Pre-Calculus School Year: 2018-2019 Instructor: Winter Valero Email: wvalero@materacademy.com Class Location: Room 218 Phone Number: Office Location: Room 218 Office Hours: M-F 2:40 pm - 3:00 pm Catalog Course Description: Topics include: Linear, quadratic, rational, exponential, logarithmic, radical, and absolute value functions and their graphs; operations on functions; inverse functions; properties of logarithms; systems of equations and inequalities; non-linear inequalities; applications and modeling. It also covers topics including right triangle trigonometry; trigonometric functions of special angles; graphs of trigonometric functions and their inverses; trigonometric identities including sums and differences of angles, double angle, half angle, power reduction, sum to product, and product to sum; trigonometric equations; introduction to vectors; parametric equations; polar coordinates; arcs and sectors; dampened waves; complex numbers. Textbook and Other Required Materials: Precalculus, 5th Edition. Robert Blitzer Registration: It is your responsibility to make sure that you are registered for this course. Be sure to obtain a copy of your schedule to verify the reference number and that you do not have any outstanding fees. If your name does not appear on your instructor s class roll by the first day of the mini-term as being registered and having paid for the class, you will not receive a grade for this course, and you will have to retake it next term, regardless of whether you continue to sit in on the class. Attendance: The number one key to educational success is to attend classes. Class attendance will be recorded daily. Students are responsible for any work missed when absent. Frequent absences will impact your grade. You should make it an effort to be in class, and on time. Lateness is disruptive, then, try to access the class from the rear door whenever it is possible, minimizing your interruption. Instructor Support: Please make an appoint to stop by if you have any questions or concerns about class policies or the course material. Come prepared with specific questions and bring your work so I can best meet your needs and facilitate your success.
Student Learning Outcomes: 1. Use correct mathematical notation and terminology. 2. Read and interpret graphs. 3. Students will be able to use the unit circle to define the six trigonometric functions. 4. Students will be able to graph the sine, cosine, and tangent functions. 5. Students will be able to fit a sine or cosine function to a given graph. 6. Students will be able to work with radians and to solve circular motion problems. 7. Students will be able to solve right triangles. They will be able to draw a sketch in an applied problem when necessary. 8. Students will be able to solve non-right triangles using the law of sines and the law of cosines. 9. Students will be able to prove trigonometric identities. 10. Students will be able to apply addition and subtraction, double-angle and half-angle formulas. 11. Students will be able to graph the inverse sine, cosine, and tangent functions. 12. Students will be able to solve problems that require the inverse trigonometric functions. 13. Students will be able to solve trigonometric equations. These may require the formulas outlined in SLO 2. 14. Students will be able to work with the trigonometric form of complex numbers. This includes DeMoivre s formula. 15. Students will be able to work with the Euler form i r e of complex numbers. 16. Students will be able to add and subtract vectors in two dimensions. They will be able to use the dot product to project one vector onto another and to determine the angle between two vectors. They will be able to solve a variety of word problems using vectors 17. Students will be able to work with polar coordinates; this includes graphing in polar coordinates and transforming an equation with polar coordinates into one with rectangular coordinates, and vice versa. 18. Students will be able to graph parametric equations in two dimensions that involve trigonometric functions. Calculators: Scientific and graphic calculators are allowed to use in this course, unless it is specified for a given activity. Minimum requirement: the scientific calculator. Check the availability of trigonometric (sin, cos, tan) and inverse trigonometric (sin-1, cos-1, tan-1 ) functions in your calculator.
Portfolio: Portfolios are required for all students. The portfolio is to be kept current and may be collected on any random day for review and scoring. This portfolio may not be used for any other class. Portfolios shall include the following: a) Cover page with your name, your instructor s name, the subject, and day/time the class meets. b) Class syllabus c) All tests and quizzes included d) Remediation plan together with professor and/or department chair visit record e) Textbook and/or class notes for each section covered f) Homework completed for every section covered Grading Scale: The final grade for the course will be calculated by the following table: Online HW 25% (Four units) In class Tests: 25% (Based on the average of the four tests) Quizzes: 15 % (Based on the average of all quizzes) Classwork: 35% (Based on the average of all classwork) Incomplete. The grade of I (Incomplete) is given in the rare case that a student is PASSING a class but for some extenuating circumstance is unable to complete the last part (usually the final exam) of the class. You MAY NOT leave the room once you have begun taking an exam. If a student leaves the room during an exam, the test will be collected and graded as a completed exam. The test will not be returned to the student for completion when return to the room. Any student found cheating, will receive an F. Any student found cheating, will receive an F for the course. Academic Integrity: Students in this class must know, observe, and not compromise the principles of academic integrity. It is not permissible to cheat, to fabricate or falsify information, to submit the same academic work in more than one course without prior permission, to plagiarize, to receive unfair advantage, or to otherwise abuse accepted practices for handling and documenting information. The grade for this course includes the judgment that the student s work is free from academic dishonesty of any type. Violations or infractions will be reported to the Director of Admissions and Student Services and may lead to failure of the course and other sanctions imposed by the College. Cheating: A student caught cheating will receive a zero for that assignment and be put on notice of probationary status in the class. Any repeat incident of academic dishonesty (cheating in any form) will result in expulsion from the class and a failing score. Disability Services: Accommodations are available for students with disabilities; please visit Student Services in 211 and see Ms. Jeanette Perez.
