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PreCalculus A & B Seaholm High School 2016-2017 Syllabus Mr. Caughell E-mail: [email protected] Twitter: ec08bps Course Description PreCalculus is the study of functions, analytical trigonometry, advanced algebra, and analytical geometry. The graphing calculator is used to develop understanding of concepts and to aid in problem solving. Course Overview Functions and Their Graphs Students evaluate functions and find their domains. They analyze graphs of functions, identify graph shifts, reflections, and non-rigid transformations of functions. Students find arithmetic combinations and compositions of functions as well as finding the inverse of functions graphically and algebraically. Polynomial and Rational Functions Students sketch and analyze graphs of quadratic and polynomial functions. They use long division and synthetic division to divide polynomials by other polynomials. They determine the number of rational and real zeros of polynomial functions and find them. Students perform operations with complex numbers in the complex plane. They determine the domain, find asymptotes, and sketch the graphs of rational functions. Exponential and Logarithmic Functions Students learn to recognize, evaluate, and graph exponential and logarithmic functions. They will rewrite logarithmic functions with different bases, use properties of logarithms to evaluate, rewrite, expand, or condense logarithmic expressions. Students will solve exponential and logarithmic equations; use exponential growth and decay models and use logarithms to solve real-life problems. They will fit exponential and logarithmic models to sets of data. Trigonometric Functions Students learn to describe an angle using degree and radian measure. They will identify a unit circle and its relationship to real numbers and evaluate trigonometric functions of any angle. Students will explore fundamental trigonometric identities, sketch their graphs, evaluate their inverses, and evaluate the composition of trigonometric functions. Students will then use trigonometric functions to model and solve real-life problems. Analytic Trigonometry Students will use trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions. Using trigonometric identities, standard algebraic techniques, and inverse trigonometric functions, students will solve trigonometric equations. They will use sum and difference formulas, multiple-angle formulas, power-reducing formulas, half-angle formulas, and product-sum formulas to rewrite and evaluate trigonometric functions. Students will use the Laws of Sines and Cosines to solve oblique triangles and find areas of oblique triangles. They will perform operations on complex numbers written in trigonometric form and find the powers and nth roots of complex numbers. Sequences and Series Students will use sequence, factorial, and summation notation to write the terms and sums of sequences. They will learn to recognize, write and use arithmetic and geometric sequences. They will use the Binomial Theorem and Pascal’s triangle to calculate binomial coefficients and write binomial expansions. Limits and an Introduction to Calculus Students will estimate limits and use properties and operations of limits. They will find limits by direct substitution and by using the dividing out and rationalizing techniques. They will approximate slopes of tangent lines, use the limit definition of slope, and use derivatives to find slopes of graphs. Students will also find limits of summations and use them to find areas of regions bounded by graphs of functions. Tentative Course Units Trimester A Chapter P: P.4, P.5 Chapter 1: 1.1, 1.2, 1.3, 1.4, 1.5 Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 Chapter 3: 3.1, 3.2, 3.3, 3.4, 3.5 Chapter 9: 9.1, 9.2, 9.3, 9.5 Trimester B Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 Chapter 5: 5.1, 5.2, 5.3, 5.4, 5.5 Chapter 6: 6.1, 6.2, 6.5 Chapter 12: 12.1, 12.2 Course Materials Textbook: PreCalculus with limits: A graphing approach, 3rd Ed. by Larson, Hostetler, & Edwards: Prentice Hall Graphing calculator (TI-83+ or similar) and a dedicated math 3-ring binder Homework Policy Homework will be assigned during every class period and checked the next class period. The problems must be written on your paper and have all work shown with answers to receive credit. If you are unable to complete a problem, you must show evidence of effort to receive credit. Questions regarding homework problems will be answered each day. Periodically, there will be homework quizzes. A homework quiz consists of a few problems from the current homework. You will be allowed to copy that problem directly from your homework onto your quiz paper. It will be graded for correctness. Your overall homework grade will be worth 10% of your trimester grade. Late assignments will not be accepted unless you had an excused absence. Absence and Make-Up Policy Students will be allowed two class periods for each excused absence to make-up any work that was assigned on the day of the excused absence. The return day is considered the first class period. Students will be required to submit any work that was previously assigned and due the day of their excused absence on the day they return. Tests or quizzes that are missed due to an excused absence must be made up in a timely manner. Make arrangements with me upon your return to schedule a make-up assessment. No make-up assessments will be given during class time. Make-up tests and quizzes are YOUR responsibility. Students who have an excused absence on the day of a quiz or a test will be required to make up that quiz or test in the testing center. The testing center is room A205 and is open from 5:45 a.m. to 7:15 a.m., Monday through Friday—NOT DURING X-BLOCK. Make-up work, quizzes, or tests will not be accepted for unexcused absences. Assessments All of the assessments (tests & quizzes) are to remain in the classroom, in whole or in part. Mr. Caughell will make them available for the student and parent/guardian to review in the classroom. No part of any assessment may be copied, photographed, taken, or otherwise disseminated from the classroom without Mr. Caughell’s prior, express written permission. Electronic devices are NOT permitted at all in class on the day of assessments. Bonus Points for Assessments If you take all of the announced tests and quizzes in your class period on the day they are given during the first six week cycle of the trimester, you will earn bonus points that will be factored into your grade. The same will hold true if you take all of the announced tests and quizzes in your class period on the day they are given during the second six week cycle of the trimester. Class Participation Education is an interactive process. As the instructor, it is my responsibility to teach the material to you. As the student, your responsibility is to learn. In order to achieve this goal, you are expected to participate appropriately in class. There are a variety of ways to accomplish this, such as: asking and/or answering questions or working problems on the board. Grading Scale A AB+ B BC+ 93+ to 100 90+ to 93 87+ to 90 83+ to 87 80+ to 83 77+ to 80 C CD+ D DE 73+ to 77 70 + to 73 67+ to 70 63+ to 67 60+ to 63 59 and below Trimester Grade Tests Quizzes Homework 60% 30% 10% TOTAL 100% Final Course Grade: Trimester Grade (80%) Final Exam (20%) MP3 Players and Similar Devices Any MP3 Player or similar device that has any capabilities in addition to playing music is NOT permitted at any time in the classroom. An MP3 Player or similar device that can ONLY play music will be permitted on occasion as determined by me, provided you are able to follow the class rules. This is at my discretion and is considered a privilege in my classroom that may be revoked. Cell Phone and Similar Devices Cell Phones and similar type devices are NOT permitted in my classroom at ANY time without my prior, express permission. Classroom Rules At no time may anyone photograph, video tape, record, disseminate, electronically copy, or other similar type activities anyone or anything in Mr. Caughell’s classroom without Mr. Caughell’s prior written consent. All of the classroom and school rules will be followed at all times. Mathematics Department, Seaholm High School Student Transfer Policy Students may transfer to a different math course during the first three weeks (15 class periods) with teacher approval. They will be graded only on subsequent work in their new course, but be responsible for all of the content of the course in terms of future tests/quizzes and the final exam. Students may transfer to a different math course between the three-week point and six week point (30 class periods) with teacher and department head approval. The grades from their previous course will count as 30% of their trimester grade. The grades from their new course will count as 50% of their trimester grade. The final exam will count as 20% of their trimester grade. Again, students will be responsible for all of the content of the course in terms of future tests/quizzes and the final exam. There will be no student transfers after the six-week point (30 class periods). Students may do a Drop/Fail from the course after six weeks.