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L-135: Pre-calculus Syllabus
Fall, 2002
Ellen Knapp email: knappe@philau.edu
Learning Center office phone: (215)951-2554
Office hours (subject to change):
Monday: 11:00 12:00; 2:00 - 3:00
Tuesday: 12:00 2:00
Wednesday: 9:00 - 12:00
Thursday: 1:00 - 2:00
Friday: 10:00 12:00
Appointments by phone, or at the Learning Center front desk .
Call (215)951-2799 to make an appointment. In addition to (or instead of)
making an appointment with me, you can drop into the Learning Center to get help
from a peer tutor or make an appointment with another professional tutor. You
can call the same number ((215)951-2799) to find out when there are peer tutors
for this class.
COURSE OBJECTIVE:
A function is a rule that determines a specific unique outcome given a
particular input (or set of inputs.) A function is mathematical when its rule is
defined in mathematical terms. When mathematical functions are used by business
people, scientists, engineers, designers, economists, educators, psychologists,
architects, etc. to model situations in the "real world" it is usually
because they seek the answer some variation of the question "What if?"
The main objective of this course is to show you how to
use functions to simplify real world situations, putting you in a position from
where you can pose "What if?" questions and receive reasonable
answers. A second objective of this course is to prepare you to take calculus
next semester.
A basic understanding of algebra will be critical to these course objectives.
I will spend the first two weeks doing an algebra review. However, I assume that
students in this course have completed at least two years of high school
algebra. Please see me NOW if you do not think you have the appropriate
background. I will not require that you drop the course. I will work with you
individually on prerequisite skills.
TEXT:
PRECALCULUS , Larson/Hostetler, Houghton-Mifflin,
New York, 2001.
REQUIREMENTS FOR THE STUDENT :
1. You should read each section before it is presented in class, with a
special eye open to terms that are new, and algebra that is unfamiliar. If you
are ready with questions before I present new material, it will be much easier
for you to follow the lecture. READ THE BOOK WITH A PENCIL IN YOUR HAND! Do
example problems as you come to them. Fill in missing steps, or indicate
questions to ask in class. Use space next to a solution of an equation to
explain the steps. Make up similar problems.
2. I expect you to complete daily homework assignments by the time the next
class meets. In general, a student should spend at least two hours outside of
class preparing for each hour in class. Therefore, I give daily assignments
that I believe can be finished in 1 - 1 1/2 hours . The additional time should
be spent reading the next chapter, reviewing previous material, studying for a
test or quiz, or working on a computer assignment. I will regularly check and
give grades for homework assignments, and in class group assignments. They
will count towards your final grade. If you are having trouble completing a
homework assignment on your own, get help! "I didn't understand the
material" is not an excuse for incomplete homework. Expect me to question
you: "When you realized that you didn't understand, what did you
do?" Here are some activities you can engage in if you cannot do the
homework: Look back over the chapter and find a similar problem completed in
the text. Try that problem, following the steps in the book. Actually work the
problem with pencil and paper, don't just read it. Do it several times, if
necessary, until you can do it completely on your own. Then go back and try
the homework again. You can also do the same thing with problems that I did on
the board in class. Usually the examples that I do will be different than the
ones in the book. Keep all your work to show me. Try a classmate, a friend, a
peer tutor at the Learning Center, or make an appointment with me. I don't
expect students to do every problem in every assignment. I do expect them to
do most of the problems in most of the assignments.
3. I expect complete honesty throughout the course. Anyone caught cheating on
a test or quiz will be required to leave the course with a failure. However,
cooperation in completing homework assignments is encouraged.
4. Attendance is required! Let me know ahead of time when a commitment or
illness will cause you to miss class. (Call and leave a message or email me in
the case of an illness.) Each unexcused absence beyond three will cause a
three point drop in your final grade. In addition, some lessons will include
in-class assignments where students earn points for correctly answered
problems. If you are absent, you are still responsible for completing the next
homework assignment. You are still responsible for all material covered and
information disseminated. Call a classmate to find out what you missed.
"I wasn't in class Wednesday" is not an acceptable excuse for
anything.
5. Each student will need at least a scientific calculator. A scientific
calculator is one that has keys for sin, cos, tan, ln, log,  and
 .
A graphing calculator is strongly recommended. If you are purchasing one now,
I recommend a TI-83 Plus.
