• Mr. Kurzius
  • Room 31
  • Period B3, 2025–26

Course Description

Explore the concepts, methods, and applications of differential and integral calculus. You’ll work to understand the theoretical basis and solve problems by applying your knowledge and skills. You’ll learn how to determine expressions and values using mathematical procedures and rules; connect representations; justify reasoning and solutions; and use correct notation, language, and mathematical conventions to communicate results or solutions.

AP Exam

The AP exam is scheduled for Monday, May 11 at 8 a.m. The exam is 3 hours and 15 minutes long and includes 45 multiple-choice questions and 6 free-response questions. A calculator is not permitted on 30 of the multiple-choice questions and 4 of the free-response questions. You can find more details on the AP Calculus AB exam page.

Units of Study

  1. Limits and Continuity Explore how limits allow solving problems involving change and to better understand mathematical reasoning about functions.

  2. Differentiation: Definition and Fundamental Properties Apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.

  3. Differentiation: Composite, Implicit, and Inverse Functions Master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.

  4. Contextual Applications of Differentiation Apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms

  5. Analytical Applications of Differentiation Explore relationships among the graphs of a function and its derivatives, and learn to apply calculus to solve optimization problems.

  6. Integration and Accumulation of Change Apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. Apply properties of integrals and practice useful integration techniques.

  7. Differential Equations Solve certain differential equations and apply that knowledge to further understand exponential growth and decay.

  8. Applications of Integration Make mathematical connections that will allow solving a wide range of problems involving net change over an interval of time and to find areas of regions or volumes of solids defined using functions.

Text and Resources

We will use the book Calculus for AP (2nd ed.) as reference and for homework assignments, though I recommend Khan Academy as a first stop for any extra practice. They have both an AP Calculus AB course and a Get ready for AP Calculus course. I suggest reviewing the latter prior to any new chapter.

And here are the related College Board resources.

Grading

  • The official grade book exists on Canvas, with Genesis only having a (possibly unreliable) copy
  • There are about three quizzes each marking period
  • There is also one exam at the end of each marking period
  • All work is due the day of a quiz or exam and late work will receive only partial credit
  • Grading is point-based, though assignments are worth roughly 10%, quizzes 40%, and the marking period exam 50% of your grade