I. Course Prefix/Number: MAT 149
Course Name: Precalculus
Credits: 5 (5 lecture; 0 lab)
III. Course (Catalog) Description
IV. Learning Objectives
B. Recognize the basic characteristics and graphs for the following functions: polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric.
C. Apply algebraic techniques to trigonometric expressions, identities, and triangles.
D. Recognize the basic characteristics and graphs of the conic sections.
E. Apply the concepts associated with vectors and their operations.
F. Apply the concepts of sequences and series.
G. Solve parametric equations.
H. Solve and graph polar equations.
I. Use technology for graphing and evaluating functions:
1. Generate the complete graph for the elementary functions.
2. Solve equations involving elementary functions.
V. Academic Integrity
• plagiarism (turning in work not written by you, or lacking proper citation),
• falsification and fabrication (lying or distorting the truth),
• helping others to cheat,
• unauthorized changes on official documents,
• pretending to be someone else or having someone else pretend to be you,
• making or accepting bribes, special favors, or threats, and
• any other behavior that violates academic integrity.
There are serious consequences to violations of the academic integrity policy. Oakton's policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.
Details of the Code of Academic Conduct can be found in the Student Handbook.
VI. Sequence of Topics
1. Operations on functions: combinations
2. Graphing techniques
3. Translations and Rotations
4. Inverse functions
B. Polynomial functions: graphs and zeros
1. Quadratic functions
2. Polynomial functions of higher degree
3. Remainder and Factor Theorems
4. Complex zeros of polynomial functions
5. Fundamental Theorem of Algebra
C. Rational functions and conic sections
1. Rational functions and their graphs
2. Conic sections
a) Center at origin
D. Exponential and logarithmic functions
1. Exponential functions and their graphs
2. Logarithmic functions and their graphs
3. Properties of logarithms
4. Solving exponential and logarithmic equations
E. Find the intersection of two polynomial functions (substitution method)
F. Sequences and series
1. Fundamentals of sequences and series
2. Arithmetic sequences
3. Geometric sequences
4. Applications G. Trigonometric functions
G. Trigonometric Functions
1. Measurement of angles
2. Circular functions
3. Graphs of sines and cosines
4. Graphs of the other trigonometric functions
5. Inverse trigonometric functions and their graphs
6. Trigonometric identities
a. Pythagorean identities
b. Sum and difference formulas
c. Multiple and half angle formulas
d. Sum-to-product; product-to-sum
7. Solving trigonometric equations
a. Complex numbers and their trigonometric form
b. Solving right triangles
c. Law of Sines, Law of Cosines
d. Roots and powers of complex numbers
e. Polar coordinates
f. Parametric equations
1. Geometric and algebraic representation of vectors
2. Basic operations with vectors
1. Generate the complete graph of each trigonometric and inverse trigonometric function including setting a proper window, tracing and zooming.
2. Graphically locate the x-intercepts, the relative extrema and determine asymptotic behaviors.
3. Solve equations graphically, numerically and/or symbolically.
VII. Methods of Instruction
Methods of presentation can include lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate.
Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
Course practices include attending class, completing homework assignments, participating in discussions and taking quizzes and exams.
IX. Instructional Materials
Textbooks can also be found at our Mathematics Textbooks page.
A graphics calculator is required. A TI-83/84 will be used for instructional purposes.
X. Methods of Evaluating Student Progress
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam.
XI. Other Course Information
If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the ASSIST office in the Learning Center. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.