6. This one isn't a requirement, just a suggestion. The most organized
students I ever met used the following: A loose leaf notebook with four
sections -- one section for class notes, one section for assigned homework
problems, one for all of their old tests and quizzes, and one section for all
"extra" work -- practice problems, work done with a tutor, etc. I
strongly suggest this method of organizing your math work.
GRADING: (subject to change)
3 classroom tests (take 4, drop one).......300 pts ....37.5%)
8 quizzes (take 10, drop 2)..................200 pts ....(25%)
5 computer assignments..................
.100 pts.....(12.5%)
final exam ......................
.........200 pts.....(25%)
____________________________________________
Total points................................... 800 pts.....100%
A................................744 C+..............................616
A-...............................720 C................................576
B+..............................696 C-...............................560
B................................664 D+..............................528
B-...............................640 D................................480
Dates of full period tests: (subject to change)
Test #1: Algebra Review - September 20
Test #2: Non-asymptotic Functions October 11
Test #3: Asymptotic Functions November 1
Test #4: Trigonometric Functions December 6
There will be a 15 minute quiz every Friday
when there is not a test.
TESTING POLICY :
THERE ARE NO MAKEUP'S OF TESTS OR QUIZZES!!
(not subject
to change.)
You get to drop your lowest test grade. If you miss a test, that test grade
will be the one dropped. If you miss a second test, your score in the final exam
will be averaged in as your score on the missing grade. If you miss a third
test, a 0 will be averaged in as your grade. You will be able to drop 2 out of
10 quizzes. If you know ahead of time that you will be absent on a test or quiz
day, I may be able to arrange an alternate (earlier) test time. Talk to me in
that case. However I never give make ups of tests or quizzes after they have
been administered!!!!
COMPUTER LABS :
As you can see under the grading heading, you are responsible for completing
five computer lab assignments. It is best to complete these on the program Maple
that is on th e hard drives of the eight computers at the Learning
Center. You need to bring your own 3.5" diskette on which to save your
work. It is also possible to complete the labs on a graphing calculator.
However, since you will not have the advantage of the lab aide to help and
correct your work, you are less likely to receive a good grade on the lab.
(Almost everyone who completes a lab at the Learning Center receives an A on
it.)
Due dates for computer labs
(to be announced) :
Lab #1: Graphs of Linear Function
Lab #2: Shifting Functions
Lab #3: Rational Functions
Lab #4: Exponential Functions
Lab #5: Trigonometric Functions
COURSE OUTLINE: (subject to quite a bit of
change.)
Prerequisites: Algebra Review
P.1 Real Numbers p. 10: 25 - 33 odd; 37 -61 odd (also use
interval notation); 91- 96; 99, 100, 101, 113 - 125 odd.
P.2 Exponents and Radicals p. 23: 9 - 61; 71 - 81 odd,
127, 130.
P.3 Polynomials and Factoring p. 33: 1 24 all; 39 49 all; 69,
70, 73, 74, 77, 79, 93, 94, 100, 101 123all; 139 144.
P.4 Rational Expressions p. 45: 1- 8; 19-27 odd; 33, 35,
36, 39, 39, 43,44, 49, 55, 57, 59, 67, 69, 75, 77, 81, 85.
P.5 Solving Equations p. 58: 19, 21, 27, 29, 35, 39, 55,
63, 69, 77, 83, 89, 93, 97, 109, 133, 135, 153, 155, 171,
173, 179, 189, 190, 198, 199, 201.
P.6 Solving Inequalities p. 70: 30, 32, 38, 41, 49, 54, 72, 73, 77,78,93,
100, 109, 110.
P7. Errors and the Algebra of Calculus p. 79: 1 26.
Chapter 1 Functions and Their Graphs
1.1 Graphs of Equations p. 107: 1-7 odd, 9 - 13 odd, 17 - 24, 25, 27, 72, 76,
77, 78
1.2 Linear Equations in Two p. 119: 35, 39 - 45 odd, 59, 74,75,76, 87 -
91 odd, Variables 97, 101, 107, 113, 115, 117, 119
1.3 Functions p133: 1-4, 13, 15, 23, 25, 27, 31, 40, 41, 43 - 51 odd, 73, 75,
77, 89, 94, 95
1.4 Analyzing Graphs p. 147: 1 - 19, 29- 32, 65, 67, 75
1.5 Shifting, Reflecting, and p.158: 1, 3, 9, 11, 13, 15, 19, 35, 37, 39, 43,
53, 54, 57, 59.
1.6 Combinations of Functions p. 168: 9, 13, 19, 25, 35, 37,
41, 43, 49, 51, 55 - 65 odd, 64.
1.7 Inverse Functions p. 177:1-41 odd 85, 91, 92.
1.8 Mathematical Modeling p. 187: 1, 3,4, 5, 9, 13, 15, 21,
31, 35, 37, 39.
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Chapter 2 Polynomial and Rational Functions
2.1 Quadratic Functions p. 208: 13 - 24, 37, 38, 39, 53, 54, 55, 65, 68, 77,
78, 79, 81, 83, 85,89.
2.2 Polynomial Functions of Higher Degree p. 222: 1 - 19 odd, 27 - 37 odd, 47 - 61 odd,
67,69,71,
73, 74, 75, 76, 77, 85, 87.
2.3 Polynomial and Synthetic Division p. 233: 7,9, 17, 21, 23, 29, 39, 41, 47, 51, 53, 59.
2.5 Zeros of Polynomial Functions p. 253: 11, 13, 15, 21, 245, 33, 55, 59, 63.
2.6 Rational Functions p.267: 1,5, 7, 9, 11, 15 - 20, 25 - 35 odd, 45, 47,
71, 72, 73, 75, 76,77
Chapter 3 Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs p. 296: 15 - 31 odd, 55, 65, 67, 69, 71, 85.
3.2 Logarithmic Functions and Their Graphs p.307: 1 - 49 odd, 69, 77, 78, 84 -87.
3.3 Properties of Logarithms p. 315: 9 - 12, 23, 26, 28, 32, 33, 36, 43
-48, 63, 64, 85, 87 - 91
3.4 Exponential and Logarithmic Equations p. 324: 7,9,23, 27, 35,41, 73,75, 77, 83 - 90, 97 -
100, 111, 112, 115, 117.
3.5 Exponential and Logarithmic Models p. 335: 35, 36,37, 41, 42, 44, 45, 49, 67, 71.
Chapter 4 Trigonometry
4.1 Radian and Degree Measure p. 359: 1, 5, 7, 11, 13, 15, 17, 21, 25,
29,37,49, 51, 55, 59, 60, 79, 80.
4.2 Trigonometric Functions: The Unit Circle: p. 368: 1 - 14, 17, 21, 23 - 36, 29 - 40, 43, 45
4.3 Right Triangle Trig p. 377: 1 - 6, 9., 17, 18, 19,
23-29 odd, 37-40,43, 44, 47, 61, 62, 63, 64,65,66,71, 76.
4.4 Trigonometric Functions of Any Angle p. 387: 1-23 odd, 29-36, 45-65 odd, 69, 70, 71,
85, 86, 87, 91, 93, 94, 97.
4.5 Graphs of Sine and Cosine Functions p. 396: 1-36, 37 - 43 odd, 53, 54, 65-68, 73-77 all,
81, 82, 83.
4.6 Graphs of Other Trigonometric Functions p. 408: 1-6
4.7 Inverse Trigonometric Functions p. 418: 1,3,5,17,19,37,38,49,52,53,
59-62, 91,92,95.
4.8 Applications and Models p. 428: 15, 17, 18, 20, 21, 26, 27, 49, 50.
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Chapter 5 Analytic Trigonometry
5.1 Using Fundamental Identities p. 447: 1, 2, 3, 15 - 36, 45 - 50, 57 - 62.
5.2 Verifying Trigonometric Identities p. 455: 1 - 12, 17, 21, 26, 35, 37.
5.3 Solving Trigonometric Equations p. 464: 1 - 37 odd, 67, 68.
5.4 Sum and Difference Formulas p 472: 1, 3, 23, 25, 27, 33, 34, 55, 57,
5.5 Multiple-Angle and Product-Sum Formulas
p. 482: 1, 3, 9, 11, 19, 20, 23, 35, 37, 55, 65
Review exercises p. 487: 24 - 41
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The number 3 is the exponent, also called the power.
The x is called the base.
Thats why you can say 
and why, in general,
is correct. Explain why that formula
works.
______________________________________________________________________________________
This you
can write as 
. That seems right.
Now how about using that other way of simplifying: 
.
This gives you 
. This shows that 
.
and 
and in general, 
.
as an expression that does not look like a
fraction. ______________________________
. Similarly, 
.
So, it is possible to rewrite 
as 
.
So, the following statement is also true: 
.
= 3 because (3)(3) =
9_____________________________________________
= because
because
because
because
because 
,
you could write 
=
-(
) 
(-
)