order to succeed in this course, you will have to demonstrate knowledge of the material in each unit at the 90% level or above.  On the other hand, if needed, you will be allowed more than one opportunity to test on each unit, as described below.

            If this approach does not seem reasonable to you, then you are urged to switch immediately to another open section, if one exists.

 

Class meetings:

            Classes meet Mondays and Wednesdays from 10:40 until 12:40.Usually, class will begin with an opportunity for you to ask questions about the previous night’s homework, after which the remainder of class will be devoted to new material.  Occasionally, I may feel a need to devote the entire class to covering new material.  With the help of a graduate teaching assistant, I will try to schedule several additional hours per week during which you will have an opportunity to ask questions or to review homework.  It is expected that you attend all classes regularly and on time.(Late arrivals can be very disruptive.  Frequent late arrivals are not fair to me or to your fellow students.)

 

Homework:

THE ONLY WAY TO LEARN MATHEMATICS IS TO DO MATHEMATICS.

As a result, it is important that you do an extensive number of problems on a regular basis.  There will be two kinds of homework assignments - problems from the textbook (see the attached problems list), and sample unit tests, which will be available on Blackboard.  Problems from the text should be attempted as soon as the relevant topic is covered in class.  While these problems will not be collected, you will have an opportunity to ask questions about them at the beginning of class and during recitation sections.  It is expected that you will make a serious attempt at each of them.  This is part of your responsibility to yourself as a student, and it is essential if you want to succeed.  Problems on the sample tests should be completed as you are preparing for the unit examinations.  Before you will be allowed to take an examination, you will have to demonstrate that you are able to do the sample problems.

 

Technology

            There are many technological aids which can help you get the correct answers to most of the questions, and some of them will even help you learn the material.  I encourage you to become familiar with and to make use of some of the many computer programs that help explain the material and that provide an interactive source of exercises.  I also encourage you to obtain a suitable calculator (one at least capable of evaluating logarithmic, exponential, trigonometric and inverse trigonometric functions) that you can use to help check your answers.  However, I caution you against the reliance on calculators when this is used as a substitute for real understanding.  The use of (non-graphing) calculators will be permitted on most (but possibly not all) exams.  However, I warn you that calculators often only give approximate answers (albeit to a great degree of accuracy).If the correct answer to a problem is B or %2, and you write 3.14159265359 or 1.41421356237 or some truncation or extension thereof, I will not consider this as a correct answer.

 

Testing procedures:

            All testing, with the possible exception of the final examination, will take place at the Math/Science Resource Center (MSRC), located in the basement of Curtis Hall.

            Students in the class should follow the following procedures.

1.Read the syllabus carefully to make sure that you understand all of the rules and procedures of the course.

2.You will be given a brief test on the syllabus.This test will not be graded but, if you make any errors, you will be prompted to reread the syllabus and to retake the test.You will not be allowed to take any other tests until you have successfully completed the test on the syllabus.

3.Whenever a unit is completed in class, complete the sample test for the unit and proceed to the MSRC to take the unit test.

4.You will be allowed up to three attempts at each unit test (which will change each time you take it) within a designated period of time.

5.Note that YOU WILL NOT BE ALLOWED MORE THAN ONE ATTEMPT AT A UNIT TEST ON ANY GIVEN DAY.

6.ANY ATTEMPT TO TAKE A UNIT TEST ANYWHERE BUT AT THE MSRC WILL RESULT IN A FAILURE FOR THAT UNIT.

 

Withdrawals and incompletes:

            Students may withdraw (passing) from this class at any time up to the deadline established by the college.  In order to withdraw, you must obtain my signature on a drop form and have the form signed by an advisor and processed by the deadline, paying the required fee.  Note that there is no place on the final grade sheet in which I can give a grade of W.  Unless the final grade sheet arrives with the grade of W pre-entered (which is why there is a deadline), I cannot give a grade of W.

            You should note that the department has a very restrictive policy regarding the grade of incomplete.  I am only allowed to give an incomplete to someone who has successfully completed all of the other requirements of the course with a passing grade and who is unable to take the final due to illness or another excusable reason.  In that case (and only in that case), I will give an incomplete provided that the student in question has made arrangements to take a make-up final within a short time period after the end of the semester.  Under no circumstances will a student be allowed to complete a course by attending another class and expecting the teacher of that class to administer and grade his or her exams.

