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PRECALCULUS I
TEXT: Precalculus: Enhanced with Graphing
Utilities, 53, by Sullivan and Sullivan. Each student is
also required to possess a graphics calculator.
PREREQUISITES: A student taking this course must have met one of the
following criteria:
(1) Math 4 (Algebra II)
(2) Proficiency in algebra and geometry, according to an appropriate placement
test score.
COURSE DESCRIPTION AND PURPOSE: Math 163 provides the theory and
applications necessary
for Math 271 (Applied Calculus for Business) and Math 164 (Precalculus II). This
course focuses largely
on college algebra. We will extensively discuss algebraic functions, as well as
exponential and logarithmic
functions. Also, matrix algebra is useful in solving systems of linear
equations. Hence, if your “calculus
goal” is Math 271, then this is the only precalculus course you will need. If
you plan to take Math 173
(Calculus with Analytic Geometry I), then you will either need to take Math 164
subsequently, or switch
immediately into Math 166 (Precalculus with Trigonometry).
OBJECTIVES: Students successfully completing this course will have proven
their ability to:
(1) Apply appropriate rules for simplifying polynomial, rational, radical,
exponential and logarithmic
expressions.
(2) Solve polynomial, rational, radical, exponential, and logarithmic equations,
as well as inequalities
in some cases.
(3) Investigate a variety of functions, through their definitions and graphs.
The domain for each of
the functions, in the outline below, is either all real numbers, or the union of
one or more intervals.
Incidentally, other important subsets of the real numbers include the whole
numbers, the integers,
and the rational numbers.
I. Algebraic Functions
A. Polynomials
1. Linear (degree 1)
2. Quadratic (degree 2)
3. Polynomials of degree ≥ 3.
B. Rational functions
C. Other algebraic functions, such as radicals and absolute value.
II. Exponential and Logarithmic Functions
A. Exponential functions, such as base e.
B. Logarithmic functions, such as ln.
(4) Be able to apply the topics in (1)-(3) to problem solving, particularly
business applications
(5) Solve systems of linear equations.
EXAMINATIONS: There will be three (3) examinations,
each worth 100 points; and the final exam will
be worth 150 points. No make-up tests will be given unless arrangements are made
in advance. If you
miss an exam, then the final will be increased by 100 points (in place of the
missed test). No extra credit
will be offered in this course. The tentative exam dates are Wednesday September
16, Monday October 19,
and Monday November 16. The final exam will be given only on Monday, December
14, at 12:00 noon
(note the earlier starting time).
HOMEWORK: Daily assignments will be made from the text, as an essential
element of mathematical
learning. On 10 of these class meeting throughout the semester, the instructor
will request that the student
hand in that day’s assignment. This will typically occur once a week, during the
weeks a test is not given,
until 10 assignments have been submitted. The score will be 0-5 points depending
on the amount of effort
expended. Therefore, we will have a total of 50 homework points. Late homework
will be subject to a
penalty of points without a valid excuse (leaving early or returning late from
vacations, for instance, is not
legitimate). To simplify submission of homework assignments, please begin the
problem set on a new
sheet of paper. To get us started, the first homework assignment is Section 1.2
(p. 23) #1, 2, 3, odd 7-17,
39, all 43-46, 49, 57 (a review of graphing linear equations, further study of y
= x2, and other graphs that
can be determined easily from our graphics calculator).
GRADING POLICY: Based on the last two (2) sections, there is a 500-point
total. Your score will be
converted to a letter grade based on the following scale: 100–90 = A, 89-80 = B,
79-70 = C, 69- 60 = D,
and 59 or below = F.
COURTESY AND SAFETY: Please respect others in this classroom—which means
keeping cellular
phones OFF as much as possible, avoiding any sources of distraction, and staying
for the full class. Any
exceptions to these rules should be cleared with the instructor in advance.
Disruption is not permitted!
NOVA is a place for learning and growing. You should feel safe and comfortable
anywhere on this
campus. In order to meet this objective, you should let your instructor, his
supervisor, the Dean of
Students, or Provost know if any unsafe, unwelcome, or uncomfortable situation
arises that interferes with
the learning process.
INCLEMENT WEATHER:
This will announced by 6:00 a.m.
FIRE/EMERGENCY EVACUATION PROCEDURE: In case of emergency, please follow
the
emergency procedure as posted in the classroom.
ATTENDANCE AND PARTICIPATION: Education is a cooperative endeavor between
the student and
the professor. Successful learning requires good communication between students
and instructors.
Therefore, regular attendance, arrival on time, and active participation are
important and expected. If one
misses the first three (3) weeks of class, the instructor will withdraw the
student administratively from the
course. If you must be absent, it is your responsibility to inform your
instructor beforehand or as soon as
possible.
