Math 74

Precalculus

Spring, 2002

Instructor: Dr. Orin Chein

Office: 612 Computer Building

Phone: 204-7846

Office hours: To be announced. (At this moment, my schedule for the Spring semester is not yet finalized.)

E-mail: orin@math.temple.edu

Web site: http://www.math.temple.edu/~orin/courses/S02/courses.htm

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

by John Schiller and Marie Wurster

Third edition.

Prerequisite: Math 73 or placement into Math 74 based on the Temple University placement examination.

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 which 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 less 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 which 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 Tuesdays and Thursdays from 8:10 until 10:00AM. Usually, the first hour of each meeting will be devoted to new material, and the second hour will be reserved for recitation, during which we will answer questions about the previous night's homework. Occasionally, I may feel a need to devote the entire class to covering new material. 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 I will distribute with each unit. 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 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 make use of some of the many computer programs which help explain the material and which 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) which 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 or , and you write 3.14159265359 or 1.41421356237 or some truncation or extension thereof, I will not consider this as a correct answer.

Withdrawals and incompletes:

Students may withdraw (passing) from this class at any time up to the deadline established by the college (usually the end of the twelfth week of the semester), provided that they have not failed more than one unit. (Students who fail more than one unit will receive the grade of F.) 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's, 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. Make a list of items you do not understand and ASK about them during the following class or recitation or during office hours.

4. 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.

5. 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..

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

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. Go to the MSRC to set up a computer account for the course. When you have finished doing so, 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 a readiness test on the unit. Again, this test will not be graded, but any errors you make will generate new problems for you to complete before you are allowed to take the unit test.

4. When you have passed the readiness test at a satisfactory level, you may take the unit test. If you pass the unit test with 90% or better, you have completed the unit and may commence the next unit. If you fail to achieve a 90% level, new sample problems will be generated, Again, you will have to complete and take a new readiness test based on these new problems before you will be allowed to retake the unit test (which will be similar to but not identical with the original). If you fail the unit test a second time, you will have come to one of the TA's or myself to prepare for the test, and we will have to certify your readiness before you will be allowed a third try. Normally, except as described below, you will only be allowed three attempts at a unit test, so do not waste your attempts when you are not properly prepared.

5. Students who receive 80% or better on their third attempt at a unit test but who fail to achieve 90%, may be afforded a fourth attempt, at my discretion.

6. In order to prevent students from falling too far behind the class, there will be a limited time period (usually 2 weeks from the day I complete a unit) during which they must achieve the 90% level on the unit test. Note that STUDENTS WILL NOT BE ALLOWED MORE THAN ONE ATTEMPT AT A UNIT TEST ON A GIVEN DAY.

7. Students who fail to achieve a 90% level on a unit test within the designated time period will be deemed to have failed the unit. Failure of a single unit at the 80% level or above will result in a maximum possible grade in the course of B. Failure of a single unit at a level below 80% will result in a maximum possible grade in the course of C-. (Students who receive such a grade will receive CORE credit for the course, but will not be allowed to proceed to Calculus.) Failure of more than one unit will result in an automatic grade of F for the course.

8. Students who successfully complete all units or who complete all but a single unit will take a comprehensive departmental final examination at the end of the semester. This examination will be prepared by the departmental coordinator for this course, and may differ in format from the unit exams. (For example, it will be taken in class rather than at the MSRC, and it will probably not be a multiple choice exam.)

9. Students who have successfully completed all units will receive a final grade which is one grade level above the grade they receive on the departmental final (when possible). Students who have successfully completed all but a single unit will receive the lesser of the grade limitation described above (i.e., B or C-) and the grade received on the departmental final exam.

10. As this is an experimental approach and not all the programming kinks have been resolved, it may be necessary to change or abandon the approach during the middle of the semester. If I decide to do so, I will circulate new guidelines at that time.