# 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

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 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

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.

**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

possible.

**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
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

1/13-15 | CHAPTER 1 | GRAPHS |

1.1 | Graphing Utilities | |

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 | |

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 | |

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 |

A.7 | Complex Numbers | |

4.6 | Complex Zeros; Fundamental Theorem of Algebra | |

3/3-5 | Review for Exam 2 | |

EXAM 2 | ||

A.10 | nth Roots; Rational Exponents | |

3/10-12 | Spring Break | |

3/17-19 | CHAPTER 5 | EXPONENTIAL AND LOGARITHMIC FUNCTIONS |

5.1 | Composition of Functions | |

5.2 | One-to-one Functions; Inverse Functions | |

3/24-26 | 5.3 | Exponential Functions |

5.4 | Logarithmic Functions | |

5.5 | Properties of Logarithms | |

3/31-4/2 | 5.6 | Logarithmic and Exponential Equations |

5.7 | Financial Models | |

5.8 | Exponential Growth and Decay | |

4/7-4/9 | Review for Exam 3 | |

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 | |

4/21-23 | 11.4 | Matrix Algebra |

4/28-30 | 11.5 | Partial Fraction Composition (if time permits) |

5/7 | FINAL EXAM |

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