Advanced Calculus AB & BC

 

Advanced Calculus is the high school equivalent of introductory college level Calculus course. 

Advanced Placement Calculus (also known as AP Calculus, simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. 

Students should have taken Algebra II or Pre-Cal before they they AP Calculus. It normally takes at least a couple of months to go over the materials and so you should leave enough time before the AP Calculus exam, which is typically scheduled in May. There are two exams:AB and BC. AB is roughly the first semester and BC is roughly the second semester of college level calculus course. BC is a little more advanced but there’s a lot of overlapping between the two. Students could choose to take either of the two exams but normally students with strong math background would just take AP Calculus BC exam.

AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including more advanced integration techniques such as integration by parts, Taylor series, parametric equations, vector calculus, polar coordinate functions, and curve interpolations).

This Advanced level course will be taught as a combination of two AB/BC syllabi. So students planning to cover either one can take this course.

Topics to be covered:

  • Unit 1: Limits and Continuity
  • Unit 2: Differentiation: Definition and Fundamental Properties
  • Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
  • Unit 4: Contextual Applications of Differentiation
  • Unit 5: Analytical Applications of Differentiation
  • Unit 6: Integration and Accumulation of Change
  • Unit 7: Differential Equations
  • Unit 8: Applications of Integration
  • Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
  • Unit 10: Infinite Sequences and Series

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