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AP Calculus AB Syllabus
Teacher: Mr. Steve Wyss
Office: B217
Email: Steve_Wyss@dpsk12.org
Voicemail: (720) 424-1806
Course Overview
This is a college level differential and integral
calculus course. This course is designed to give students a solid
conceptual understanding of calculus as well as prepare students to
take the AP exam in May. This course covers all topics included
in the Calculus AB topic outline given at the AP College Board
website. Additional calculus topics are covered before and after
the AP exam. My goals are for students to understand Calculus
conceptually, to use Calculus techniques ( with facility ), to
appreciate the rich applications of Calculus and overall beauty of
mathematics. Another goal of this course is to address the “why”
and “how” the mathematics works. Students must be able to
communicate mathematically symbolically, by writing and by giving oral
presentations of math problems. A final goal is that students can
use the graphing calculator technology to model, investigate and
discover mathematics. I will elaborate on these goals as you read
further. Overall, I try to give my students a balanced approach
to learning Calculus.
Course Outline
Chapter 1 Prerequisites Review ( 1-2 weeks )
1. Trigonometry
2. Review function families expressed as graphs,
equations and tables and their characteristics ( e.g., domain, range,
symmetry, one-to-one )
Chapter 2 Limits and Continuity ( 3-4 weeks )
1. Rates of Change
2. Limits at a Point
a. Properties of limits
b. One and Two sided limits
3. Limits involving infinity
a. Asymptotic behavior
b. End behavior
c. Properties of limits
d. Visualizing limits
4. Continuity
a. Continuity at a point
b. Discontinuous functions
i. Removeable discontinuity
ii. Jump discontinuity
iii. Infinite discontinuity
iv. Intermediate value theorem for continuous functions
5. Instantaneous rates of change
Chapter 3 Derivatives ( 5-6 weeks )
1. Definition of the derivative
a. Derivative at a point
b. Begin to stress the relationship of the graph of f and f prime
c. One sided derivatives
2. Differentiability
a. Local linearity
b. Numerical derivatives using the calculator
c. Differentiability and continuity
d. Intermediate value theorem for derivatives
3. Derivatives of algebraic functions
4. Derivative Rules when combining functions
5. Applications to velocity, acceleration and other rates of change
6. Derivatives of trigonometric functions
7. Chain Rule
8. Implicit Differentiation
a. Differential method
b. y prime method
9. Derivatives of inverse trigonometric functions
10. Derivatives of logarithmic and exponential functions
Chapter 4 Applications of the Derivative ( 6 weeks )
1. Extreme values of functions
a. Local extrema
b. Global extrema
2. Using the derivative
a. Mean value theorem
b. Rolle’s theorem
c. Increasing and decreasing behavior
3. Analysis of graphs using the first and second derivatives
a. Critical values
b. First derivative test for extrema
c. Concavity and points of inflection
d. Second derivative test for extrema
4. Optimization problems
5. Linearization and Newton’s method
6. Related Rates
**End First Semester
Chapter 5 The Definite Integral ( 6 weeks )
1. Approximating areas
a. Riemann sums
b. Trapezoid rule
c. Definite integrals
2. Definite Integrals and antiderivatives
a. Average Value Theorem
3. Fundamental Theorem of Calculus Parts 1 and 2
Chapter 6 Differential Equations and Mathematical Modeling ( 5 weeks )
1. Antiderivatives and slope fields
2. Integration using u-substitution
3. Separable differential equations
a. Exponential growth and decay
b. More slope fields
c. General differential equations
i. Newton’s law of cooling
ii. Logistic models
4. Numerical Methods
a. Euler’s methods
Chapter 7 Applications of Definite Integrals ( 2-3 weeks )
1. Summing rates of change
2. Particle motion
3. Areas in the plane
4. Volumes
a. Volumes of solids with known cross sections
b. Volumes of solids of revolution
i. Disk method
ii. Shell method
**The second semester material leaves us 3-4 weeks to prepare for the
AP exam. During this time we go over released multiple choice and
free response questions as well as other selected review problems and
activities.
Teaching Strategies
1. I set high expectations for my students at the beginning of the school year.
2. Students often work in groups of 3-4 on activities
given in class. Collaboration is encouraged and expected.
3. Students must be able to use the technology to
model and solve Calculus problems. I give many problems to my students
to allow them to do this.
4. Students must be able to communicate mathematics
and explain solutions to problems both verbally and in written
reports.
5. Students are given a list of Pre-Calculus terms
and definitions at the start of the year. It is important that
students have quick recall of these terms and definitions.
6. Lecture is used to introduce topics and give explanations, where needed.
7. I emphasize many ways to model and solve Calculus
problems. Students must be able to solve algebraically,
numerically and graphically.
