Download Pre-Calculus Syllabus - Birmingham Public Schools

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.