 

Help

            Help, when needed, is available during my office hours, during the office hours of my TA, and from the MSRC tutors.

 

A final remark:

I suggest the following routine for this course (as well as for any other mathematics course you may take):

1.      Try to read the next scheduled section of the text BEFORE it is covered in class.  It is not necessary that you understand it completely, but try to get an idea of what it is about and where any difficulties you may have in understanding it lie.

2        Pay attention in class and try to take as careful notes as you can.  ASK QUESTIONS about material you do not understand.

3.  AFTER class, reread the text and your notes, and try to fill in any gaps that may exist in your notes.

4.      Make a list of items you do not understand and ASK about them during the following class or recitation or during office hours.

5.      Attempt all of the assigned problems.  Answers to many of the problems are contained at the back of the book; but do not rely on this as a crutch.  If you need to consult the answers to guide you through some problems, that is OK; but, if you find that you have to "massage" most of your work to get the answers in the back of the book, then it is time to make an appointment to see me.  No solutions or answers will be available to guide you when it comes time to take a test.

6.      When studying for each test, review your notes and the text and try some of the supplementary problems at the end of each chapter.  If you have been keeping up with the work and doing all of the above as you go along, it should not be necessary to "cram" for the test; a brief review is all that should be needed.

 

Assigned problems:

            The following exercises constitute a minimal homework assignment.  Each exercise represents a type of problem that you are expected to be able to solve.  If a certain type gives you difficulty, you should try more exercises of that type, until you feel comfortable with the related concept.

            In addition to the exercises on the list below, you should DO ALL THE TRUE-FALSE AND FILL-INS that appear in assigned sections.  At the end of each chapter, you should do a liberal sampling of the review exercises.

            The answers to the true-false, fill-ins and odd numbered exercises and complete solutions for all review exercises may be found in the back of the book, but, as I said above, use this to check your work, not as a crutch to simply get the correct answer.

            I am contemplating using Blackboard so that you can get immediate feedback on your homework.  We will see how this works as the semester progresses.

Review exercises

            Chapter P: Review exercises: pp 45-46: # 1-20

            Chapter 1: Review exercises (pp 93-94): 1-15, 19-21, 23, 24, 28, 31, 32, 34, 36.

            Chapter 2: Review exercises: pp 173-174: # 1-34

Section 3.1 (pp 184-186): 11-19, 23-40, 43-57, 61-65

Section 3.2 (pp 192-194): 11-46

Section 3.3 (pp 197-198): 11-48

Section 3.5 (pp 210-211): 1-17 odd, 27-32

Section 3.6 (pp 221-223): 11-19, 21-29, 31-43, 45-48, 51-53

Section 4.1 (pp 256-257): 11, 13, 16-25, 35, 37, 39, 45-53, 57-61, 65,66

Section 4.2 (pp 265-266): 11, 13, 15, 17-26

Section 4.3 (pp 276-277): 11, 13-27, 29-40

Section 4.4 (pp 284): 11-21 odd, 22-35

Section 4.5 (pp 294-295): 11, 13-19

Section 5.1 (pp 312-313): 11-21 odd, 25-29, 34-37, 39, 42-49

Section 5.2 (pp 317-319): 11, 12, 14, 15, 17-39, 41-43, 47-53 odd

Section 5.3 (pp 325-326): 11-32, 35-45

Section 5.4 (pp 336-338): 1-17 odd

Section 6.1 (pp 346-348): 11-24

Section 6.2 (pp 359-360): 11-38, 45-59

Section 6.3 (pp 366-367): 11-26

Section 6.4 (pp 381): 11-21

Section 6.5 (pp 381-383): 11-23

Section 7.1 (pp 388-389): 11-18, 21-34

Section 7.2 (pp 399-400): 11-15, 17, 18,21, 25, 27, 29, 30, 31

Section 7.3 (pp 407-409): 11-29

Section 7.5 (pp 426-427): 11-55

Section 7.6 (pp 434-435): 11-50, 55-58

Section 7.7 (pp 441-442): 11-37,43-46

Section 7.8 (pp 448-449): 11-42, 46-62