TABLE OF CONTENTS TOPICS CONTENTS # CLASSES 1. REVIEW. EQUATIONS AND INEQUALITIES AND THEIR GRAPHS POLYNOMIAL RATIONAL EXPONENTIAL AND LOGARITHMIC AND THEIR GRAPHS SYSTEMS OF EQUATIONS. NEWTON S THEOREM TRIGONOMETRIC 2. SOLVE LINEAR, QUADRATIC, ABSOLUTE VALUE AND RADICAL EQUATIONS. 3. LINEAR, QUADRATIC, ABSOLUTE VALUE AND RADICAL INEQUALITIES. 4. TEST 1 5. FUNTIONS, THE GRAPH OF A FUNCTION AND THEIR PROPERTIES. 6. COMPOSITE FUNCTION. DOMAIN OF A COMPOSITE. ONE TO ONE FUNCTION. THE INVERSE FUNCTION. 7. TEST 2 8. QUADRATIC FUNCTION. GRAPH AND PROPERTIES. 9. POLYNOMIAL EQUATIONS AND INEQUALITIES. FUNDAMENTAL THEOREM OF ALGEBRA AND ITS CONSECUENSES. 10. TEST 3 11. RATIONAL EQUATIONS AND INEQUALITIES. 12. GRAPH POLYNOMIAL AND RATIONAL AND ANALYZE THEIR PROPERTIES. 13. TEST 4 14. EXPONENTIAL EQUATIONS AND INEQUALITIES. 15. LOGARITHMIC EQUATIONS AND INEQUALITIES. 16. TEST 5 17. EXPONENTIAL AND LOGARITHMIC. GRAPH AND THEIR PROPERTIES. 18. APPLICATIONS FOR GROWTH AND DECAY. 19. TEST 6 20. SYSTEM OF EQUATIONS. LINEAR SYSTEMS. 21. NON LINEAR SYSTEMS. 22. THE BINOMIAL THEOREM. NEWTON S THEOREMS. 23. TEST 7 TRIGONOMETRY SECTION. 24. Angles in sexagesimal system. 25. Trigonometric ratios. 26. The Unit Circle. 27. Simple trigonometric equations in the first quadrant. 28. TEST 8
29. Trigonometry for obtuse angles. Angles in the first revolution. RIGHT TRIANGLE TRIGONOMETRY CIRCULAR TRIGONOMETRIC ANALYTIC TRIGONOMETRY ADDITIONAL TOPICS IN TRIGONOMETRY DISCRETE MATHEMATICS 30. Solve Trigonometric equations in the first revolution. 31. Special Angles. 32. Trigonometric Functions and Complements/Co-function. 33. Basic trigonometric identities. 34. TEST 9 35. Trigonometric Identities of double angle, half angle sum of angles and difference of angles. 36. Solve complex trigonometric equations including coterminals. 37. TEST 10 38. Application of trigonometry. Angles of Elevation/Depression. 39. TEST 11 40. Graphs of Sine and Cosine. 41. Graphs of Other Trigonometric Functions. 42. Inverse Trigonometric Functions. 43. Applications of Trigonometric Functions. 44. Identity Formulas Trigonometric Equations. 45. TEST12 46. The Law of Sines. 47. The Law of Cosines. 48. Polar Coordinates. 49. Graphs of Polar Equations. 50. TEST 13 51. Directed Line Segments and Geometric Vectors. 52. Vectors in the Rectangular Coordinate System. 53. Applications Using Vectors. 54. TEST14 TOTAL
I,, Student ID, have understood and discussed the terms and conditions exposed in the course syllabus for The Pre-Calculus and Analytic Trigonometry Class already given to me by MEd. Winter Valero, professor of the course, on the first meeting at the classroom designed by imater Preparatory Academy together with Doral College Institute. By signing this release, I enter in contract with my course instructor and agree with my responsibility over the completion of the terms and conditions of this course syllabus to meet the appropriate development of the educational objectives and learning outcomes of this subject., Student signature Date