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# SYLLABUS FOR PRE-CALCULUS MATH

COURSE DESCRIPTION (4 credits) (4 lecture hours per week)
This course covers a review of algebraic operations, trigonometric functions, trigonometric identities and equations,
applications of trigonometry, exponential and logarithmic functions, and analytic geometry. Graphing calculators
(TI – 83 or comparable models) are required. Prerequisite: MATH 1314 or departmental approval

INTRODUCTION
The purpose of this course is to develop an understanding of the properties and graphs of elementary algebraic and
transcendental functions. This includes polynomial, rational, trigonometric, exponential and logarithmic functions.
Topics studied will also include analytical geometry and limits. The course is designed for students who are
preparing to study calculus.

COURSE OBJECTIVES
Upon completion of the course, the student is expected to have a good understanding of the function concept and the
graphs of polynomial, rational, trigonometric, exponential and logarithmic functions. The student must also be able
to identify and graph conic sections, evaluate limits, and to use the concepts presented in The Factor Theorem and
the Fundamental Theorem of Algebra to find zeros of polynomial functions. Mathematics majors and those needing
knowledge of calculus will be able to take MATH 2413 after completion of this course. The student must
demonstrate an understanding of the topics covered in the course through testing.

END OF COURSE ASSESSMENT EXAM: An assessment exam will be administered at the end of the semester.
The exam will be a minimum of 5% of the course grade.

METHODS FOR ACCOMPLISHING OBJECTIVES
A. Lecture
B. Special Problem Sessions
C. Instructional Media
D. Unit Examinations
E. Peer Tutoring
F. Faculty Tutoring

EVALUATION PROCEDURES
A. Unit Exams
B. Class Assignments
C. End of Course Assessment Exam
C. Final Exam

Letter grades will be assigned according to the following scale:
90 – 100 => A 80 – 89 => B 70 – 79 => C 60 – 69 => D 0 – 59 => F

BIBLIOGRAPHY
Text: Precalculus with Limits (2007) by Larson/Hostetler

COURSE OUTLINE

A. Polynomial and Rational Functions
2. Polynomial Functions of Higher Degree
3. Polynomial and Synthetic Division
4. Complex Numbers
5. Zeros of Polynomial Functions
6. Rational Functions
7. Nonlinear Inequalities

B. Exponential and Logarithmic Functions
1. Exponential Functions and Their Graphs
2. Logarithmic Functions and Their Graphs
3. Properties of Logarithms
4. Exponential and Logarithmic Equations
5. Exponential and Logarithmic Models

C. Trigonometry
2. Trigonometric Functions: The Unit Circle
3. Right Triangle Trigonometry
4. Trigonometric Functions of Any Angle
5. Graphs of Sine and Cosine Functions
6. Graphs of Other Trigonometric Functions
7. Inverse Trigonometric Functions
8. Applications and Models

D. Analytic Trigonometry
1. Using Fundamental Identities
2. Verifying Trigonometric Identities
3. Solving Trigonometric Equations
4. Sum and Difference Formulas
5. Multiple-Angle and Product-to-Sum Formulas

1. Law of Sines
2. Law of Cosines
3. Vectors in the Plane
4. Vectors and Dot Products
5. Trigonometric Form of a Complex Number

F. Topics in Analytic Geometry
1. Lines (optional)
2. Introduction to Conics: Parabolas
3. Ellipses
4. Hyperbolas
5. Parametric Equations
6. Polar Coordinates
7. Graphs of Polar Equations

G. Analytic Geometry in Three Dimensions (optional)
1. The Three-Dimensional Coordinate System
2. Vectors in Space
3. The Cross Product of Two Vectors
4. Lines and Planes in Space

H. Limits and an Introduction to Calculus
1. Introduction to Limits
2. Techniques for Evaluating Limits
3. The Tangent Line Problem
4. Limits at Infinity and Limits of Sequences (optional)
5. The Area Problem (optional)