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This AP Calculus course is designed with the intent for students to incorporate the concepts of all previous math courses and expand upon these concepts with the implementation of Limits. Emphasis is placed upon the multi-representational approach to calculus where problems and their solutions are explored and interpreted graphically, numerically, analytically and verbally. Students will also be required to explain their answers in written form and will also be asked to compare their written response to the AP grading rubric and explain why they feel they should receive that grade. Students are required to use graphing calculators with the capabilities ascribed by the College Board: (apcentral.collegeboard.com). These calculators will be used in a variety of ways including multi-representation of equations (graphs and tables) and also for conducting explorations with various functions and how different values change the look of the function.
Course ID: MA.12.APCalculusB_3.0.Bnet4copy
By the end of this course students will understand:
the connection between derivatives, antiderivatives, and integrals.
theorems involving integrals including the Fundamental Theorem of Calculus and the Second Fundamental Theorem of Calculus.
how to construct antiderivatives using graphs, numbers, and differential equations.
different types of functions require different methods of finding integrals
when we can't find an exact integral we can use approximation we can find approximate integrals when there is not a finite interval
use integrals to compute volumes of irregular shapes.
use integrals to solve differential equations.
use integrals to solve real world exponential growth and decay problems.
the format and topics to be addressed on the AP Calculus BC Exam and be prepared to take the exam.