2014-2015 COURSE SYLLABUS
CALCULUS HONORS: CALCULUS HONORS CURRICULUM
TEACHER - MRS. SEGURA
TEXTBOOK
Calculus: 8th Edition By: Larson, Hostetler, and Edwards
Note: Students should keep their textbooks for this class at home unless
instructed to bring them to school. A class set of textbooks is available for
use when needed.
COURSE DESCRIPTION
Topics include limits, continuity, derivatives of algebraic functions,
trigonometric, exponential and logarithmic functions, implicit differentiation
and higher order derivatives; related rates, Rolle's Theorem, Mean Value
Theorem, velocity,acceleration, curve sketching and other applications of the
derivatives; antiderivatives, Riemann sums, definite integrals, integration of
exponential and logarithmic functions, Fundamental Theorem of Calculus,
area between curves, volume.
COURSE OBJECTIVE
The course objective is to develop the students’ understanding of the
concepts of calculus and providing experience with its methods and
applications. The course will emphasize a multi-representational approach to
calculus, with concepts, results, and problems being expressed graphically,
numerically, analytically, and verbally. The course will also develop the
students’ ability to explain solutions both orally and in written sentences.
MAJOR CONCEPTS
Functions, Limits, and Continuity
The Derivative and Differentiation
Applications of the Derivative
Integration
Applications of Integration
Indeterminate Forms and Improper Integrals
Extensive use and application of the graphing calculator
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ESSENTIAL QUESTIONS
Students will be able to:
1.
2.
Functions, Limits, and Continuity (5 Weeks)
a.
Functions
1)
Define the domain and range of a function and be able to
find them.
2)
Recognize linear and non-linear functions.
3)
Distinguish polynomial functions from rational functions
and recognize the characteristics that both possess. ie:
Decartes Rule of signs, remainder theory, factor theorem,
and rational root test.
4)
Solve and graph inequalities.
5)
Analyze functions represented numerically
b.
Limits
1)
Define the limit of a function.
2)
Develop a geometric interpretation of the limit of a
function.
3)
Find left and right hand limits in order to show that the
limit exists or does not exist.
4)
Find limits of functions as the independent variable
increases without bound and be able to find infinite limits.
5)
Know selected limit theorems and be able to utilize them.
c.
Continuity
1)
Define continuity at a point and on an interval.
2)
Know selected theorems dealing with continuity including,
but not limited to, the Intermediate Value Theorem.
The Derivative and Differentiation (6 Weeks)
a.
The Derivative
1)
Define the slope of a curve.
2)
Geometrically interpret the slope of a curve.
3)
Utilize various forms of notation related to differentiation.
4)
Define the formal definition of derivative and be able to
use the definition in finding the derivative of simple
functions.
5)
Recognize, identify, and utilize differential notation.
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3.
b.
Formal differentiation
1)
Differentiate polynomial and exponential functions.
2)
Differentiate products, quotients, and trigonometric
functions.
3)
Differentiate functions with rational exponents.
4)
Use the chain rule for finding derivatives of composite
functions.
5)
Know and understand the definition of a logarithm and be
able to differentiate logarithmic and exponential functions
with bases other than e.
6)
Find higher order derivatives and relate them to velocity
and acceleration.
7)
Differentiate functions.
8)
Solve related rate problems.
c.
Implicit differentiation
1)
Define the term implicit as it applies to functions.
2)
Identify functions that are defined implicitly.
3)
Differentiate implicit functions.
Applications of the Derivative (8 Weeks)
a.
b.
c.
d.
e.
f.
g.
h.
4.
Obtain information from the first derivative; include intervals on
which the function is increasing or decreasing, relative maxima
or relative minima, and finding the equation of tangent and
normal lines.
Know selected theorems dealing with differentiationincluding,
but not limited to, Rolle's Theorem and the Mean
Value Theorem.
Obtain information from the second derivative: include concavity
and points of inflection.
Solve max-min problems involving both relative and absolute
extrema.
Solve optimization problems.
Solve problems involving rectilinear motion.
Sketch the graphs of algebraic and trigonometric functions using
the guidelines for curve sketching.
Estimate the derivative of functions represented numerically
Integration (6 Weeks)
a.
b.
Define antiderivative.
Define definite integral and know the significance of the
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c.
d.
e.
f.
g.
5.
Applications of Integration (8 Weeks)
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
6.
Find the area between two curves.
Find the volume of a solid of revolution.
Find the volume of solids with known cross sectional areas.
Solve rectilinear motion and related rate problems
whichinvolve integration.
Find the average value of a function.
Differentiate and integrate trigonometric functions and
inverse trigonometric functions.
Integrate rational functions by use of the technique of
Integration by Parts when applicable.
Integrate functions by use of the technique of making a
trigonometric substitution when applicable.
Integrate functions by use of the technique of Partial
Fractions when applicable.
Estimate the integral of functions represented numerically
Indeterminate Forms and Improper Integrals (3 Weeks)
a.
b.
7.
Reimann Sum.
Define indefinite integral.
Integrate functions involving the natural logarithm and
exponential functions.
Integrate selected problems using various elementary
integration formulas including, but not limited to, the
substitution rule and the midpoint rule.
Know the Fundamental Theorem of Calculus.
