AP Calculus AB Syllabus
Instructor: Gerald Miller
WHO SHOULD TAKE THIS COURSE: Students with highly developed algebra skills and an
interest in careers related to: engineering, the computer professions, medicine, physics,
chemistry, or math.
AP Calculus AB is a college level course. As such, AP Calculus AB WILL be extremely
demanding. THIS COURSE REQUIRES A LOT OF HARD WORK! Most problems will
involve higher order thinking skills, and logical, sequential thought processing to include
application and synthesis. A high level of skill in algebra is essential.
The psychology of calculus problem solving: A teacher can guide students through a
complex calculus problem merely by asking questions. By learning to ask questions of
yourself, you can gain the same level of problem solving skill without having a teacher
present. It’s called metacognition and IS a skill you will acquire.
Powerful calculus problem solvers also frequently use a type of free association. By
learning to associate small hints with the corresponding algebraic principle, they can often
visualize an equation for a problem even before they have fully read it. Again, it’s a skill
that can be learned.
REQUIRED MATERAIL: Text, Rogawski’s Calculus for AP 2nd Edition. W.H. Freeman and
Company, New York. 2012. Graphing calculator (students use their calculators to graph, find
zeros and points of intersection, evaluate derivatives at a point, and evaluate definite
integrals). Notebook.
ATTENDANCE: Your attendance and punctuality will determine your success in this
course to a large extent. Your absences adversely affect not only your own learning, but
also the interaction and participation level of the entire class. Therefore, everyone is
expected to be present and on time for every class. On the very rare occasion that an
absence does occur, it is the student’s responsibility to learn the material missed and
complete all missed work. The instructor is not required to review any material missed as
a result of the absence nor is the instructor required to arrange for make-up tests.
INSTRUCTION: Instruction will include guided practice, demonstration, lecture, and
cooperative learning. Study groups are encouraged outside of class. There are days
devoted only to question and answer. I encourage as many different approaches to a
problem as I can foster.
HOMEWORK: Homework is expected to be completed every night. To learn anything well
requires practice-practice-and more practice! In addition, homework lays the foundation
from which to ask questions. You should do the homework with the idea of engaging, the
concepts and doing the assignment well, not just to get it done. You should use numerical
methods as well as technology to ensure reasonable answers. You must present problems
and solutions numerically, graphically, and symbolically. Explanations and justifications of
answers are required. Working with others on your homework is encouraged. However,
copying the work of others and presenting it as your own is unacceptable. Feel free to ask
in class how to do any problem, assigned or not. You cannot expect to do well in any class if
you do not do your homework! Students are encouraged to read, study, and work ahead.
STUDENT RESPONSIBILITY: You will be expected to take part in the class by doing your
work, paying attention, and asking and answering questions. You can expect to have an
assignment every class period. We do not have time to waste.
EVALUATION: Based on the completion of material and readiness of the student, there
will be approximately six regular tests each grading period. These include teacher made
tests and AP exams per chapter. These exams include multiple choice and free response
questions. Cheat sheets will not be allowed. Each problem will be graded for procedural
correctness, as well as numerical correctness and correct use of units. Numerical answers
must be expressed in the same format as the original problem, or they will be marked
incorrect. All answers which are physically unreasonable will be marked incorrect. For
security reasons, TESTS ARE NEVER SENT HOME.
COURSE LETTER GRADES: A= outstanding maybe the top 15%. Excellent prospects for
success at the next level. B= very good, significantly above average. Very good prospects
for success at the next level. C= a lot of learning, average for those who attend regularly
and do the work. With enough work, success at the next level is likely. D= some learning
but not enough to expect success at the next level. F=little learning, no credit.
Note: “Learning” refers to skills and concepts newly acquired in this course, not to
prerequisite skills and concepts you already gained in prerequisite courses. Do not expect
you can simply coast to a good grade by using your previous knowledge of Algebra II,
Trigonometry, and Pre-Calculus.
COURSE OUTLINE:
I. Pre-Calculus Review (16 days)
1.
2.
3.
4.
5.
Real numbers, Functions, and Graphs
Linear and Quadratic Functions
The Basic Classes of Functions
Trigonometric Functions
Technology: Calculators and Computers
II. Limits (17 days)
1.
2.
3.
4.
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6.
7.
8.
Limits, Rates of Change, and Tangent Lines
Limits: A Numerical and Graphical Approach
Basic Limit Laws
Limits and Continuity
Evaluating Limits Algebraically
Trigonometric Limits
Limits at Infinity
Intermediate Value Theorem
III. Differentiation (23 days)
1.
2.
3.
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9.
Definition of the Derivative
The Derivative as a Function
Product and Quotient Rules
Rates of Change
Higher Derivatives
Trigonometric Functions
The Chain Rule
Implicit Differentiation
Related Rates
IV. Application of the Derivative (27 days)
1.
2.
3.
4.
5.
6.
7.
Linear Approximation and Applications
Extreme Values
The Mean Value Theorem and Monotonicity
The Shape of a Graph
Graph Sketching and Asymptotes
Applied Optimization
Antiderivatives
V. The Integral (19 days)
1.
2.
3.
4.
5.
Approximating and Computing Area
The Definite Integral
The Fundamental Theorem of Calculus
Net Change as the Integral of a Rate
Substitution Method
VI. Application of the Integral (13 days)
1. Area Between Two Curves
2. Setting Up Integrals: Volume, Density, Average Value
3. Volumes of Revolution
VII. Exponential Functions (23 days)
1.
2.
3.
4.
5.
6.
7.
Derivative of f(x) = bᵡ and the Number e
Inverse Functions
Logarithms and Their Derivatives
Exponential Growth and Decay
Compound Interest and Present Value
Models Involving y ˡ= k(y-b)
Inverse Trigonometric Functions
VIII. Techniques of Integration (2 days)
1. Numerical Integration
IX. Introduction to Differential Equations (6 days)
1. Solving Differential Equations
2. Graphical and Numerical Methods
HELP: Students who are not succeeding in the class are encouraged to meet with the
instructor. “Helps” classes are available. At the discretion of the instructor, “retakes” are
available.
TO SUCCEED IN THIS CLASS:
1.
2.
3.
4.
5.
Read and study each section within the unit.
Complete homework problems. Check solutions at end of text.
If having difficulty, seek help. Ask in class.
Participate in class.
Keep a meticulous notebook.
TO FAILTHIS COURSE (or any worthwhile course):
1.
2.
3.
4.
5.
6.
7.
8.
9.
Be absent a lot. Be late the rest of the time.
Daydream or sleep during class.
Don’t ask any questions or volunteer answers to questions posed in class.
Put off doing homework, or don’t do it at all.
Maintain a negative attitude towards the class or about your ability to
succeed.
Don’t get help when you need it.
Don’t retake tests when available.
Be totally unorganized and sloppy.
Give every other thing in your life a higher priority than your education.