AP CALCULUS
Mrs. Romain
romain@dboone.org
2015-2016
COURSE OUTLINE
This course is designed to provide the student with a brief review of algebra, analytic geometry and various
precalculus topics and an in-depth study of differential and integral calculus. The students will be expected
to take the A.P. Calculus “AB” exam which requires the use of a TI-89 graphing calculator.

Functions and Models
Four Ways to Represent a Function
Graphing Calculators and Computers (CAS…Computer Algebraic System)
Mathematical Models
Exponential Functions
Inverse Functions and Logarithms
Parametric Curves

Limits and Derivatives
The Tangent and Velocity Problems
The Limit of a function
Calculating Limits using Limit Laws
Continuity
Limits Involving Infinity
Tangents, Velocities and Other Rates Of Change
f  x  h  f  x
Derivatives: Using the Definition f ( x)  lim
h 0
h
The Derivative as a Function
Linear Approximations
What Does f  Say About f?

Differentiation Rules
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic Functions
Linear Approximations and Differentials

Applications of Differentiation
Related Rates
Maximum and Minimum Values
Derivatives and the Shapes of Curves
Graphing With Calculus and Calculators
Indeterminate Forms and L’Hospital’s Rule
Optimization Problems
Antiderivatives

Integrals
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
The Fundamental Theorem of Calculus
The Substitution Rule
Additional Techniques of Integration
Approximate Integration
Improper Integrals

Applications of Integration
More about Areas
Volumes
Average Value of a Function

Differential Equations
Modeling with Differential Equations
Direction Fields and Euler’s Method
Separable Equations
Exponential Growth and Decay

AP Exam Review (approximately 2 weeks)

Additional Topics (Topics which are not covered on the AP Calculus AB test, but will
benefit students in their college calculus studies.)
Integration by Parts
Cylindrical Shells
Length of a Curve
Logistic Growth Model
Euler’s Method
Polynomial Approximation and Series
Parametric & Vector Functions & Polar Curves (Time permitting)
EVALUATION / GRADING
1. Tests: 1 – 2 per quarter (100 points each)
2. Quizzes (Point value varies)
NOTE: All tests and quizzes have calculator and non-calculator active questions.
3. Homework problem sets (Collected &/or checked as needed)
4. AP Exam
Students expected to take in May. According to school policy, a student who does not take the
AP exam will not receive the 10% weight on their report card grade.
5. Final Exam must be taken if a student chooses not to take the AP exam in May.
Given in June (1/9th of total grade for the year)
GENERAL POLICIES
1. Students are expected to come to class prepared. They should have textbook, notebook and pencils.
Textbooks will be covered! All tests and quizzes MUST be completed in PENCIL!!
2. Students should be in class and in assigned seats when the bell rings. Homework will be checked immediately
at the beginning of class. Sharpening pencils, picking up paper or using the lav pass are all activities
which should be done before class begins!
3. Students will be given warnings after their first three class latenesses. Detention will be assigned following the
fourth lateness.
4. Extra help is provided after school on Tuesdays and Thursdays. I am often available on Wednesdays as well,
but check with me first for availability.
MAKE-UP PROCEDURE
Make-up procedure due to excused absence:
a) If absent only one day and a test or quiz is missed, be prepared to take the makeup
the day you return. No extra time will be allowed.
b) If absent only one day and it is the day before a test or quiz, be prepared to take the
test/quiz with the class the following day when you return to school.
c) All assignments which were due on a day when the student is absent are to be
handed in upon returning to school.
d) After an extended absence all work must be made up within 2 weeks of returning
to school. (Any work that is not completed within the two-week period will be given a zero
grade.)
** If you are absent, please check my web site for assignments. If you have questions and need to contact me
during the day (7:30am – 2:30pm), e-mail me at romain@dboone.org.
** Quote from the authors of your text
“Remember the two golden rules of algebra and trigonometry:
1. DON’T GET BEHIND! The course moves too fast and it’s hard to catch up.
2. WORK LOTS OF PROBLEMS! Everyone needs to practice, and problems show where you
need more work. If you can’t solve the homework problems without help, you won’t be able
to do them on exams.”
Textbook website provides full support at
www.interactmath.com