Course Syllabus for AP Calculus, 2014 – ’15 school year
Mr. Patrick Kosal
pkosal@iss.k12.nc.us
I.
(704) 799-8555 x1610
twitter.com/mrkosal
Course Overview:
AP Calculus is a course designed to meet the College Board Advanced Placement AB standards. Students
are expected to take the AP Test for Calculus AB at the end of the year. This is a very challenging mathematics
course, being the equivalent of one semester of college calculus. Students entering the class should have performed
strongly in Algebra 2 and Pre-Calculus to be at standard.
The main instructional technique will be large group lecture, with students writing down notes, examples, and
working out practice problems throughout the lesson. However, students will also be expected to connect prior
knowledge to new topics through discussion, both in large and small groups. Discussing how the topics are related
to each other will provide a necessary connection that we can use to fuel further lessons. Use of a graphing
calculator will also be necessary to interpret difficult functions and data sets and to test hypotheses about functions
and their behavior.
Our class will focus on the big ideas of basic calculus with a focus on problem-solving, exploring problems from
multiple angles, and how to use a graphing calculator to assist in visualize and understand a given scenario. By
mastering the building blocks of calculus (limits, derivatives, and integrals), students will be able to view the world
through the eyes of calculus to appreciate the beauty and application of higher-level mathematics.
II.
Requirements:
1. Textbook (Calculus. James Stewart. 5th Edition. Brooks/Cole Publishing.), 3 Ring Binder, Paper (notebook
& graph), Graphing Calculator, and Pencils
2. Completion of Daily Work and Constructive use of class time
3. Active participation in class discussions and a Positive Attitude!!
** Each student in AP Calculus class must have a graphing calculator to use each day in class (calculators may be
checked out from the LNHS media center, but most students prefer to purchase their own). Preferred calculators
for this course are TI-83 or -84s, but TI-89 or -92 calculators may be used as well. We will be using calculators to
visualize functions of varying types as we predict their behavior and notice trends in data. The instructor will be
using the TI-Smartview program to model calculator use on the computer / projector, while the TI-Navigator system
will also be used to collect and interpret data quickly for instant feedback.
III.
Assignments & Make-Up Work:
1.
For each lesson, students will be assigned practice problems from the textbook, practice AP tests, or other
resources. Answers for said practice problems will always be posted on my school website. I would recommend
“bookmarking” my webpage since you’ll be referencing it often. Please check my Twitter feed or my school
website to see what work you’re responsible for prior to your return.
2.
Students, it is your responsibility to obtain notes, handouts, and assignments when you are absent.
3.
I am available for extra tutoring before and after school in my classroom (610). Please take advantage of
these sessions, whether you were absent or simply need some extra help – you will not be alone!! I keep normal
school hours of 7:30 a.m. until 4:00 p.m. Make it a point to stop by, but don’t wait until the last minute; my room is
very, very crowded on mornings / afternoons right before a test.
4.
Quizzes and Tests are my main way of assessing your progress and will be given regularly. Each Friday
students can expect a quiz or test to be given so be prepared! As with the AP Test, some of the assessments will be
non-calculator and some will be calculator-required. Occasionally I will use multiple choice questions in my
assessments so students can apply problem-solving techniques. When free-response problems are assigned, students
will always be expected to support their answers with mathematical evidence and written explanations.
5.
I do not allow re-testing for AP & Honors-level courses, so be sure to adequately prepare for examinations.
Taking good notes, attending tutoring sessions for extra practice, keeping up on assignments, and participation in
class discussions / activities is the most effective way for an AP Calculus student to earn high marks on exams.
IV.
Assessments:
First Three Nine Weeks
1. Cumulative Exams (100 points each)
2. Quizzes (10 – 50 points each); one to two a week
3. Cumulative Nine-Week Exam (200 points)
4. Random Homework Checks (10 points each)
V.
