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AP Calculus BC

The Fine Print

Course Goals

  • To offer a multifaceted approach to calculus: students will learn to express concepts, results and problems graphically, numerically, analytically and verbally.

  • Students will learn to use technology to help experiment, solve problems, interpret results and support conclusions. We will use graphing calculators and Desmos (an online graphing program) towards this end.

  • Students will learn problem-solving techniques that will maximize computational efficiency while minimizing computational errors.

The course is organized around the following foundational concepts of calculus:

  • I. Limits: Students will gain a solid, intuitive understanding of limits and be able to compute one-sided limits, limits at infinity, infinity limits and the limit of a sequence.

  • II. Derivatives: Students will learn to use different definitions of the derivative and be able to apply derivative rules and properties. Students will also become familiar with a variety of real-world applications of the derivative, including related rates, optimization, and growth and decay models.

  • III. Integrals and the Fundamental Theorem of Calculus: Students will gain a firm understanding of area, volume and motion applications of integrals as well as the use of the definite integral as an accumulation function. The relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus will also be emphasized.

  • IV. Series: Students will become familiar with various methods for determining convergence and divergence of a series. Subsequently, students will learn to use power series to approximate an arbitrary function near a specific value. The generalization to Taylor and Maclaurin series for approximating common functions will also be studied.

Prerequisites

  • Students must have completed the equivalent of the high school math sequence: Algebra 1, Geometry, Algebra 2/Trigonometry, Precalculus, or Integrated Math 1,2,3 Honors. 

  • If you did not take Trigonometry/Precalculus, or have only taken Integrated Math 1,2,3, a Precalculus class is strongly recommended before you take AP Calculus BC.

  • Students must be familiar with all advanced topics in algebra, trigonometry, analytic geometry, elementary functions: linear, polynomial, rational, transcendental (trigonometric, exponential and logarithmic), inverse functions, and piece-wise defined functions.

  • Are you ready? Take a Diagnostic Test. 

 

Course Details

  • Please see the FAQ for class days/times/breaks.

  • All classes will be recorded, so students have the option to participate live or watch the recorded videos after the classes have been completed. 

 

Instructor Demo

  • See a Zoom Demo: Shin Yen demonstrates her instructional approach and previews some of the technology resources that she and students will be using in the class.

Course Resources

Textbook and Homework:

 

Calculator:

  • TI-84 series, or

  • TI-Nspire series 

  • Whatever you have used for high school math is fine.

  • If you are looking to purchase your first college-level graphing calculator, the instructor strongly encourages the TI-Nspire CAS for its ease of use and capabilities.

  • See #14 in the FAQ.

 

Web Resources:

  • WebAssign

  • GeoGebra free application for students to visualize 2D and 3D geometric shapes and their properties

  • College Board Website: comprehensive databank of past exam questions

  • LarsonCalculusforAP.com: This companion website to the text offers multiple tools and resources to supplement learning.

  • CalcView: The website contains video solutions of selected exercises in the text. Students can use smartphone QR code readers to scan codes next to the problems and go directly to video solutions.

  • CalcChat: The website contains step-by-step solutions to all odd-numbered exercises in the text. Students can also chat with a tutor during the hours posted at the site.

  • Khan Academy and Coursera video resources

Technical resources:

We use ZOOM for live meetings. U.S. and international students need:

  • An internet connection

  • A computer with a web-cam

  • Recommended: a headset with a microphone (but your built-in computer audio and microphone will work if necessary)

 

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