VIRGINIA HIGHLANDS COMMUNITY COLLEGE
COURSE OF
STUDY
MTH 164 Precalculus Mathematics
II SPRING 2008
INSTRUCTOR:
Susan Clark Fleming
Office: OTC 1218 e-mail: sfleming@vhcc.edu
Web Page- www.vhcc.edu/sfleming Phone: 276-739-2513
COURSE DESCRIPTION:
Presents trigonometry, analytic geometry, and sequences and series. Prerequisite: MTH 163 or equivalent. (Credit will not be awarded for both MTH 164 and MTH 168.) Lecture 3 hours per week.
BROAD GOALS:
Goals of the course are to gain conceptual and analytical understanding of triangles, vectors, conic sections, parametric equations, sequences and series. Appropriate use of technology will be employed in such a way as to enhance, as opposed to substituting for, analytical and conceptual competence.
SPECIFIC OBJECTIVES:
Trigonometry
1. Be able to represent on a circular model each of the six basic trigonometric functions of any multiple of 30 degrees, 45 degrees, `pi/6 radians or `pi/4 radians.
2. Apply the circular model of trigonometric functions to the graphing of sine and cosine functions with amplitude, angular frequency, vertical shift and phase shift parameters.
3. Apply the circular model of trigonometric functions to the modeling of real-world applications.
4. Apply the circular model to simple harmonic motion, including damped and undamped motion.
5. Solve any triangle given sufficient information.
6. Use area formulas to find areas of given triangles.
7. Model real-world situations using triangles and interpret the solutions of the triangles.
8. For any trigonometric function construct the angle representing the inverse function of a given number in its domain.
9. Find complete solutions to trigonometric equations.
10. Prove or disprove trigonometric identities.
11. Apply sum and difference formulas, double and half-angle formulas for trigonometric functions.
Polar Coordinates, Vectors, Complex Numbers
1. Plot points in polar coordinates and graph equations in polar coordinates.
2. Convert equations and expressions as needed between rectangular and polar coordinates.
3. Solve equations in polar coordinates.
4. Represent complex numbers in the complex plane; represent addition and multiplication of complex numbers in the complex plane.
5. Apply deMoivre's Theorem to find roots and powers of complex numbers.
6. Represent vectors, their sums and their differences in the coordinate plane.
7. Find, both in coordinate form and as magnitudes and angles, sums and differences of vectors specified by coordinates or angles and magnitudes.
8. Apply vectors to relative velocities.
9. Use the dot product to find the angle between two vectors or to determine whether two vectors are parallel, orthogonal or neither.
10. Use the dot product to decompose a vector into orthogonal components.
11. Use the dot product to compute the work done by a constant force acting through a given displacement.
12. Apply vectors and dot products in 3 dimensions.
Conic Sections
1. From sufficient information about the vertex, directrix and focus of a parabola determine the equation of the parabola or from its equation determine the vertex, directrix and focus of a parabola.
2. Use the characteristics of parabolas to solve applied problems to which parabolas are relevant.
3. From sufficient information about the center, foci and vertices of an ellipse determine the equation of the ellipse or from its equation determine the center, foci and vertices of an ellipse.
4. Use the characteristics of ellipses to solve applied problems to which ellipses are relevant.
5. From sufficient information about the center, foci, vertices and asymptotes of an hyperbola determine the equation of the hyperbola or from its equation determine the center, foci, asymptotes and vertices of a hyperbola.
