PRECALCULUS SYLLABUS – Ms.
Anderson - 2008-2009
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Prerequisite: Successful completion of Advanced
Algebra. [It is strongly recommended at least a grade of C have been earned in
Advanced Algebra.]
Statement of
purpose: This course
examines the number systems of elementary mathematics and the study of
elementary, trigonometric, circular, and inverse functions. Basic content
comprises the algebra of real numbers, polynomials, analytic geometry,
exponential and logarithmic functions. Sequences, series, limits, complex
numbers, the conic sections, and an introduction to Calculus will also be
covered. Attention is given to the understanding of concepts and the application
of those concepts. Polar coordinates and additional topics will be included as
time permits.
Calculator: Students will be assigned a TI‑84+ Silver
Edition calculator to be used during class and on homework and tests.
Textbook: Precalculus with
Limits,
by Larson, Hostetler, 2007. Publisher: Houghton Mifflin Company.
Workbook: Student Notetaking
Guide.
This notebook organizer is designed to help students organize their notes and
to provide section-by-section summaries of key topics and other helpful study
tools. This is also available from the textbook online site.
Textbook
Online Site:
http://college.hmco.com/mathematics/larson/precalculus_limits/1e/resources.html
Teacher
Web Site:
See DHS home page - Academics - Math or link to
http://dist428.org/dhs/depts/math/anderson
Math
Department Web Site:
See DHS home page - Academics - Math or link to
http://dist428.org/dhs/depts/math
COURSE
OUTLINE
SEMESTER I
Chapter 1-
Functions and Their Graphs
Chapter 1
addresses functions and their representation on the Cartesian plane. Students
begin the chapter by applying the distance and midpoint formulas and by
identifying intercepts, symmetry, and slope of graphs. These are used to
categorize functions and represent simple transformations of these functions.
Composition of functions, inverse of functions, and functions as models for
real-world data are studied.
Chapter 2- Polynomial
and Rational Functions
In this
chapter, the student learns to analyze and graph polynomial and rational
functions. The chapter begins with identifying key characteristics and creating
graphs of quadratic and other polynomial functions. First and second
derivatives are used to find max/min points and points of inflection to aide in
graphing polynomial functions. Students learn to find real and complex roots,
asymptotes, intercepts, and holes as they graph polynomial and rational
functions. The chapter concludes with problems using nonlinear inequalities.
Chapter
3-Exponential and Logarithmic Functions
This chapter
begins with writing, graphing and recognizing the basic characteristics of
exponential and logarithmic functions. Students use these functions to model
real-world problems, including compound interest and radioactive decay, among
others from a variety of contexts. They expand their skills by using the
properties of logarithms and exponents to manipulate expressions and solve
equations.
Chapter
4-Trigonometry
In this
chapter, students learn how to evaluate and graph the trigonometric functions,
their inverses, and reciprocals. The chapter begins by introducing radian
measure and the definition of trigonometric functions of the unit circle and
using reference angles to find the trigonometric functions for any angle. The
chapter also covers graphing trigonometric functions, reciprocals, and
inverses, using their basic characteristics. Students use trigonometric ratios
to solve problems in a variety of contexts.
Chapter
5-Analytic Trigonometry
Chapter 5
addresses the strategies for simplifying expressions and solving equations by
using trigonometric identities. Students learn how to rewrite/simplify trigonometric
expressions using identities and how to verify identities. Trigonometric equations
written in quadratic form and equations containing more than one angle will be
solved, followed by equations containing sums and differences of angles.
Students will rewrite trigonometric expressions that contain functions of
multiple or half-angles.
SEMESTER II
Chapter
6-Additional Topics in Trigonometry
This chapter
applies trigonometry to oblique triangles, using the Law of Sines and Law of
Cosines. Trigonometry is used to
solve real-world problems. Students learn how to write and perform operations
on complex numbers in trigonometric form, including powers and roots of complex
numbers.
Chapter
9-Sequences and Series
In Chapter 9,
students analyze sequences and series and expand binomials. (The probability of
events will be covered only as time allows.) Methods of representing sequences
and series, including summation notation are studied for arithmetic, geometric
and other sequences. Students expand binomials by using Pascal’s triangle and
the Binomial Theorem. Proofs by mathematical induction will be included.
Chapter 10-Topics
in Analytic Geometry
Students work
with conic sections and equations in rectangular forms. The distinguishing
features of the circle, parabola, ellipse, and hyperbola in both the general
forms and the standard forms of their equations are used to create graphs and
solve problems involving conic sections. Polar coordinates and graphs of polar
equations will be studied, only as time allows. (Rotations of conic sections
and polar equations of conics will be omitted.)
