AP Calculus AB
Mathematics reveals her secrets only to those who approach her with pure love, for her own beauty.
Archimedes
Welcome!
Course Overview
This full-year course is equivalent to the first semester of college calculus. All topics required by the College Board for AP Calculus AB are covered. College credit may also be earned based on the AP Calculus exam or college credit exams. Students are expected to have a conceptual understanding of all mathematics explored prior to this course.
Goal
- receive college credit for Calculus for their work done while in high school through
- the AP Calculus AB exam,
- a college credit exam offered by the university the student will be attending;
- be able to function well next year in college regardless of where the university is on the traditional calculus vs reformed calculus spectrum.
- be able to successfully tutor other students in this subject next year.
- truly enjoy his or her calculus experience.
The goal of this course is for all of the enrolled students to learn all aspects of the AP Calculus AB curriculum well enough to:
Topics Covered
- Change
- Calculus allows us to generalize knowledge about motion to diverse problems involving change.
- Derivatives allow us to determine rates of change at an instant by applying limits to knowledge about rates of change over intervals.
- Derivatives allow us to solve real-world problems involving rates of change.
- Definite integrals allow us to solve problems involving the accumulation of change over an interval.
- Definite integrals allow us to solve problems involving the accumulation of change in area or volume over an interval.
- Limits
- Reasoning with definitions, theorems, and properties can be used to justify claims about limits.
- Reasoning with definitions, theorems, and properties can be used to justify claims about continuity.
- Reasoning with definitions, theorems, and properties can be used to determine a limit.
- L’Hôspital’s Rule allows us to determine the limits of some indeterminate forms.
- Definite integrals can be approximated using geometric and numerical methods.
- Analysis of Functions
- Existence theorems allow us to draw conclusions about a function’s behavior on an interval without precisely locating that behavior.
- Recognizing that a function’s derivative may also be a function allows us to develop knowledge about the related behaviors of both.
- Recognizing opportunities to apply derivative rules can simplify differentiation.
- A function’s derivative can be used to understand some behaviors of the function.
- The Fundamental Theorem of Calculus connects differentiation and integration.
- Recognizing opportunities to apply knowledge of geometry and mathematical rules can simplify integration.
- Solving differential equations allows us to determine functions and develop models
AP Calculus AB is roughly equivalent to a first semester college calculus course devoted to the following topics:
Academic Dishonesty
Any action or attempted action which may result in creating an unfair academic advantage for oneself or an unfair advantage or disadvantage for any other member of the academic community will not be tolerated.
(http://sa.berkeley.edu/conduct/integrity/definition/)
Communicating Mathematically
One often-neglected piece of mathematics is communicating your results. During the course you will be given multiple opportunities to practice communicating mathematically, both in writing and orally. I believe the ability to communicate mathematically is as important a skill as being able to do the mathematics itself.
You will be given opportunities on a regular basis to present your solutions to problem in various settings. You are expected to ask questions about problems you were not able to do on your homework assignment. You may then volunteer to present your solution to that problem. On other occasions, all students will be required to present a short solution. Students are also asked to explain their reasoning and to justify their answers on their written homework assignments and assessments on a regular basis.
My Beliefs
I believe everyone can, and should, learn mathematics. I feel mathematics is more about the thought processes, which occur while solving problems rather than just getting the right answers. We will be using technology to expand our abilities to solve problems, however, it is important to understand what the technology is doing, to ensure accuracy in our work.
AP Calculus AB Exam
- Monday, May 8, 2027 at 8:00 a.m..
- Section I
- Multiple Choice
- 42 Questions | 1 hour and 40 minutes | 50% of Final Exam Score
- Part A
- 29 Questions
- 62 Minutes
- Calculator not allowed
- Part B
- 13 Questions
- 38 Minutes
- Graphing calculator required
- Section II
- Free-Response
- 6 Questions | 1 hour and 30 minutes | 50% of Final Exam Score
- Part A
- 2 Questions
- 30 Minutes
- Graphing calculator required
- Part B
- 4 Questions
- 60 Minutes
- Calculator not allowed
The exam is 3 hours and 15 minutes long and has two sections — multiple choice and free-response. A graphing calculator is required for parts of the exam. (see below)