III. Textbook. Precalculus, by Robert Blitzer. Third edition. Prentice Hall. 2007. IV.
Course description. An integrated study of elementary functions and equations, ...
Syllabus - MATH 2412 - Precalculus I. Course number and title MAT 2412: Precalculus II. Instructor Dr. Jaime L. Hernández, B.S., Ph.D. Phone: 713-718-2223, box: 30085 # E-mail:
[email protected] Conference hours: by appointment III. Textbook Precalculus, by Robert Blitzer. Third edition. Prentice Hall. 2007. IV. Course description An integrated study of elementary functions and equations, analytic geometry, trigonometry, vectors, mathematical induction, parametric and polar functions, sequences, series and the Binomial Theorem. The course is intended to prepare the student for a first course in calculus. V. Course prerequisites Before enrolling in this course, the student must have successfully completed both MATH 1314 (College Algebra) AND MATH 1316 (Plane Trigonometry) with a grade of "C" or better. VI. Student Learning Outcomes and Objectives Student Learning Outcomes
Course Objectives 1.1 Develop and use various problem-solving techniques. 1.2 Recognize functions as ordered pairs.
1. Represent and manipulate algebraic and trigonometric functions and relations algebraically, graphically, and numerically, including partial fraction decomposition and finding zeroes of functions.
1.3 Determine the graph of an algebraic equation or function. 1.4 Understand synthetic division. 1.5 Develop partial fraction decomposition. 1.6 Find the zeros of real functions 1.7 Solve polynomial equations. 1.8 Utilize the six basic trigonometric functions.
2. Engage in algebraic and trigonometric problem solving and modeling.
2.1 Apply the Law of sines and the Law of cosines for various types of situations. 3.1 Verify various trigonometric identities.
3. Synthesize algebraic and trigonometric facts and laws into proofs.
3.2 Find the powers and roots of complex numbers using DeMoivre’s Theorem. 4.1 Understand basic vectors (2 dimensional).
4. Analyze and manipulate equations between various two dimensional systems such as rectangular, polar, vector representations, conic systems and axes manipulations, as well as solving equations in these systems.
4.2 Convert points in a rectangular coordinate system to polar coordinates. 4.3 Recognize algebraic formulas relating to circles, parabolas, ellipses, and hyperbolas.
4.4 Use translation of axes, rotation of axes, and polar equations of conics. 5.1 Recognize the use of arithmetic and geometric sequences. 5.2 Use summation notation to represent a series. 5. Investigate and perform summations and predictions on geometric, algebraic and binomial sequences and series.
5.3 Understand and use the Binomial theorem. 5.4 Understand mathematical induction. 5.5 (Optional) Understand the basic concepts of limits.
VII. Specific course instructional goals This course shall aim to accomplish the following general goals: 1. To strengthen the students’ ability to think and reason critically, rigorously and logically. 2. To further develop the students’ quantitative skills and knowledge. 3. To introduce the fundamental concepts for courses in calculus and for applications in related fields. 4. To review the techniques for solving equations and inequalities. 5. To devlop and illustrate problem-solving techniques. 6. To review the concept of function and the various types of functions and their graphs. 7. To review division of polynomials and synthetic division. 8. To instruct the techniques for partial fraction decomposition of a rational expression. 9. To review how to solve polynomial equations and find zeros of polynomial functions. 10. To review the six basic trigonometric functions and their graphs. 11. To review basic trigonometric identities and how to solve trigonometric equations. 12. To introduce the Laws of Sines and Cosines and their applications. 13. To introduce DeMoivre's Theorem. 14. To study 2- and 3-dimensional vectors and their applications. 15. To study parametric equations and their graphs. 16. To introduce the polar coordinate system and study polar equations and their graphs. 17. To present algebraic equations for the various nondegenerate conic sections. 18. To introduce the rotation and translation of axes. 19. To introduce the Binomial Theorem and mathematical induction. 20. To study arithmetic and geometric sequences and series. VIII. Course expectations The student shall: 1. Meet the course prerequisites by the time the course starts. 2. Attend all class sessions in a timely manner. 3. Involve him(her)self in class discussions by taking clear and organized notes, asking questions and/or answering inquiries from the instructor. 4. Read, while assuring comprehension, the sections in the textbook as they are covered in class. 5. Complete homework assignments by the time they are due. 6. Study (includes reading the textbook, completing homework assignments, reviewing class notes, seeking help from the instructor or any other recognized authority in the subject, etc.) for as long as it takes to ensure understanding of the course material and successful performance in the course. 7. Perform satisfactorily in all written assessment tools.
