SYLLABUS                                                                Last revised 12/01/03

MAT 115  -  PRE-CALCULUS

 

 

Instructor:__________________________________Office:__________________________

Phone:_____________________________________  E-mail:__________________________

 

Lead Instructor:  Richard Diefenbach           Office:  J1013

Phone:  618/634-3317                                                 E-mail:   Richardd@shawnee.cc.il.us

 

 


Credit Hours:  Five (5)  Lecture hours per week.

 

Prerequisites: Geometry (Mat 042) and Intermediate Algebra (Mat 114) with a grade of C or better or satisfactory math background in high school.

 

Course Description:

An integrated college‑level course in the elementary functions of College Algebra and Trigonometry.  Includes a study of number systems, equation and inequality solving, functions and graphing, linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions, systems of equations and inequalities, binomial expansions, analytic trigonometry, and applications of trigonometry.  Graphing calculators will be used in this course.

 

Textbook(s) and Supporting Materials:

College Algebra and Trigonometry and Pre-calculus, 2nd ed., Lial, Hornsby, and Schneider, Addison Wesley Longman, 2001

Supplementary Materials, A set of instructional videos in on reserve in the Shawnee Community College library.  Any student needing additional instruction is encouraged to make use of these videos.

Calculator:  Each student is required to have a graphing calculator.  A Texas Instrument

TI-83 is recommended. There are a limited number of calculators for loan on a first come basis.

 

Course Objectives:

            1.  To guide the student in his/her study of pre-calculus.

            2.  To provide for student development in the following areas:

                        knowledge of the real & complex number systems

                        knowledge of solving polynomial, rational, radical, exponential, logarithmic &                             trigonometric equations and solving inequalities

                        knowledge of  functions and their graphs including:

polynomial functions

rational functions

exponential functions

logarithmic functions

trigonometric functions

                        Knowledge of systems of equations and inequalities

                        Understanding of binomial expansion

                        knowledge of analytic trigonometry including verifying identities and using                                               various trigonometric formulas

                        knowledge of applications of trigonometry including Law of Sines, Law of                                             Cosines, and vectors

            3.  To increase the student's mathematical vocabulary.

4. To provide the student with a mathematical background in those areas which will                        benefit him/her in future work.

5. To provide for student awareness of the role of pre-calculus in all of higher                                

    mathematics.

6.  Students will become adept at using graphing calculators.

 

Instructional Modes:

1.         lecture/discussion (primary mode)

2.         constant effort will be made to keep student motivated

3.         students will be encouraged to verbalize their thoughts both in class and out of class

4.         creative thinking will be sought for and rewarded

5.         provisions will be made for individual differences in interests and ability with the constant goal of providing maximum motivation

6.         the chalkboard will be used extensively to provide a visual aid to understanding

7.         the overhead projector may also be used as a visual tool whenever appropriate

8.         more than one approach to a given topic will be used whenever possible to aid student understanding and acceptance.

 

Student Expectations:

            1.         Attend class regularly and be on time.

            2.         Read and prepare assignments prior to class. 

            3.         Turn in assignments on time.

4.         Be prepared for exams over assigned material.  Take tests at regularly                           scheduled times unless extenuating circumstances interfere.  Quizzes may be                   announced or unannounced.

 

Student Evaluation:

Hour tests will be given along the way.  A comprehensive final will be given at the end of the course.  The final will count 200 points and each hour test will count 100 points.

***Specifics on the grading procedure and/or a tentative course schedule, developed by the instructor, may accompany this syllabus.

 

Office Hours: 

Office hours will be posted on the bulletin board outside the instructor’s office.  Other times are possible by scheduling individual appointments at mutually convenient hours.  Students are encouraged to consult regularly with the instructor regarding class progress or other topics of concern.

 

Inclement Weather Policy:

Become familiar with the inclement weather policy of Shawnee Community College.  It will be read in all classes and posted in the cafeteria or student lounge.

 

Academic Dishonesty or Plagiarism:

Review the college policy regarding academic dishonesty in the Student Handbook.

 

College Policy:

Administrative policy prohibits the following:  eating, drinking, or using tobacco in the classroom; bringing children or other unauthorized individuals to the classroom.

 

Attendance Policy:

Each student is expected to attend all class meetings.  The student is expected to be on time and ready to begin class with the proper materials at the beginning of each class period. If a student will be unable to attend class, it is their responsibility to contact the instructor to obtain homework assignments and other information.

 

Topical Outline:        

1.      Algebraic Expressions

  1. Real Numbers and Their Properties
  2. Order and Absolute Value
  3. Polynomials; The Binomial Theorem
  4. Factoring Polynomials
  5. Rational Expressions
  6. Rational Exponents
  7. Radical Expressions

2.      Equations and Inequalities

a.        Linear Equations

b.       Linear Applications and Modeling

c.        Complex Numbers

d.       Quadratic Equations

e.        Quadratic Applications and Modeling

f.         Other Types of Equations

g.        Inequalities

h.        Absolute Value Equations and Inequalities

3.      Relations,  Functions, and Graphs

a.       Relations and the Rectangular Coordinate System; Circles

b.       Functions

c.       Linear Functions

d.       Equations of Lines; Curve Fitting

e.       Graphs of Relations and Functions

f.         General Graphing Techniques

g.       Operations and Composition

4.      Polynomial and Rational Functions

a.       Quadratic Functions; Curve Fitting

b.       Synthetic Division

c.       Zeros of Polynomial Functions

d.       Polynomial Functions: Graphs, Applications, and Models

e.       Rational Functions: Graphs, Application, and Models

f.         Variation (Optional)

5.      Exponential and Logarithmic Functions

a.        Inverse Functions

b.       Exponential Functions

c.        Logarithmic Functions

d.       Evaluating Logarithms and the Change-of-Base Theorem

e.        Exponential and Logarithmic Equations

f.         Applications and Models of Exponential Growth and Decay

6.      Trigonometric Functions

a.        Angles

b.       Right Angles and Trigonometric Functions

c.        Finding Trigonometric Function Values

d.       Solving Right Triangles

e.        Radian Measure

f.         The Unit Circle and Circular Functions

g.        Graphs of the Sine and Cosine Functions

h.        Graphs of Other Circular Functions (Optional)

7.      Trigonometric Identities and Equations

a.        Fundamental Identities

b.       Verifying Trigonometric Identities

c.        Sum and Difference Identities

d.       Double-Angle and Half-Angle Identities

e.        Inverse Trigonometric Functions

f.         Trigonometric Equations

g.        Equations Involving Inverse Trigonometric Functions

8.      Applications of Trigonometry

  1. Oblique Triangles and the Law of Sines
  2. The Law of Cosines
  3. Vectors and the Dot Product
  4. Application of Vectors

9.      Systems of Equations and Inequalities

a.        Linear Systems of Equations

b.       Matrix Solution of Linear Systems

c.        Determinant Solution of Linear Systems

d.       Partial Fractions

e.        Systems of Inequalities

f.         Properties of Matrices

g.        Matrix Inverses

10.  Analytic Geometry

a.       Conic Sections

11.  Further Topics

  1. The Binomial Theorem

 

NOTE:            The above schedule and procedures in this course are subject to change in         the event of extenuating circumstances.  

 Instructor’s Page: