and solve for x, by doing appropriate algebraic simplification.
In this document are the following sections:
Office Hours:
MW 4:05 - 5:35 p.m.
TH 10:35 - 11-35 a.m.
Other times available by appointment. Just ask.
Text: Calculus, Hughes-Hallett,
Gleason, et. al., Wiley, 1994
Student Answer Manual
Optional: Student Solution Manual
Course Goals: In this course, you will learn to:
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Calculator or Computer: You will need access to a graphing calculator or equivalent computer program.
As much as possible in this course, we will present every topic four ways: verbally, graphically, numerically, and algebraically. Based on the evidence available here at ACC and from other schools around the country, we believe that this approach will strengthen your mathematical abilities and intuition significantly. In order to use this approach, each of you must have access to some form of technology (graphing calculator or computer program) that enables you to (easily and quickly)
Graphing calculators (such as the TI-83) will do all of these and can be bought for as little as $90. If you already have a graphing calculator that you own or have borrowed, start out using it. (It will be very useful to have the manual for it too.) If you do not have a graphing calculator and want to buy one, I recommend the TI-83. Don't buy a different one (even cheap from a pawnshop or a friend) until you have talked with me about the pros and cons of each type of calculator.
Several good public-domain computer graphing programs are available, including one for Windows, one for DOS that runs on 10-year-old computers, and one for Macs. Check the math Website (http://www.austincc.edu/math/) for information about buying graphing calculators and downloading computer software. By the first class day of the second week, you must learn to graph a function and find zeroes of it using at least one form of technology.
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Time Commitment: You must work on this material at least
8 to 10 hours per week outside of class in order
to succeed in this course. Some of this time should be spent working
on the material by yourself, but you should also spend at least
two hours per week working with other students or in a tutoring
lab. This enables you to get your questions answered efficiently
and to practice explaining material to others. Both of these will
enhance your understanding of the material.
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Syllabus/Calendar/Testing Schedule:
Week 1: 1.1-1.5
Week 2: 1.6-1.9
Week 3: 1.10-1.11, Test
Week 4: 2.1-2.3
Week 5: 2.4-2.6
Week 6: 2.7-2.8, Test, 3.1
Week 7: 3.2-3.4
Week 8: 3.5, 4.1-4.3
Week 9: 4.4, Test, 4.5
Week 10: 4.6-4.8
Week 11: 4.9, 5.1-5.2
Week 12: 5.3, Test
Week 13: 5.5-5.6
Week 14: 5.6-5.7
Week 15: 6.3-6.5
Week 16: Final Exam
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You will learn calculus by thinking about problems and about the concepts, asking questions about them, working on them with other people, thinking more about them yourself, and writing up solutions to problems and possibly explanations of the concepts. That you do the homework and how you do it is crucial. I'll give you further guidance during the semester. The first set of guidelines is included in this handout, as is the homework assignment for the first three weeks. Throughout, you should keep your homework solutions organized, with every page clearly labeled with the section number and problem number.
The homework will be turned in five times, at the time of each test, with a possible grade of 20 on each part. (Total possible grade of 100.) Do not wait until you turn in the homework to get feedback from me on your solutions. That will be too late for you to benefit from the help in studying for your test. Instead, you are expected to be getting feedback on a daily basis, during class and during office hours. Also, if you want specific feedback on your method of solution, you can turn in any homework problem with the daily quiz any day and mark it "For feedback".
If a problem is listed on the homework and then I assign it as
a daily quiz problem also, you should turn it in for the quiz
and then, when you get it back, reinsert it in your homework notebook
at the appropriate place.
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Test 1 -- through Chapter 1
Test 2 -- through Chapter 2
Test 3 -- through Chapter 4, section 4
Test 4 -- through Chapter 5, section 3
Test 5 (final exam) -- through Chapter 6
A student who misses a test or who a low grade on a test may petition
to have that test grade replaced by the grade on the last test.
Such a written petition must be turned in within approximately
one week of the time the test is returned and must include
(1) a description of what went wrong and how that will be avoided
in the future (2) all the problems on the test, worked correctly
(in order), and (3) the original test. Only one such substitution
will be allowed.
A: 90-100 / B: 80-89 / C: 70-79 / D: 60-69 / F: below 60
W Withdrew from course. This is a completely neutral grade, not passing or failing. You may be withdrawn if you miss as many as 4 classes or if you fail to meet course objectives, but I make no promise to do so. If you wish to withdraw, you must fill out the form before the deadline.
I Incomplete. This grade (I) will be given only in very rare circumstances. Generally, to receive a grade of I, a student must have taken all examinations, be passing, and have a personal tragedy occur within the final three weeks of the course which prevents course completion.
If you believe that I have made a mistake on grading anything,
write a note of explanation on a separate sheet of paper, staple
it to the paper, and turn it in for re-grading. I am happy to
discuss this with you outside of class, but grades will never
be changed or corrected "on the spot". Such corrections
must be made very soon after the paper was originally graded.
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The purpose of doing homework is not to fill pieces of paper with
math problems. It is to enhance the way you think about mathematical
problems. Keep in mind that a major goal is to be able to work
the homework problems (and others similar to them) in test-like
conditions. Most things that students find confusing on tests
were, at first, confusing to them in the homework as well. So,
if you keep careful track of your questions, and the help and
answers you get, you will be making an excellent study tool for
yourself.
