MATH 163 PRECALCULUS I
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
(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
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 the Thursdays of February 5, March 5, and
April 9. The final exam will be given only on Thursday, May 7, at 8:00 a.m. (note the earlier starting
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.
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.
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
WITHDRAWAL POLICY: To drop the course, one must
officially withdraw. The last day to withdraw
for adjustments in tuition is January 28; and the final deadline to receive a W or change to audit is March
27. 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
(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
(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):
|1.2||Intercepts ; Symmetry; Graphing Key Equations|
|1.3||Solving Equations Using A Graphing Utlility|
|1.4||Lines—determining slopes and linear equations|
|1/22||CHAPTER 2||FUNCTIONS AND THEIR GRAPHS|
|A.9||Interval Notation; Solving Inequalities|
|2.1||Functions: Definition, domain, range, operations|
|1/27-29||2.2||The Graph of a Function|
|2.3||Properties of Functions|
|2.4||Library of Functions; Piecewise-defined Functions|
|2.5||Graphing Techniques; Transformations|
|2/3-5||Review for Exam 1|
|CHAPTER 3||LINEAR AND QUADRATIC FUNCTIONS|
|3.1||Linear Functions, their properties, and linear models|
|2/10-12||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|
|2/17-19||4.2||Properties of Rational Functions|
|4.3||The Graph of a Rational Function|
|4.4||Polynomial and Rational Inequalities|
|2/24-26||4.5||Real Zeros of Polynomial Functions|
|4.6||Complex Zeros; Fundamental Theorem of Algebra|
|3/3-5||Review for Exam 2|
|A.10||nth Roots; Rational Exponents|
|3/17-19||CHAPTER 5||EXPONENTIAL AND LOGARITHMIC FUNCTIONS|
|5.1||Composition of Functions|
|5.2||One-to-one Functions; Inverse Functions|
|5.5||Properties of Logarithms|
|3/31-4/2||5.6||Logarithmic and Exponential Equations|
|5.8||Exponential Growth and Decay|
|4/7-4/9||Review for Exam 3|
|4/14-16||CHAPTER 11||SYSTEMS OF EQUATIONS AND INEQUALITIES|
|11.1||Solving Systems of Linear Equations: Substitution and Elimination|
|11.2||Systems of Linear Equations: Matrices|
|4/28-30||11.5||Partial Fraction Composition (if time permits)|