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# Course Syllabus-Precalculus

Course Description:
This course is designed to add depth and breadth to a student’s mathematical background before
embarking on a study of the methods of calculus. The course covers a review of algebra, linear,
compositions and inverses of functions; theory of polynomials with the Fundamental Theorem of
Algebra; trigonometric functions and identities; additional topics and applications.
3 credits. Prerequisite: MAT-108 and MAT-130 or MAT-125 or equivalent.

Course Objectives
Upon successful completion of the course, the student will be able to:
1. Solve and graph linear equations and inequalities.
2. Solve and graph quadratic equations and inequalities.
3. Solve and graph absolute value equations and inequalities.
4. Identify a function from its equation and graph.
5. Use the properties of graphing such as symmetry, translations, reflection, compression
and stretching to graph functions.
6. Perform operations on functions including the sum, difference, product, quotient and
composition of functions.
7. Perform operations on complex numbers.
8. Perform long division on polynomials.
9. Perform synthetic division on polynomials.
10. Use the Remainder Theorem to evaluate polynomials.
11. Use the Factor Theorem to show whether (x-c) is a factor of a polynomial.
12. Graph polynomial functions using roots and end behavior of the function.
13. Identify the equations of a polynomial.
14. Graph rational functions using asymptotes, intercepts and end behavior.
15. Find the inverse of a function.
16. Solve and graph exponential functions.
17. Solve and graph logarithmic functions.
18. Evaluate trigonometric functions of real numbers.
19. Graph trigonometric functions.
20. Recognize and verify trigonometric identities.
21. Solve trigonometric equations.
22. Evaluate inverse trigonometric functions.
23. Identify the important parts of a conic section from its equation.
24. Find the equation of a conic section.

Course Requirements
Students are expected to attend all scheduled classes, do the homework assigned each day
for the next class, take tests, and be active participants in the class.

Student Evaluation and Testing
Student evaluation may include in-class testing, class attendance, participation in
policy.

Required Text, Tools, and/or Supplies:
Precalculus: A Concise Course. Larson, R. and Hostetler, R. Houghton Mifflin Co., 2007.
Graphing calculator such as the TI-83 Plus or TI-84
Student Solutions Manual, DVD series, Eduspace OnLine Learning Environment

Non-discrimination and Disability Statements:
Southern Maine Community College is an equal opportunity/affirmative action institution and

If you have a disabling condition and wish to request accommodations in order to have
reasonable access to the programs and services offered by SMCC, you must register with the
disability services coordinator, Mark Krogman, who can be reached at 741-5629.
(TTD 207-741-5667) Further information about services for students with disabilities and the
accommodation process is available upon request at this number.

Course Evaluation: Students may evaluate the course online and anonymously by going to
“Resources for Current Students” at the SMCC homepage and selecting “Evaluate Your
Courses.” The online course evaluation is available to students two weeks prior to the end date
of the course. Students cannot see a course grade online until the online course evaluation is
completed.

Required Course Topics, MAT 140 Chapter 1-6 as follows:

CHAPTER 1
1.1 Rectangular coordinates
1.2 Graphs of functions
1.3 Linear Equations in Two Variables
1.4 Functions
1.5 Analyzing Graphs of Functions
1.6 A Library of Parent Functions
1.7 Transformations of Functions
1.8 Combinations of Functions: Composite functions
1.9 Inverse Functions
1.10 Mathematical Modeling and Variation

CHAPTER 2
2.2 Polynomial Functions of Higher Degree
2.3 Polynomial and Synthetic Division
2.4 Complex Numbers
2.5 Zeros of Polynomial Functions
2.6 Rational Functions
2.7 Nonlinear Inequalities

CHAPTER 3
3.1 Exponential Functions and Their Graphs
3.2 Logarithmic Functions and Their Graphs
3.3 Properties of Logarithms
3.4 Exponential and Logarithmic Equations
3.5 Exponential and Logarithmic Models

CHAPTER 4
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
4.5 Graphs of Sine and Cosine Functions
4.6 Graphs of Other Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Applications and Models

CHAPTER 5
5.1 Using Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Solving Trigonometric Equations
5.4 Sum and Difference Formulas
5.5 Multiple-Angle and Product-to-Sum Formulas

CHAPTER 6
6.2 Introduction to Conics: Parabolas
6.3 Ellipses
6.4 Hyperbolas