SYLLABUS
for
AP CALCULUS BC
(Key to side scripts (C2, C3, C4 and C5) found on page 5)
Philosophy:
C2
C4
Textbook:
According to the College Board, “an AP course in Calculus consists of a full high
school academic year of work that is comparable to calculus courses in colleges
and universities. It is expected that students who take an AP course in calculus
will seek college credit, college placement, or both, from institutions of higher
learning.” We will be devoted to learning topics in differential and integral
calculus while practicing excellent study skills necessary to be successful here
and in the future. We will cover all topics outlined by the College Board as well
as additional topics that are important to the overall understanding of Calculus.
You will find an outline of the course attached. Emphasis will be placed on
developing strong, effective study techniques, and refining communicative
mathematical language skills. We will work together to be sure that each of you
can communicate in the language of mathematics. You will have to explain your
answers using clear and concise steps, in written sentences and/ or verbally to
the class. Solving a problem is not enough; justifying and explaining are equally
as important!
Stewart, James, Calculus Concepts and Contexts (2nd Edition). United States,
Brooks/ Cole, 2001
AP Calculus BC Course Outline
Broad Overview Using Stewart’s Calculus Concepts and Contexts
More Detailed Outline on pages 6-12
Unit I. Functions and Models ( A Review of PreCalculus)
1.1 Four Ways to Represent a Function
1.2 Mathematical Models
1.3 New Functions from Old Functions
1.4 Graphing Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
1.7 Parametric Curves
Unit II. Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using Limit Lawa
2.4 Continuity
2.5 Limits Involving Infinity
2.6 Tangents, Velocities, and Other Rates of Change
2.7 Derivatives
2.8 The Derivative as a Function
2.9 Linear Approzimations
2.10 What Does f’ say about f?
Unit III. Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Rates of Change in the Natural and Social Sciences
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Derivatives of Logarithmic Functions
3.8 Linear Approximations and Differentials
IV. Applications of Differentiation
4.1 Related Rates
4.2 Maximum and Minimum Values
4.3 Derivatives and Shapes of Curves
4.4 Graphing with Calculus and Calculators
4.5 Indeterminate Forms and l’Hospital’s Rule
4.6 Optimization Rules
4.7 (Applications to Economics) and 4.8
(Newton’s Method) will be covered after the AP
exam
4.9 Antiderivatives
V. Integrals
5.1 Areas and Distances
5.2 The Definite Integral
5.3 Evaluating Definite Integrals
5.4 The Fundamental Theorem of Calculus
5.5 The Substitution Rule
5.6 Integration by Parts
5.7 Additional Techniques of Integration
5.8 Integration Using Tables and Computer Algebra Systems
5.9 Approximate Integration
5.10 Improper Integrals
VI. Applications of Integration
6.1 More about Areas
6.2 Volumes
6.3 Arc Length
6.5 (Applications to Physics and Engineering)
and 6.6 (Applications to Economics and
Biology) will be covered after the AP Exam
6.4 Average Value of a Function
VII. Differential Equations
7.1 Modeling with Differential Equations
7.2 Directions Fields and Euler’s Method
7.3 Separable Equations
7.4 Exponential Growth and Decay
7.5 The Logistic Equation
VIII. Infinite Sequences and Series
8.1 Sequences
8.2 Series
8.3 The Integral and Comparison Tests; Estimating Sums
8.4 Other Convergence Tests
8.5 Power Series
8.6 Representations of Functions as Power Series
8.7 Taylor and Maclaurin Series
Expectations: It is expected that each student MASTER the topics assigned each day. This may
be accomplished by oneself, by working in small study groups, by working with
an older sibling, friend or parent, or by seeing me for extra help outside of class.
C3
C5
The time it takes a student to accomplish the goal will be personal, however, I
would expect a student, on average, to devote 45-90 minutes per day outside of
class to calculus. Calculus is a topic that demands that you work daily. The
homework assignments demand that you justify your solutions. Problems will
describe functions in a number of ways: graphically, numerically, analytically
and verbally. You must be able to work with all the ways! A calculator next to
the problem means that a calculator is necessary for the problem. Please describe
what the calculator gave you on your homework assignment. Homework
assignments will be graded with the use of rubrics. Answers are not simply right
or wrong; points will be rewarded for correct steps, justification and solutions.
C3
C3
C4
It is also expected that you “are able to work with functions represented in a
variety of ways: graphical, numerical, analytical or verbal.” You “should
understand the connections among these representations.” I will expect you
to have complete mastery of the mathematical topics covered in previous math
classes. If you have any holes, see me outside of class to fill them in!
There are many days in the schedule at the end of this document devoted to
practicing Free Response Questions from past Advanced Placement Exams or
Free-Response-Like (Challenge) Questions (in BOLD ITALICIZED- C4’s) that I
have collected over the years. I feel these questions are incredibly important to
our study of Calculus. First, they will allow us to work with functions in a variety
of ways. Sometimes the functions will be given graphically, sometimes
numerically, sometimes analytically and sometimes even verbally! This will
allow me the opportunity to emphasize the connections among these
representations and will allow you the opportunity to see the many ways data can
be given.
These Free Response or Challenge Problem days will also give us the opportunity
that you are increasing your ability to communicate mathematics. You will be
expected to justify all work on your paper. After collecting your papers, we will
create a solution together on the SmartBoard. You will then be asked to create a
rubric based on our solution in a small group. You will discuss why some actions
received more points than others. When completed, students will explain their
rubrics. We will compare student rubrics to either the College Board rubric or my
rubric. This process will help you realize what is expected in the world of
mathematics as justification. It will also help in your understanding of the topics.