8. Obtain individualized help from the instructor during conference hours (to be announced in class) or by appointment, when necessary. 9. Make use of the tutorial help available in the Math Lab and Tutoring Center as needed. IX. Course policies and regulations 1. The final exam will be used to substitute at most ONE missing exam grade. This will be allowed rarely, ONLY under exceptional circumstances, and at the instructor’s discretion. A student missing an examination shall provide original, appropriate documentation justifying their absence in order to be given this opportunity. This exam is required, comprehensive and counts as TWO grades (200 points). 2. Class attendance and timeliness are not only appreciated but REQUIRED and will be recorded. Any student missing over 12.5% of the class time (8 hours or 4 lecture periods) MAY BE DROPPED from the course. Walking in late or leaving early over 20 minutes to a lecture will be considered an absence. The student is responsible for materials covered during his/her absences. Please inform the instructor of any circumstances which may be causing excessive absenteeism or tardiness.The student is ultimately responsible for dropping officially from the course and a grade of "F" may result if the student stops attending the class but does not drop the course. 3. No "W’s" or "WF’s" will be assigned past the last day to officially withdraw from a course as scheduled in the HCCS academic calendar. After such date, only the grades A, B, C, D or F will be used for evaluation. 4. A scientific or, preferably, graphing calculator may be used for homework assignments and tests. The student will bring it to the lecture sessions for class discussions and work. The instructor reserves the right to NOT allow the use of graphing calculators in certain exams. In such cases, the students will be advised in advance by the instructor. 5. Scholastic dishonesty can result in dismissal from the entire Houston Community College System and will not be tolerated. Any student caught "cheating" in a test will be dropped from the course with a grade of "F." Any talking, sharing of information in any manner, or referring to books or notes during an examination will be considered dishonest behavior. Please refer to the Student Handbook for more information on student conduct. 6. Americans With Disabilities Act (ADA): Any student with a documented disability (e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable accommodations must contact the Disability Services Office at the respective college at the beginning of each semester. Faculty is authorized to provide only the accommodations requested by the Disability Support Services Office. For questions, please contact Donna Price at 713-718-5165 or the Disability Counselor at your college. At the Southwest College, please contact Dr. Becky Hauri at 713-718-7910. 7. Homework will be assigned regularly and its completion and comprehension will be monitored through class discussions. The student is responsible for completion and understanding, and should use class discussions and conference hours to obtain help when having difficulties with the material. 8. Class meets twice a week for two hours. Exams may last one hour (with the exception of the final exam which lasts 2 hours) and cover only half of the class time. The rest of the time on exams days may be devoted to either review (if before the exam) or to start new material (if after the exam). 9. Students must exhibit appropriate behavior and be attentive during class. Any student who disrupts the class will be asked to leave. Any student who naps or falls asleep in class will be marked as absent. So, please: no side conversations or snoozing! 10. Instructor will devote part of the first lecture for student advising. Students are welcome to ask questions pertaining to major math requirements, course prerequisites, course sequences, and other related topics on that or any other day. 11. Students are encouraged to meet with the instructor if their performance does not meet their expectations. 12. All cell phones and pagers must be turned off in the classroom for the duration of the class. 13. Students who fail/withdraw a course twice and enroll in such course three or more times may soon face significant tuition/fee increases at HCC and other Texas public colleges and universities. If you consider course withdrawal because you do not earn passing grades, confer with your instructor or counselor as early as possible about your study habits, homework completion, test-taking skills, attendance and punctuality, course participation, and opportunities for tutorial help or other assistance that might be available. 14. Online Tutoring Services: Houston Community College offers FREE online tutoring in a variety of subjects, including mathematics, English and writing. To register and take advantage of these Online Tutoring Services, go to www.hccs.askonline.net. Your questions will be answered by a qualified HCC tutor or faculty member within 24 hours (usually under 6 hours). 15. Sexual Harassment: It is a violation of HCCS policy for an employee, agent, or student of the college to engage in sexual harassment as defined in the EEOC guidelines (EEO/AA Compliance Handbook 47). X. Course outline 1. Unit 1 : Review of algebra, functions and their graphs, partial fractions and basic trigonometry Sections to be reviewed: 1.2 - 1.7, 1.9; 2.2 - 2.6; 4.1 - 4.8 Sections to be covered: 7.3 Number of hours: 12
Assessment: Test 1 2. Unit 2: Analytic trigonometry Sections to be covered: 5.1 - 5.5 Number of hours: 10 Assessment: Test 2 3. Unit 3: Law of Sines, Cosines, Polar Coordinates and Equations, Vectors Sections to be covered: 6.1 - 6.7 Number of hours: 10 Assessment: Test 3 4. Unit 4: Analytic geometry and Parametric Equations Sections to be covered: 9.1 - 9.6 Number of hours: 16 Assessment: Test 4 5. Unit 5: Sequences, series, mathematical induction and the Binomial Theorem Sections to be covered: 10.1 - 10.5 Number of hours: 10 Assessment: Test 5 XI. Assessment tools and their weights The following tools shall be used to evaluate the students’ performance: 1. Five in-class examinations (as listed above): 500 pts. 2. Final examination (comprehensive and required): 200 pts. Total number of points used for evaluation: 700 pts. Examinations may include both multiple choice and open-ended problems. Student must show all supporting work to get credit, even for multiple choice questions. No credit may be given for right answers given without supporting work. The instructor reserves the right to not allow the use of graphing calculators in certain exams. Up to 15 bonus points may be added at the instructor’s discretion to the student’s total score based on attendance, punctuality, effort, shown interest and class participation. XII. Grading scale The following scale will be used at the end of the semester to assign a course grade based on the overall course total of points obtained when the scores of all the exams are added together. However, this scale is subject to change at the instructor’s discretion. 700 - 630......................A 629 - 560......................B 559 - 490......................C 489 - 420......................D 419 - 0......................F XIII. Instructional resources available to the student The student shall use the following resources to facilitate learning and improve academic performance: 1. Textbook 2. Conferences with the instructor held by appointment 3. Lectures, problem-solving and review sessions conducted by the instructor 4. Graphing or scientific calculator 5. Peer tutoring or study groups 6. Math Lab and Tutoring Center 7. Student’s Solution Manual and Study Guide 8. Meetings and discussions of the Math Club 9. Precalculus references in the Library 10. Online tutoring available at www.hccs.askonline.net