Chapter 12
–Limits and Introduction to Calculus (with extras)
This chapter is
a compact introduction to calculus. It defines the limit of a function and
covers the techniques of finding limits. Students learn differentiation
techniques and the theory and application of the derivative. Use of derivatives
for finding the slope of tangent lines and critical points in order to graph
functions is reviewed. Students learn to find the limits of functions at infinity
and convergence and limits of sequences. The concept of integration is
introduced, and rules of integration are used to solve applications, such as
area under a curve.
Student
Expectations:
You are
expected to bring the textbook, calculator, paper, and pencil and pen to class
each day. You will not be allowed to leave to get any of these items. You are
expected to be in your seat, ready to work when the bell sounds. School tardy
and disciplinary policies will be followed.
You will be
assigned a TI‑84+ Silver Edition calculator to be used during class
and on homework and tests. The calculator should be with you in class each day.
Homework assignments will require the use of your calculator. If you own a
different graphic calculator, please let me know.
You are
expected to be courteous and respectful to other students and to any teacher.
Disrespect will not be tolerated. If disciplinary action is necessary, the
student's class participation grade will be affected. In addition, in certain
situations, a discipline report will be filed with the assistant principals’
office. Any behavior that disrupts the educational climate will not be
tolerated.
Attendance:
Attendance in
class is mandatory and necessary for comprehension and class participation. In
accordance with school policy, your parents should call the attendance office
to report your absence before 7:45 A.M. when school starts. You are responsible
for missed assignments, quizzes, and tests. If you are present the day before
an announced quiz or test, but absent on the day of the test, you are expected
to take the quiz or test the day you return. Please see me before school to
arrange a time to make up the quiz or test. Tests or quizzes will be made up
outside of class time, unless there is no possible time to do this. No work
will be made up for unexcused absences. Unannounced class participation quizzes
will be given periodically. There will be NO make-ups on these quizzes. You
must be in class to participate.
Types of
Assessment and Purpose of Assessment:
Two types of
assessment will happen in this class: assessment FOR learning and assessment OF
learning. Assessment FOR learning is assessment that is frequent, sometimes
informal, and done as you are learning. It is used to tell you about what you
know and need to learn to improve. Some examples might be oral or daily quizzes,
practice problems, homework problems, or class discussions. Many times this
assessment is not used to figure your grade, but can sometimes be used as part
of your grade. Assessment OF learning is more formal, takes place after learning,
and measures an achievement level. It is usually used to determine your grade,
and includes things such as written quizzes and chapter tests. Other
assessments OF learning happen outside the class setting, such as ACT, PSAE,
and other standardized tests.
Grading
Procedures and Homework:
Students'
grades will be reported on Skyward Family & Student Access. You can link to
this site from the teacher’s home page. Contact the DHS main office for your
account log on and password, as well as parent account log on and password. 815-754-2100
Students’
grades (assessment of learning) will be determined by performance on class
activities, homework quizzes, quizzes and tests. Unannounced quizzes may also
be given and will be added to the total grade -- remember, no make-ups on
unannounced quizzes. Homework is required and homework quizzes will be counted
in the grade determination. Chapter tests are generally 100 points and quizzes
range from 30‑70 points. Homework quizzes will range from 5-25 points and
might be given up to three times in a chapter.
Following first
quarter grades, the grade for the second progress report and second quarter
will be the cumulative grade of both quarters. During second semester, the same
applies for third and fourth quarter grades. Semester grades will be figured
with the following weighted values: 80% for first and second quarter [or third
and fourth quarter] cumulative grade and 20% for the semester exam.
Homework
Homework will
be assigned almost everyday and may or may not be collected at the following
class meeting. Homework is required, whether it is collected or not. You are
also expected to use and complete the Student Notetaking Guide for each section. This may be completed
before or after completing the section.
All work for
this class must be done in a neat and orderly fashion, in pencil. You must show
all necessary steps in arriving at your solution. A list of answers is not
acceptable. Include your name, page number, and problem numbers assigned. You
must do the homework assignments to be eligible for extra credit problems on
tests and quizzes.
Extra Help
If you need
extra help, I will be available [on most days] before school at approximately
7:00 A.M., during 3rd hour and after school. Occasionally, I will
have a meeting or another appointment, and hence, will not be available at
these times. If you know ahead of time that you want extra help, let me know
and I can tell you if I have a conflict. Other arrangements for extra help may
be possible by appointment. Let me know immediately if you are having
difficulty. You may also get help from math teachers by signing out of study
hall to the Math Tutoring Lab, room 228A, if you cannot meet me at the above
times.