Define the natural logarithm as an integral function and be
able to use its properties.
Identify indeterminate forms when evaluating a limit and to
use L’Hopital’s Rule to find the limit when it exists.
Evaluate improper integrals.
Extensively use and apply the graphing calculator
a.
Experiment with a graphing calculator to discover new ideas and
concepts
b.
Interpret results and support conclusions with a graphing
calculator
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COURSE REQUIREMENTS
Each student should bring to class each day their calculator, writing utensil
and a 3-ring binder. All Calculus Honors students are required to obtain a
Texas, graphing calculator TI 84 Plus for use in the classroom.
The 3-ring binder (1” minimum) should contain the following items and
sections:
1) Syllabus
2) Course Outline
Sections:
3) Warm-up problems
4) Class-notes
5) Homework
6) Quizzes
7) Tests
A divider should be labeled and placed in front of each section of the binder.
Homework will be assigned most days and will be collected most days. Tests
and Quizzes are posted on the course outline. In the event of an absence,
tests and quizzes should be made up the day after returning to school (after
school & not during class). Students will have one day per excused absence
once returning to school to make-up any missed tests or quizzes. Athletes
who will be out part of the day are still responsible for turning in their work
on the assigned date. Athletes who miss a test should be prepared to take
the test the following day. All tests will be accumulative with emphasis on
the new material.
*The following is a Rubric for homework assignments
Incomplete Heading – Minus 5 pts
Late Assignments:
1 day – Minus 10 pts
2 days – Minus 20 pts
3 days + - Zero (No Credit)
No work – No credit (problems will be marked incorrect if there
isn’t any work.)
Every activity in this class will be timed strictly with no exceptions unless
medical documentation is provided. Students will have 45 minutes to
complete tests and 15 minutes to complete quizzes.
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Tutoring is available every day before and after school. Tuesdays is
mandatory tutoring for those students who do not quite understand the
material.
GRADING SCALE
The following is a percentage distribution for end-of-quarter grades:
Tests
Quizzes
Homework / Classwork
1st Quarter Percentage
2nd Quarter Percentage
Semester Exam
55%
35%
10%
40%
40%
20%
At the end of the semester, the two quarters will be 80% of the semester
grade plus 20% of the semester exam to equal the semester grade.
Students must ensure their 3-ring binders are up to date at all times and
turn them in at the end of each quarter to be graded. The notebook grade
will count as one test grade.
BEHAVIOR EXPECTATIONS
Cheating on homework, tests, quizzes, or any other graded
assignment, will result in a grade of 0 for the assignment, along with
disciplinary action.
Students must be in their assigned seats with their calculator, notebook and
writing utensil when the tardy bell rings and remain seated for the entire
period unless instructed otherwise. Each student is expected to come to
class each day prepared with any assignments that are due and all the
materials identified under Course Requirements of this syllabus.
All rules in the Antonian Student Handbook governing student
behavior will be enforced and disciplinary action taken as written,
without exception, for violations. Students are expected to uphold the
Antonian Standard. Please be familiar with the handbook and ask any
questions if anything is unclear.
No cell phones…$50 fine and given to the Dean of Students with Disciplinary
Action.
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Restroom use must be done prior to class starting. Don’t wait until the bell
to ask me to use the restroom. The restroom pass can be used in case of
emergencies.
No items other than the binder, pencils, and calculator are allowed on the
desktop. Backpacks are not allowed in the classroom.
When students are absent then please email me at asegura@antonian.org
for homework assignments. In addition, parents may use this address for
any questions or comments.
Gum chewing, eating, or beverages are not allowed in the classroom.
Water bottles are allowed per administration. Detention will be given for
these infractions.
TEACHING STRAGEGIES
1.
Learning by Discovery
Occasionally, each unit is introduced with a discovery lesson.
Exploration and discovery are great ways for students to learn, because
these methods help students have more ownership in the material being
covered than they would be using a traditional lecture approach. The
discovery lessons are done in groups of two or three students.
2.
Graphing Calculator
Many of the discovery lessons rely heavily on the use of the graphing
calculator. The calculator helps students develop a visual
understanding of the material that they would not otherwise have. My
students use a graphing calculator almost every day in class for
explorations and in assignments to analyze functions and justify
solutions. For example, the students use the calculator to approximate
the values of derivatives and definite integrals obtained through
analytical means in order to verify that the answers are reasonable.
However, many homework problems and about half of the problems on
quizzes and tests are done with and without the use of the graphing
calculator. We spend time in class discussions talking about the types
of questions that they must know how to work with their calculators and
the types of questions that they must know how to work without their
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calculators. We also discuss the techniques needed to use the
calculator most efficiently (storing functions in a graphing page, storing
values that will be used later in the problem, etc.).
3.
Various of Representations/Opportunities
Students are given many opportunities to work problems presented in a
variety of ways: graphical, numerical, analytical, and verbal. Most
problem sets in this primary textbook are written with a variety of
representations, so problems are assigned utilizing a graph or tabular
data whenever possible. Students are asked to give verbal explanations
and each student is given the opportunity to communicate their
reasoning in words.
4.
Justification of Answers
Students are to justify their answers on homework, quizzes, and tests,
and that they write the justifications in sentences. It is important that
work is shown and that the work is written the correct way.
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