The best way to learn and understand a topic is to teach it! In the creation of
rubrics, you will be teaching the importance of explanation and justification in
reaching a solution! (Free Response or Free Response-Like Questions are
italicized in the attached schedule.)
I will also expect that each of you will take the AP exam at the end of the year
unless the college you have chosen does not accept the scores or has their own
placement tests.
Calculators:
C5
“The use of a graphing calculator in AP Calculus is considered an integral
part of the course. Students should be using this technology on a regular
basis so that they become adept at using their graphing calculators.” I require
that each of you have a TI-83, TI-84 or TI-89. I can loan one to you if needed,
just see me. We will have both calculator and non-calculator assessments
throughout the year.
We will be using calculators almost daily. They are an integral part of the study
of calculus. We will use them in a variety of ways. I will project a TI-84 Smart
View on the SmartBoard so we can work together. We will use LISTS to
approximate and find limits in chapters 2, 3 and 5. LISTS will also help us
explore sequences and series in chapter 8. We will learn to use NDERIVE and
FNINT to confirm our numerical derivatives and integrals. We will write
programs to create Slopefields and perform Euler’s Method. This will help in the
understanding of the processes as well as help us check our solutions. We will us
TABLES to find functional values and experiment with hypotheses regarding
limits, integrals, sequences and series. The calculators help us visualize many
topics. I have BOLDED days (C5’s) that are extremely heavy in calculator use on
the daily schedule at the end of this document. These are the days that we will
use the calculators to help solve problems, experiment, interpret results and
support conclusions! We will use them to discover calculus! The calculators
will be expected to be in class and functioning every day, though.
The College Board is very specific about what a graphing calculator is allowed to
do on the exam:
“1) plot the graph of a function within an arbitrary viewing window,
2) find the zeros of functions (solve equations numerically)
3) numerically calculate the derivative of a function, and
4) numerically calculate the value of a definite integral.”
The above capabilities are those that you should master. Also, the calculator may
be able to do other things for you, but you should be sure to know how to
complete the process without the calculator!
Assessments:
Homework: Homework will be collected and GRADED each day. The grade will be a
combination of correctness and effort. This method of grading encourages
students to really think through a problem and not give up. This is a necessary
trait to be successful on an AP exam. I will expect justification and clear
C4
solutions to open-ended questions. I will also expect that you can verbalize
C5
solutions when asked to explain an idea in class. The calculator symbol next to a
problem means that a calculator will be required. Please explain the calculator
use on your paper and write down any equations, graphs, etc that you use on the
homework.
Quizzes:
Quizzes will be both announced and unannounced. Quiz topics will range from
questions from readings to homework type questions to AP or AP-like free
response and multiple-choice questions. Points will be rewarded for correct steps,
correct answers and justification!!
Tests:
Tests will be an evaluation of how well you have mastered the topics that were
covered. Tests will have questions that look similar to homework as well as
questions that force you to look at the topics in different ways. Calculus is
learning how to apply what you have learned to common and NEW situations.
Tests will be combinations of multiple choice, short answer and free write
questions. Some will require a calculator, others will not. Work must be shown
for every type of question! Points will be rewarded for correct steps, correct
answers and justification! Justification can be in the way of clear concise steps
and/or written words and explanations. All graphs and tables must be labeled.
Open ended questions will be grading using rubrics.
Grading:
Grades will be weighted in the following way:
Absences:
Homework
Q1
30%
Q2
30%
Q3
25%
Q4
20%
Quizzes
20%
20%
25%
30%
Tests
50%
50%
50%
50%
I strongly encourage that you do not miss class unless absolutely necessary. This
class will move at an extremely rapid pace- missing a single class may mean
missing an entire topic that is necessary for the AP exam! In the case that you
must miss, here is the absence policy:
Planned:
Before a planned absence, a student MUST see me to discuss how work
will be made up. It is my discretion if the work must be turned in before
you leave or after. Not seeing me before a planned absence will result in
zeros for every missed assignment- NO exceptions.
Unplanned:
In the case of an unplanned excused absence, you will have the same
number of days to make up the work that you missed as the number of
days you were absent. It is YOUR responsibility to find out what you have
missed and find the help necessary to learn the lessons. You may make
an appointment to see me for extra help, but please copy the notes from
a friend and read the section before seeing me. This will ensure that our
time together is utilized in the best possible way.
AP Calculus can be one of the most challenging and rewarding classes you have ever taken.
This requires that you dedicate yourself to a year of hard work. Make a commitment to
yourself that you will give all that you can. It really is worth it. I’m looking forward to the year
ahead!
Key:
C2:
The course teaches all topics associated with Functions, Graphs, and Limits; Derivatives;
Integrals; and Polynomial Approximations and Series as delineated in the Calculus BC Topic
Outline in the AP Calculus Course Description.
C3:
Evidence of Curricular Requirement: The course provides students with the opportunity to
work with functions represented in a variety of ways- graphically, numerically, analytically,
and verbally- and emphasizes the connections among these representations.
C4:
The course teaches students how to communicate mathematics and explain solutions to
problems both verbally and in written sentences.
C5:
The course teaches students how to use graphing calculators to help solve problems,
experiment, interpret results, and support conclusions.