You can keep track of those questions and answers as part of your
homework pages or on separate pages. Decide which of these will
encourage you to pay the most attention to them and do it that
way.
As you do your homework in each chapter, keep a record on a cover
sheet. List all the problem numbers in the assignment for
each section and put a symbol beside each to indicate your progress.
| Symbol | Meaning |
| check | It was complete and correct the first time I did it. |
| x check | Something was wrong when I first did it, but I corrected it. |
| ? check | I had a question at first, but I got that answered and then did it correctly. |
| ? | I had a question and never got it answered. |
| x | I got it wrong and never did find out why. |
| ok | I didn't have time to do it, but I'm sure that I could have done it correctly. |
| blank | I just didn't get it done. |
| check + | Exemplary solution! |
The following factors will be considered in assigning a grade.
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1.1: 1, 3, 11, 13, 14
1.2: 1, 5, 7, 9, 13, 16, 21
Handout on Preliminary Precalculus Review (included here): 1, 2, 3, 4, 5, 6, 7, 8
1.3: 3, 5, 7, 9, 11, 15, 17
1.4: 1, 3, 4, 8, 11, 15, 19
1.5: 1, 2, 3, 4, 5, 6, 8, 13, 15
1.6: 3, 5, 6, 7, 11, 15, 20, 21, 22
1.7: 1, 5, 9, 13, 16, 21, 23, 27, 33, 35, 38
1.8: 1, 3, 7, 11
1.9: 3, 5, 9, 13, 15, 17, 23, 24, 29
1.10: 1, 15, 19, 20, 21, 22, 25, 31, 35, 41, 48
1.11: 1, 5, 9, 13, 15, 19, 25
Chapter Review: 1, 5, 7, 13, 17, 21, 27, 31, 35, 41, 43, 47
General method to be followed for problems 1 - 4:
and solve for x, by doing appropriate algebraic simplification.
For each of the following functions, find the x intercepts and find the values of x where it is undefined.
on 
on 
5. A company manufactures chairs. The cost is $20 per chair if you buy 100 or fewer chairs. If you buy between 101 and 600 chairs, the price decreases by $0.02 per chair for every chair in excess of 100. Assume that they won't sell more than 600 chairs in one order. (I know that's unrealistic, but it's easier this way!)
a. Compute the total revenue for the sale of (i) 90 chairs, (ii) 100 chairs, (iii) 101 chairs, (iv) 102 chairs, (v) 103 chairs.
b. We want to write a algebraic function so that we can sketch a graph and use that graph to enable us to see what number of chairs sold will generate the maximum revenue. At first, let's ignore the possibility of selling fewer than 100 chairs. Let x be the number of chairs sold in excess of 100. Now write the revenue as a function of x. Be sure that you give the limits on the domain of x along with the function.
c. Graph the function on the appropriate domain.
d. What name does this type of function have? How do you find the maximum or minimum value of this type of function? (Hint: Think about the word: vertex.)
e. Find the maximum value of the function. What value of x gives it?
f. Now, let's reconsider the original problem statement. Which values for number of chairs are possible that we have ignored in our algebraic function? Are all of them relevant to this discussion of maximum revenue? Are any of them? Why or why not?
g. Write this sentence, but with the blanks correctly filled in:
"According to the work I have shown, for an order, the maximum
revenue of ______ is generated by selling _____ chairs."
6. A company manufactures chairs. The cost is $20 per chair if you buy 100 or fewer chairs. If you buy between 101 and 600 chairs, the price decreases by $0.02 per chair on the entire order. Assume that they won't sell more than 600 chairs in one order. We want to write a algebraic function so that we can sketch a graph and use that graph (or do some algebra) to enable us to see what number of chairs sold will generate the maximum revenue.
a. Compute the total revenue for the sale of (i) 90 chairs, (ii) 100 chairs, (iii) 101 chairs, (iv) 102 chairs, (v) 103 chairs.
b. At first, let's ignore the possibility of selling fewer than 100 chairs. Let x be the number of chairs sold in excess of 100. Now write the revenue as a function of x. Be sure to give the limits on the domain of x along with the function.
c. Graph the function on the appropriate domain.
d. What name does this type of function have? How do you find the maximum or minimum value of this type of function? (Hint: Think about this word: vertex.)
e. Find the maximum value of the function. What value of x gives it?
f. Now, let's reconsider the original problem statement. Which values for number of chairs are possible that we have ignored in our algebraic function? Are all of them relevant to this discussion of maximum revenue? Are any of them? Why or why not?
g. Write this sentence, but with the blanks correctly filled in:
"According to the work I have shown, for an order, the maximum
revenue of ______ is generated by selling _____ chairs."
7. Discuss the difference in the problem statement for problems 5 and 6.
a. What differences did this make in the solution, both in the process and in the result?
b. Did the computations you did in part a help you when you began to write the function?
c. How would you pick the particular values to use in part a if
you were doing a problem like this again?
8. Redo problem 5, but write the revenue function as a function
of the actual number of chairs, c. (Rather than the number
of chairs more than 100, which we called x.) How does that
change the form of the function? Does it change the answer? Which
do you think is easier - doing it like number 5 or doing it like
this?
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* For the official handout and homework, refer
to what is handed out in class. While I intend to update the Web
versions regularly, I may forget to do so from time to time. You
can expect that it will be accurate as of the time of the last
update. Last updated December 22, 1997. mparker@austincc.edu
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