AP Calculus AB
Mr. Yegge
Prerequisite: a grade of B or better during both semesters in Precalculus or an A both semesters in Honors
Algebra 2
Text: Single Variable Calculus: Early Transcendentals (6th edition) by James Stewart
COURSE DESCRIPTION:
This course is designed for upper classmen with a solid mathematics background implying a
strong grasp on algebraic fundamentals. The primary concern is to develop the student’s conceptual
understanding of calculus by learning the methods of differentiation and integration and applying them
with a graphical, numerical, and analytical approach.
COURSE OBJECTIVES:
This course will:
1. Introduce the student to methods of mathematical proof.
2. Introduce the student to the concepts of limits, derivatives, and integrals.
3. Emphasize a deep conceptual and theoretical understanding of calculus as opposed to a purely
computational approach.
4. Prepare students for the Advanced Placement exam by exposing them to all applicable topics
and providing experience with the applications.
DAILY MATERIALS
1. Mechanical Pencils (NO pens)
2. 3-ring binder with paper (for this class only)
3. Calculus book
4. Graphing Calculator (preferably TI-89 or TI-89Titanium)
CLASS EXPECTATIONS
My main objective in teaching AP Calculus is to enable you as students to appreciate the beauty of
calculus and receive a strong foundation that will give them the tools to succeed in future mathematics
courses. Success in this class, however, does not come without hard work. To begin the learning process, I
encourage you to work on all problems alone, to prepare you for the exam format. But you should realize
right away that you have many additional tools at your disposal, including peers or graphing calculator. It
is important for you to form study groups to allow you the opportunity to collaborate on the current concept
or the homework assignments. In addition to problem sets from the textbook, I assign previous year’s free
response questions every time we complete a topic that is being asked in the question. These problems
allow you the opportunity to show a conceptual understanding of calculus and explain your critical thought
process and solutions in written form. I then give you time to describe verbally, in front of the class, what
concepts the problem required you to use and how you applied these concepts to the problem. Throughout
this course, you will become very proficient at deciphering the meaning of various applications in calculus,
not only through utilizing your logical thinking skills, but with the additional visual help of your graphing
calculator. You are required to have a graphing calculator and it is highly suggested that you use the TI-89.
I stress the four required functionalities of graphing technology:
1. Finding a root
2. Sketching a function in a specified window
3. Approximating the derivative at a point using numerical methods
4. Approximating the value of a definite integral using numerical methods
The graphing calculator gives a visual representation of the concepts being discussed so you are able to
understand a situation through a graphical and numerical approach. But you will learn that it is not
sufficient to prove an idea without verifying it analytically. If you can grasp the reasons behind a concept
through each of these approaches, you can usually figure out how to apply the idea to the current problem.
ASSIGNMENT REQUIREMENTS
1. Set up papers correctly with assignment, period, and name.
2. Write each problem down before solving .
3. NEATLY show ALL necessary work
4. Get the correct solution. If you are having trouble with certain problems, ask your peers before
class or during group work, or ask me when we discuss the assignment in class.
5. Homework will be checked for completion randomly throughout the quarter.
6. Late work and some incomplete work will be accepted for half credit. If you are absent the day
of collection, you may turn it in for full credit on the day you return.
GRADING STRUCTURE
The percentages for the mathematics department are as follows:
A = 100-90%
B = 89-80%
C = 79-65%
D = 64-50%
F=49-0%
The percentage distribution for this class is as follows:
10% = AP Free Response Portfolio
5% = Class Notes
20% = Homework
50% = Tests
15% = Cumulative Semester Final
Homework should be completed by the following day after it was assigned, so you are prepared with
questions from the assignment. Active participation and completion of the homework is the only way to
stay current with the complex material in this course. AP Calculus requires tedious computation and
constant problem solving. Without attempting and pushing through these problems on your own, it is very
easy to fall behind in the first couple weeks and never recover. If you have any trouble, try to figure out the
process and solution for all problems before coming to class by asking your peers. Often times, I will give
time in class to work collaboratively on assignments. I will then answer all remaining problems, before
continuing on to the next topic. Make a solid effort to be here on the days of quizzes and tests. If you are
absent, then you must take the test you missed on the day you return as long as you were present for all the
material covered on the test.
_________________________________________________________
I have read the above Class Expectation Syllabus for Mr. Yegge’s class and understand them.
____________________________
Student Signature
__________
Date
_______________________
Parent Signature
_________
Date
___________________________________
Parent’s E-mail address
CLASS OUTLINE :
1st Quarter
1. Limits
a. Intuitive notion of a limit
b. Evaluate limits graphically, numerically, and analytically
c. Properties of limits
d. Continuity and it’s properties
e. Limits involving infinity
2. The Derivative
a. Average rate of change of a function
b. Slopes of curves using the difference quotient (the derivative)
c. Differentiation rules
i. Power rule
ii. Sum rule
iii. Product rule
iv. Quotient rule
v. Chain rule
2nd Quarter
3.
d. Derivatives of trigonometric functions
e. Higher order derivatives
f. Implicit differentiation
g. Differentials
h. Inverse trigonometric functions and their derivatives
Applications of the Derivative
a. Position (f), velocity (f’), and acceleration (f”)
b. Related rates
c. Extrema of a function
d. Rolle’s Theorem and the Mean Value Theorem
e. First derivative test and curve sketching
f. Concavity and the second derivative
g. Optimization problems
3rd Quarter
4. The Integral
a. Antiderivatives
b. Sigma notation and Riemann sums (approximating area)
c. Area under a curve
d. Definite integrals
e. Properties of definite integrals
f. The Fundamental Theorem of Calculus
g. Average value of a function and the mean value theorem of integration
h. Integration by u-substitution
i. Trapezoidal rule
j. Integrals of inverse trigonometric functions
4th Quarter
5. Logarithmic and Exponential Functions
a. Derivatives and integrals involving logarithmic functions (ln & loga)
b. Derivatives and integrals involving exponential functions
c. Logarithmic Differentiation
6. Applications of the Integral
a. Separable differential equations
b. Slope fields
c. Area bounded by two curves
d. Solids of revolution : Disk and Washer method
7. Review for the AP exam