AP Calculus AB Syllabus
Instructor: Ms. Rebecca Padgett
Course Outline
We cover all topics listed in the AP® Calculus Course Description. Additionally, we cover an
introduction to integration by parts, L’Hopitals’ Rule, and finding volumes of revolution by shells. The
primary textbook we use is Calculus of a Single Variable, 9th edition, by Larson, Hostetler, and
Edwards.
The stated objectives of this course are:
1. The student will be able to communicate his knowledge of mathematics to others.
2. The student will become a problem solver.
3. The student will understand the importance of calculus and its relationship to the real world.
4. The student will be able to transfer learning from calculus to other areas.
5. The student will become confident of his/her ability to work mathematical problems.
6. The student will be well prepared for the AB Calculus Advanced Placement exam.
Topics covered during 1st Semester
Sections in Text
Topics Covered
1.1
Overview of Calculus Ideas
1.2, 1.3
Limits of a Function – graphically, analytically, and numerically
1.4
Continuity of Functions and One-Sided Limits
1.5
Infinite Limits / Asymptotes
Teacher generated Graph Sketching
Assessment
2.1
Derivatives and Difference Quotient
2.2
Differentiation Rules
2.2
Rates of Change
2.3
Product and Quotient Rules
2.4
Chain Rule
2.3
Higher Order Derivatives
2.5
Implicit Differentiation
Assessment
3.1
Extrema
3.2
Rolle’s Theorem and Mean Value Theorem
3.3
Increasing and Decreasing Functions
3.3
1st Derivative Test
3.4
Concavity and 2nd Derivatives
3.5
Limits at Infinity
3.6
Curve Sketching
3.7
Optimization Problems
Assessment
2.6
Related Rates
3.9
Linear Approximation / Differentials
Teacher generated Introduction to Slope Fields
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Topics covered during 2nd Semester
Sections in Text
Topics Covered
Lab
Relationship between Area under a curve and Distance Traveled
4.1
Antiderivatives and Indefinite Integrals
4.2
Area under a Curve
Teacher
Left and Right Hand Sums, Midpoint Sums, Trapezoidal Sums
generated
and 4.6
4.3
Riemann Sums and Definite Integrals
4.4
Fundamental Theorem of Calculus
4.5
Integration by U Substitution
Assessment
Teacher generated Exponential Functions
Teacher generated Logarithmic and Natural Logarithmic Functions
5.4, 5.1, 5.2
Derivatives of Logarithmic and Exponential Functions
5.3
Inverse Functions
5.5
Bases other than e and applications
5.8, 5.9
Inverse Trigonometric Functions, derivatives and integrals
Assessment
7.7
Indeterminate Forms / L’Hospital’s Rule
5.6
Growth and Decay Applications
5.7
Differential Equations / Separation of variables
Assessment
6.1
Area between two curves
6.2
Volume / Disk method
6.3
Volume / Shell method
6.2
Volume / Cross Sections
6.4
Arc length and surfaces of revolution
6.5
Work problems
AP exam Practice
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Teaching Strategies
I will serve as a coach and facilitator of learning in the AP Calculus AB class. There will be direct
instruction, lab activities, exploratory and investigative learning, and differentiated instruction as the
instructor determines is necessary and useful.
Technology and Computer Use
In my calculus course, graphing calculators play an instrumental role in problem solving. Students are
required to learn to use a TI-89 calculator in class, even if they do not own one. There are a few extra
TI-89s available for the few students who choose to use a TI-84 instead. However, all students must
have a graphing calculator of some kind. We will use the calculators to solve derivative and
integration problems, evaluate data for labs and application problems, as well as do practice AP
exam problems.
I will communicate with students and parents via SharpSchool where assignments and
recommended additional resources are posted.
Grading Policy: Grades are calculated based on total points.
Tests/Projects: 50-100 points
There will be 2-3 tests given per 9 weeks.
Each test will be comprised of calculator and non-calculator portions, as well as both
multiple choice and free-response components. I will use old AP questions when
possible.
Quizzes: 10-50 points
Will provide assessment of smaller, usually more independent concepts.
Make-up quizzes may or may not be given: if not, the test grade will replace the missed
quiz grade in the case of an excused absence.
Homework: 5-10 points
Assigned daily
It is important that students complete the homework in order to understand the
concepts, not just to obtain the correct answer, thus it is encouraged to complete it
without the aid of your notes.
Assignments will be graded mostly on effort.
Primary Text
Larson, Hostetler and Edwards. Calculus of a Single Variable. 9th edition. Boston: Houghton Mifflin
Company, 2002.
Additional Information:
Calculus is an extremely challenging and rewarding class in which you are going to be required to
think about math on an entirely different level than you may be accustomed to. I encourage each
of you to take advantage of all the opportunities for extra practice and working together. In order to
truly understand these calculus concepts, you have to work difficult problems and consider
alternative ways of thinking.