Precalculus

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Catalog Description

MAT 200: PRE-CALCULUS
4 credits, 5 hours
4 classroom hours, 1 lab hour

Prerequisite: MAT096/MAB096, minimum score of 25 on the CUNY Mathematics Assessment Test

This course is intended as a preparation for the study of Calculus. Functions and their graphs will be analyzed theoretically within a framework that emphasizes their appearances in applied settings. Particular attention will be placed on polynomial, exponential, logarithmic, and trigonometric models. The use of graphing utilities as analytical tools will be emphasized. Each student is required to have a graphing calculator (approximate cost $90.00).

Instructional Objectives

During the semester, the instructor will endeavor to:

1) Reinforce and further explore functional patterns as a naturally occurring phenomena.

2) Investigate verbal, numerical, graphical, and symbolic representations of functions.

3) Enable students to critically analyze linear, power, and exponential models both algebraically and graphically.

4) Examine rigid and non-rigid transformations both experimentally and analytically.

5) Introduce and explore the inverse function concept and to relate inverse functions to the corresponding original functions.

6) Introduce logarithmic functions as inverses of the exponential functions and to analyze the theoretical consequences of this inverse relationship.

7) Introduce the trigonometric functions and their inverses, present a comprehensive treatment of the sine and cosine functions, and explore applications of them.

8) Facilitate the students' use of graphing utilities as analytical tools.

9) Promote the development of written analyses of mathematical concepts.

Performance Objectives

At the end of the semester, the student will be able to:

1) Interpret functional patterns and to create functions describing them.

2) Convert one representation of a function to another.

3) Form linear, power, and exponential models and to apply them in the solution of real-world problems.

4) Employ rigid and non-rigid transformations algebraically and graphically as problem solving tools.

5) Compute inverse functions and to use their properties to obtain more precise algebraic and graphical information about the corresponding original functions.

6) Solve exponential and logarithmic equations and to graph exponential and logarithmic functions both in abstract forms and in the applications of exponential models.

7) Perform computations involving the trigonometric functions and their inverses in both theoretical and applied settings and to graph the sine and cosine functions.

8) Use graphing utilities as aids in the solution of problems.

9) Complete written reports on various topics in the Pre-calculus subject area.

Evaluation

1) Laboratory Writing Assignments and Quizzes

2) Five Examinations

3) Project

Remarks About Evaluation

1) Several laboratory writing assignments will be collected during the semester. Each assignment should be submitted by its due date. Assignments turned in late may not receive full credit. These assignments will be evaluated primarily on their mathematical content and precision. In addition, quizzes on lab material may be given at various times during the term.

2) Each of the five examinations will be given in class. Approximately 60% of each exam is completely technical in nature while the other 40% is applications-oriented.

The project should be submitted by its due date which will be sometime during the week before the final exam week. Papers turned in late may not receive full credit. The project should provide a more complete analysis of material covered in class or else provide an analysis of any Pre-Calculus level material not directly covered in class. Consult your instructor for suggestions for possible topics and/or approval of your chosen topic. The project should contain both algebraic and graphical analysis where appropriate. It is expected that your writing style will have matured as a result of the previous writing assignments. Consequently, clarity of presentation will be just as big a factor as mathematical content and precision in the evaluation of the project.

Textbook

PRE-CALCULUS Graphing & Data Analysis Second Edition by Michael Sullivan, Michael Sullivan III Published Prentice Hall, Inc. (2001, 1998)

General Comments

1) The specific topics listed in the following lesson plan and the principles of evaluation listed above areboth subject to minor modification by the instructor.

2) The instructor will assign homework relevant to the topics in the course. Each student is strongly encouraged to complete these assignments to the best of his or her ability consistently throughout the semester. Generally speaking, the student that follows this recommendation will maximize his or her understanding of the subject matter and achieve optimal performance on examinations.