WITHDRAWAL POLICY: To drop the course, one must officially withdraw. The
last day to withdraw
for adjustments in tuition is September 10; and the final deadline to receive a
W or change to audit is
November 2. The award of W after the last day of class requires official
documentation, the Dean’s
signature, and very unusual circumstances.
FURTHER TIPS FOR IMPROVING PERFORMANCE AND REDUCING CONFLICT:
(1) Please devote two (2) hours outside of class for every hour inside
class.
(2) For additional help, one should make use of the Tutoring Center (CG 407),
and the Math Lab
(which has software and videos, CG 405). Their services are free.
(3) IF YOU HAVE A DOCUMENTED DISABILITY THAT REQUIRES AN ACCOMODATION,
please contact Campus Disability Services and your instructor within the first
two (2) weeks of
class. The memorandum they provide is confidential.
ACADEMIC DISHONESTY: When college officials award
credit, degrees, and certificates, they must
assume the absolute integrity of the work you have done; therefore, it is
important that you maintain the
highest standard of honor in your scholastic work. The college does not permit
academic dishonesty.
Students who are not honest in their academic work will face disciplinary action
along with an “F” for the
course. Procedures for disciplinary measures and appeals are outlined in the
student handbook. In the most
extreme cases, academic dishonesty may result in dismissal from the college.
Academic dishonesty, as a
general rule, involves one of the following acts:
(1) Cheating on an examination—including the giving, receiving, or soliciting of
information and the
unauthorized use of notes or other materials.
(2) The use of any material purported to be the unreleased contents of a
forthcoming examination.
(3) Substituting for another person during an examination or allowing another
person to take your place.
(4) Plagiarism, or taking credit for another person’s work or ideas, without
acknowledging the source.
(5) Knowingly furnishing false information, or forgery, to the college.
TENTATIVE SCHEDULE (the instructor reserves the right to modify as needed):
Week of
| 8/24-26 | CHAPTER 1 | GRAPHS |
| 1.2 | Intercepts; Symmetry; Graphing Key Equations | |
| A.6 | Solving Equations | |
| 1.3 | Solving Equations Using A Graphing Utlility | |
| 1.4 | Lines—determining slopes and linear equations | |
| 8/31-9/2 | CHAPTER 2 | FUNCTIONS AND THEIR GRAPHS |
| A.9 | Interval Notation; Solving Inequalities | |
| 2.1 | Functions: Definition, domain, range, operations | |
| 2.2 | The Graph of a Function | |
| 2.3 | Properties of Functions | |
| 9/9 | 2.4 | Library of Functions; Piecewise-defined Functions |
| 2.5 | Graphing Techniques; Transformations | |
| 9/14-16 | Review for Exam 1 | |
| ************ EXAM 1 ************************************ | ||
| CHAPTER 3 | LINEAR AND QUADRATIC FUNCTIONS | |
| 3.1 | Linear Functions, their properties, and linear models | |
| 9/21-23 | 3.3 | Quadratic Functions and Their Properties |
| 3.5 | Inequalities Involving Quadratic Functions | |
| CHAPTER 4 | POLYNOMIALS AND RATIONAL FUNCTIONS | |
| 4.1 | Polynomial Functions and Models | |
| 4.5 | Real Zeros of Polynomial Functions | |
| 9/28-30 | 4.2 | Properties of Rational Functions |
| 4.3 | The Graph of a Rational Function | |
| 4.4 | Polynomial and Rational Inequalities | |
| 10/5-7 | A.7 | Complex Numbers |
| 4.6 | Complex Zeros; Fundamental Theorem of Algebra | |
| 10/14 | Review for Exam 2 | |
| ************* EXAM 2 ************************************* | ||
| A.10 | nth Roots; Rational Exponents | |
| CHAPTER 5 | EXPONENTIAL AND LOGARITHMIC FUNCTIONS | |
| 5.1 | Composition of Function | |
| 10/26-28 | 5.2 | One-to-one Functions; Inverse Functions |
| 5.3 | Exponential Functions | |
| 5.4 | Logarithmic Functions | |
| 11/2-4 | 5.5 | Properties of Logarithms |
| 5.6 | Logarithmic and Exponential Equations | |
| 11/9-11 | 5.7 | Financial Models |
| Review for Exam 3 | ||
| 11/16-18 | ************** EXAM 3 ************************************** | |
| 5.8 | Exponential Growth and Decay | |
| CHAPTER 11 | SYSTEMS OF EQUATIONS AND INEQUALITIES | |
| 11.1 | Solving Systems of Linear Equations: Substitution and Elimination | |
| 11/23 | 11.2 | Systems of Linear Equations: Matrices |
| 11/20-12/2 | 11.4 | Matrix Algebra |
| 12/7-9 | 11.5 | Partial Fraction Composition (if time permits) |
| Review for Final | ||
| 5/6 | FINAL EXAM | |