Use of Calculators
The graphing calculators are used to help students develop an intuitive
feel for concepts before they are approached through typical algebraic
techniques. Each of my students has a graphing calculator of
their own or I will check one out to them for the year ( TI – 83 plus
). We use them daily to investigate, discover and reinforce many
concepts of Calculus. For example, we use them for finding
zero’s, sketching functions in a specified window, finding derivatives
at a point using numerical methods and finding definite integrals using
numerical methods. I also have students write Riemann sum
programs to find approximate areas under curves. I also model
tangent lines along a function and slope fields with the graphing
calculators so my students develop a better feel for these
concepts. Students are frequently given graphs or tables to work
out the Calculus problems as well as by using more analytic or
algebraic arguments. On all unit tests students are given a
Calculator active set of problems and Calculator non-active set of
problems.
Projects
1. Create a function to match a famous
person. Students must state their function ( as a rule or
multiple rules for a piecewise function ) and graph their
function. Then use the characteristics of the rule and/or graph
to relate back to their famous person somehow.
2. Ultimate demonstration of derivative domination
( ). This project has 3 components and is given near
the conclusion of Chapter 3. The first component is that students
must develop a unique method for remembering the many rules of
differentiation and present it to the class. Usually students
write a song, poetry, perform a play, read a story, or design a visual
art piece. The second component is that students must write a paper on
differentiation. This includes explanation of what a derivative
is ( graphically, analytically and numerically ) , creation of 2 unique
applications problems, several student made up derivative skill
problems and a student analysis of common mistakes. The third
component is that students must come to the teacher outside of class
time and take a 15 minute, 10 question derivative test. Student
must have all rules memorized and must do 10 complex derivatives.
3. How many licks ( tootsie roll pop problem )
? Students are given this problem after studying related
rates. Students must conduct a lab by eating tootsie roll pop and
then they must determine the rate at which the volume of the pop is
changing at any instant. Students also determine how long ( or
how many licks ) it takes to consume the pop. Students must do a
written report for this project.
4. Applications of definite integrals model.
Students must develop a 3-D physical model of a volume of a solid
of revolution. Students can choose to demonstrate the disk or
shell idea and must present their model to the class.
Textbook
Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel
Kennedy. Calculus—Graphical, Numerical, Algebraic. 2nd ed. New
Jersey: Pearson Education, Prentice Hall, 2003 ( ISBN 0-13-063131-0 ).
Prerequisites
Students must complete an authorized Pre-Calculus course before taking
this course. Students must be able to demonstrate that this
prerequisite has been met.
Student Evaluation
1. Tests and Quizzes ( 60% ): This section of a
students grade consists of unit tests, daily warm-up quizzes and
cumulative final exams. Students must show all work and explain
their processes in order to receive full credit.
2. Homework and Projects ( 35% ): Homework is
assigned every class period. Homework that is to be turned in
must include all work and/or explanation depending on what the question
is. Students should expect a heavy workload because this is a
college level course. Students will be able to revise homework
problems that are collected and graded. A revision is allowed on
each problem that was attempted and turned in on time. A revision
score can be no higher than 90%. No late work on any homework
will be accepted.
3. Participation ( 5% ): It is essential that
students participate as a way of sharing ideas, questioning and testing
themselves to see if they understand. Students must present
homework, class work or quiz problems to the class 5 times per
semester.
Grading Scale
93 – 100 A
84 – 92 B
77 – 83 C
70 – 76 D
69 or less F
Supplies
1. Notebook to keep all notes and assignments.
2. Graph paper
3. Graphing Calculator ( TI – 83 Plus or higher )
4. Ruler and Protractor
5. Textbook
Attendance
Work missed due to an excused absence may be made up for full
credit. Make up work must be turned in no more than a week after
the excused absence. It is the students responsibility to get all
assignments, notes, etc when absent. I strongly recommend that
each student shares phone numbers or email to aid in getting caught up
after an absence. I expect no one to have an unexcused absence in
this class; however, in the event that this happens all the work due
that day will not be accepted for credit.
All assignments are posted online at: http://dsa.dpsk12.org
Academic Honesty
Honesty, respect and integrity are cornerstones of this class.
Any behaviors less will not be tolerated and a referral will be
written.
Extra Help
Tutoring will be offered after school from 3 – 4 pm on Thursdays.
Accessories
No cell phones, music players, pagers, food or drink are allowed in class. Students may have bottled water.
Signature Slip
I have read the syllabus for my AP Calculus AB class and I understand
the policies. Furthermore, I pledge that I will neither give nor
receive aid on any quiz, test, or project unless instructed to do so by
the teacher. I understand that dishonoring this pledge will
result in no credit for the assignment.
Student Name ( Print ) ___________________________
Student Signature _______________________________
I have read the syllabus for my son’s/daughter’s AP Calculus AB Math class and I have read the student honor pledge above.
Parent/Guardian Name ( Print )______________________
Parent/Guardian Signature__________________________
Parents: Please check whether you would like to check your
student’s grade using infinite campus, or if you would prefer to have a
paper progress report sent home with your student once every 3 weeks:
_____ I will check my student’s progress using Infinite Campus
_____ I will check my student’s progress with paper reports sent once every three weeks
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