Fourth Nine Weeks
1. Calculus Manual (300 points)
2. Cumulative Exams (100 points)
3. Quizzes (10 - 50 points)
4. Random Homework Checks (10 points each)
Topics Covered:
A. Limits, Functions, Graphs, and Continuity (3 weeks)
Objectives: The student will be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
describe the idea of finding a limit
evaluate limits algebraically
evaluate limits from a graph or table
find equations of vertical and horizontal asymptotes
determine the end behavior of a function
determine whether a function is continuous at a point
classify discontinuities as “removable”, “jump”, or “infinite”
understand and apply the “Intermediate Value Theorem”
understand and apply the “Extreme Value Theorem”
B. The Derivative (12 weeks)
Objectives: The student will be able to:
1. describe the meaning of a derivative
2. find the derivative of a function using the limit definition of a derivative
3. find whether a function is differential at a point
4. find whether a function is locally linear at a point
5. determine and explain how being continuous and differentiable are related
6. use the theorems on differentiable on differentiation to find derivatives of polynomial and rational
functions (Power Rule, Product Rule, Quotient Rule, & Chain Rule)
7. find the equation of the tangent line to a curve at a point
8. find the equation of the normal line to a curve at a point
9. understand average and instantaneous rate of change
10. apply implicit differentiation
11. find higher order derivatives
12. find the derivative & tangent line for an inverse function
13. using the 2nd derivative and points of inflection to determine concavity of a function
14. graphing the derivative from data, both by hand and with a graphing calculator
15. apply derivatives to solve Related Rate and Optimization problems
16. understand the definition of the derivative using the symmetric difference quotient
17. understand and apply the Mean-Value-Theorem
18. use the First and Second Derivative Test
19. connect F (x ) and F (x ) with the graph F (x )
20. find derivatives of Polynomial, Rational, Exponential, and Trigonometric Functions
21. solve Rectilinear Motion problems
22. determine an anti-derivative for a given function
C. Applications of Integrals (6 weeks)
Objectives: The student will be able to:
1.
2.
3.
4.
5.
approximate areas under a cure with left-hand, right-hand, midpoint, and trapezoid methods
use the Riemann Sum definition to calculate area under a curve
calculate areas under and between curves
understand and apply the Fundamental Theorems of Integral Calculus
evaluate definite integrals with and without a calculator
6.
7.
8.
9.
10.
11.
12.
calculate the average value of a function
find the net distance traveled by an object
find the total distance traveled by an object
use integration by “u-substitution”
evaluate indefinite integrals using the Power Rule and the Chain Rule for integration
find volumes of solids of revolution using the disk and washer method
find volumes of solids with known cross sections
D. Differential Equations (2 weeks)
Objectives: The student will be able to:
1.
2.
3.
4.
solve differential equations by the method of “separation of variables”
solve growth and decay problems, logistic problems, and other applications to differential equation
understand slope fields
sketch a slope field given a differential equation
VI. AP EXAM REVIEW (4 weeks) - AP Test: Tuesday May 5, 2015, Morning Session, 8:00 AM
Major Project for 2nd Semester:
CALCULUS MANUAL
** each student will be responsible for creating their own calculus manual that is typed, illustrated, and filled
with examples from each lesson. Manuals must be bound and are due the week before the AP Calculus Test
(due date: Tuesday, April 28th, 2015). Extra credit may be given for projects that are above and beyond the
minimum requirements
** each topic highlighted above must have at least one full page explaining its use in the world of calculus, at
least one illustration or graph that visually explains the topic, at least two example problems with written
explanations and solutions shown, and three practice problems for the reader to attempt.
** one full week will be given in class in mid-April for students to work on their Calculus Manual, while
occasional work days will also be provided throughout the school year. I also plan on assigning deadlines for
smaller sections of the project throughout the school year to check students’ progress and give feedback
Exam Calendar (Subject to Change on Teacher’s discretion) – Students may keep their most
recent graded exam to review & use in studying. On the day of the next exam, students must hand in their previous
exam.
VII.
Nine Week:
9week Exam:
1st
September 5
September 19
October 3
October 17
October 31
2nd
November 14
November 25
December 12
December 19
January 9
3rd
January 30
February 13
February 27
March 13
March 27
VIII. Additional Note from Teacher – AP Calculus is a very rigorous course designed to challenge
each student. If a student fails to put forth a strong individual effort, the teacher reserves the right to
request the student be removed from the course at the end of the first semester. I truly hope that I do not
need to make such a request. Please understand that there will be bumps in the road, but if the student is
willing to work, he or she will massively improve his or her critical thinking skills and their mathematical
ability. Each student enrolled in the course is required to pay for and take the AP exam. If you have any
further questions about the class, please feel free to contact me.