6. Use the characteristics of hyperbolas to solve applied problems to which hyperbolas are relevant.
7. Apply rotation of axes to conic sections in order to determine the nature of the conic and its characteristics.
Parametric Equations
1. Graph a given parametric equation.
2. Find the rectangular equations corresponding to a given parametric curve, and vice versa.
3. Apply the idea parametric equations to situations involving time as a parameter.
Sequences, Series and Probability
1. Find the sum of a sequence, using summation notation.
2. Determine whether a given sequence is arithmetic; if so find its sum and its general formula.
3. Apply arithmetic sequences to real-world problems.
4. Determine whether a sequence is geometric; if so find its formula and its sum.
5. Apply geometric sequences and series to real-world problems.
UNITS TO BE COVERED:
Chapter 5 – Trigonometric Functions of Acute Angles
Chapter 6 – Trigonometric Identities, Inverse Functions, and Equations
Chapter 7 – Applications of Trigonometry
Chapter 9 – Analytic Geometry Topics
Chapter 10 – Sequences, Series, and Combinatorics
METHODS and GRADING
1. Daily homework assignments will be made to provide practice on the material covered in class. Answers for many problems are located in the back of the book. It is the student's responsibility to come for help as needed. Students may also e-mail questions to sfleming@vhcc.edu.
2. Section quizzes will be given on blackboard during the semester. The quizzes will be based on the homework assignment from the previous class period. Students have until the beginning of the class period after that section was assigned to complete the quiz. The purpose of these quizzes is to encourage you to keep up with your assignments and to seek help on the problems BEFORE the next class period. Because the purpose of the quizzes is to encourage you to keep up with your work, these quizzes cannot be made up if you don’t get them done on time.
3. Tests will be given periodically throughout the semester, usually at the end of each chapter.
4. A comprehensive final will be required of all students. This counts 25% of the final grade.
5. Absolutely no make-up tests are given. The exam grade will be substituted for any missed tests. If you know you will be absent when a test is scheduled, you can make arrangements to take the test early. For students who do not miss any tests, the exam grade will be substituted for the lowest test grade if the exam grade is higher than the test grade.
6. Cheating in any form will not be tolerated. Any student caught cheating will receive a grade of F in the course and will be sent before the Student Judiciary Committee fro appropriate disciplinary action. Cheating includes giving as well as receiving aid on any test, quiz, or hand-in assignment. Plagiarism will be handled in the same manner.
7. The course grade will be determined as follows:
Quizzes 15%
Tests 60%
Final Exam 25%
Grading Scale:
90-100 A
80-89 B
70-79 C
60-69 D
Below 60 F
W-The college has a strict policy for withdrawing from classes and receiving a grade of W. Students who simply quit coming and do not formally withdraw will receive a grade of F.
INSTRUCTIONAL MATERIAL
TEXT: Precalculus: Graphs & Models (3rd ed.), Bittinger, Beecher, Ellenbogen, Penna. Pearson, 2006.
CALCULATOR: A graphing calculator, preferably the TI-84, is required for this class. If you use another model, you must know how to operate it with no help from the instructor.
OFFICE HOURS
MWF 11:00AM-12:00PM and 2:00PM-2:50PM
CLASSROOM ETIQUETTE
It is the instructor’s responsibility to maintain a classroom environment conducive to learning. Students who are disruptive will be asked to leave the classroom and may not be allowed to return. Be respectful of your fellow students. Even if you know what is going on, talking to your neighbor may disturb someone else who is trying to learn.
Cell phones are to be turned off and put away at the beginning of class. Answering a cell phone during class or text messaging during class may result in the student being asked to leave the classroom.
Use of iPods or other headphone devices in class is prohibited.
IMPORTANT DATES FOR SPRING 2008
Monday, January 7 - Classes Begin
Monday, January 21 - Martin Luther King, Jr. holiday - College closed - No classes
Tuesday, January 22 - Last day to add/drop a course, change from audit to credit, and receive tuition refund
Thursday - Friday, February 14-15- Faculty in-service - No classes
Monday - Friday, March 10-14 - Faculty/student spring break - No classes
Friday, March 21 - Faculty research day - No classes
Monday, March 24 - Last day to withdraw from class without academic penalty or change from credit to audit
Monday, April 7 - Open enrollment for all summer sessions and fall semester begins
Tuesday, May 6 - Last day of classes
Wednesday, May 7 - Final Exam