AP Calculus AB Syllabus
Mrs. Erin Rhody
Planning hours: 9:40-10:55
Tutoring times: 7:15-7:45 and 3:10-3:45
Phone: 839-5118
Email: erin.rhody@anderson.kyschools.us
Website: http://www.anderson.k12.ky.us/ErinRhody.aspx
Text: Calculus for AP, 2nd Edition, by Rogawski and Cannon, published by W.H. Freeman and Company
Prerequisites: Pre-AP Algebra II, Pre-Calculus and teacher recommendation
Required Materials: Graphing calculator (TI-84 is preferred), 3-ring binder to be used exclusively for
Calculus class, supplemental review materials to prepare for AP test: Barron’s “How to Prepare for the AP
Exam: Calculus” (recommended)
I. Review
(6 days)
A. Basic algebra skills - simplifying expressions, factoring, operations with polynomials
B. Graphs and models - intercepts, symmetry, points of intersections, models for data
C. Linear models and rates of change - slopes, equations, graphing, parallel and perpendicular
D. Functions and their graphs - notation, domain, range, transformations, classification, and
combinations
Students must be able to graph certain parent functions with and without the aid of a
graphing calculator.
E. Fitting models to data - linear, quadratic, exponential, logarithmic and
trigonometric using a graphing calculator
II. Limits and their properties
(18 days)
A. What is Calculus? (The tangent line problem and the area problem)
Discussion of evolution of students’ mathematical skills and abilities.
B. Finding limits graphically and numerically
C. Evaluating limits analytically
Students will use multiple properties and strategies including the Squeeze Theorem.
D. Continuity and one-sided limits
Students will determine continuity at a point and on an open interval, and determine onesided limits and continuity on a closed interval. Students are introduced to the
Intermediate Value Theorem and its applications.
E. Infinite limits and vertical asymptotes
Students must be able to distinguish between removable and non-removable
discontinuities.
III. Differentiation
(18 days)
A. The definition of derivative and the tangent line problem (revisited).
Students will understand the derivative as an instantaneous rate of change. This rate of
change is derived through a limit process.
B. Basic differentiation rules and rules of change
C. Product rule, quotient rule, trigonometric functions and higher-order derivatives
D. The Chain Rule
E. Implicit differentiation
F. Related rates
Students will use related rates to solve real-world problems.
IV. Applications of Differentiation
A. Extrema on an interval-relative and absolute
B. Rolle’s Theorem and the Mean Value Theorem
C. Increasing and decreasing functions and the first derivative test
D. Concavity and the second derivative test
(26 days)
E. Limits at infinity and horizontal asymptotes
F. A summary of curve sketching
Students will apply all of the techniques from this unit to analyze the graph of a function.
G. Optimization problems
H. Newton’s Method
V. Integration
(25 days)
A. Antiderivatives and indefinite integration
B. Summation and the area problem
C. Riemann Sums and definite integrals
Students will understand the definition of a definite integral as a limit of Riemann Sums.
D. The Fundamental Theorem of Calculus, the Mean Value Theorem for integrals, the Average
Value of a function and the Second Fundamental Theorem of Calculus
E. Integration by substitution
F. Numerical integration using the Trapezoidal Rule
VI. Logarithmic, Exponential, and Other Transcendental Functions
A. The natural logarithmic function and differentiation
B. The natural logarithmic function and integration
C. Inverse functions
D. Exponential functions: differentiation and integration
E. Bases other than e and applications
F. Differential equations: growth and decay models
G. Differential equations: separation of variables
H. Inverse trigonometric functions and differentiation
I. Inverse trigonometric functions and integration
(25 days)
VII. Applications of Integration
A. Area of a region between two curves
B. Volume: the disc method
C. Volume: the shell method
D. Arc length and surfaces of revolution
(22 days)
VIII. Integration Techniques, L’Hopital’s Rule, and Improper Integrals
A. Basic integration rules
B. Integration by parts
C. Trigonometric substitution
D. Indeterminate forms and L’Hopital’s Rule
(6 days)
IX. Calculus AP Test Review
(20 days)
Students will be issued an AP Calculus review handbook (Barron’s). We will use this book and
released AP test items to prepare for the AP exam.
Classroom activities: Students are expected to participate regularly in class discussions. Daily assignments
will be checked by the teacher and corrected as a class. Students will assist in reviewing the previous
lesson by asking and answering questions and presenting problems in a small-group or whole class settings.
Students may also, on occasion, work together in small groups to solve problems, complete an
activity, or develop a project. For example, in developing the concept of optimization, students are asked
to construct a paper box of maximum volume from a rectangle. Each group has a unique rectangle.
Groups may communicate about processes and strategies, but not identical answers.
Homework: Homework is given daily and I expect that it is completed daily. Homework is designed to
enhance skills developed in class and is typically not graded on correctness but completeness. Some
problems are extremely challenging, but I will always expect you to try something intelligent. Students’
work should be THEIR work only, but study groups are encouraged. Students will have my contact
information if homework help is needed at night. There are also several online resources dedicated to
calculus homework help. Homework is collected in chunks after several concepts have been covered.
Please, oh, please…do your homework completely and turn it in ON TIME. Late homework will not be
accepted.
Assessment: Students will be assessed on daily assignments, projects, quizzes and tests all including AP
Exam items. Quizzes will be given after one or two sections have been covered. Major tests will occur at
the end of each unit. After a sufficient number of calculus concepts have been covered, students will be
assigned weekly AP problem sets. These sets will include multiple choice questions as well as freeresponse items. The problem sets will be take-home assessments. Students are required to show all of their
work or explain all of their processes to receive credit on each item of the problem set. The Problem Sets
will alternate between calculator active and calculator prohibitive. Questions regarding these sets must be
addressed before or after school.
At the conclusion of our AP test review, each student will complete a moc AP exam worth 100
points. This exam is graded like the real AP exam, and students will be awarded a score of 1 to 5. More
information on the moc exam will be given as the end of the year approaches.
Students’ grades are determined by the ratio of points earned to total points possible. A
cumulative exam will be administered at the end of each trimester. Trimester exams are 20% of the
students’ final average. If the AP exam is taken at the end of the year it will count as the final trimester
exam.
Calculators: Students are required to obtain a graphing calculator for this course. While many operations
should be done without the aid of a calculator, several calculus problems require the support of technology
to arrive at a solution. This course will teach students how to use the calculator to examine graphs,
experiment, interpret results and solve problems. As with the AP exam, portions of each unit test will
require the use of a graphing calculator and portions will prohibit its use.
Goals: It is my goal that students in this class will learn strategies and develop the skills and techniques
necessary to becoming a good problem-solver and a logical and analytical thinker. Students should be able
to make connections among the different representations of functions (graphical, numerical, analytical and
verbal). Although it is not required, my expectation is that everyone taking AP Calculus also takes the AP
exam. Ultimately, the exposure to this kind of mathematics is good for you and will serve you well in
whatever endeavors you pursue. I hope you get a taste of the expectations and the rigor of a college-level
Calculus course.