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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.

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

• 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.

• 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.

• 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.

• 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.

• The main components of Calculus BC are advanced integration techniques, sequences and series, and polynomial approximations. Calculus BC also extends all the content learned in Calculus AB to different types of equations (polar, parametric and vector-valued).

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#### 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.

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#### Instructor Demoâ€‹

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

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#### Course Resources

##### Calculator

Required

• 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, Dr. Yen encourages the TI-Nspire CAS for its ease of use and capabilities.

• See the Calculators | Microscopes section of our FAQ.

##### Other Resources
• AP Classroom | a free databank of past exam questions

• CalcChat | a free website containing step-by-step solutions to all odd-numbered exercises in the text. Students have the option to chat with a tutor during hours posted at the site.

• CalcView | a free website containing video solutions of selected exercises in the text. Students can scan QR codes with their smartphones to go from problems to video solutions.

• Desmos.com | a free online graphing program for use in sections involving equations of lines and algebraic functions

• Larson Calculus for AP | a free companion website to the text offering multiple supplementary tools and resources

• Zoom | a free teleconferencing application

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##### Technical Resources
• Required:

• A reliable internet connection

• A computer with a web-cam

• A working microphone

• A free phone/computer scanning app (such as CamScanner and Adobe Scan)

• Recommended:

• Earbuds or a headset with a microphone (a built-in computer microphone will work if needed)

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