AP Calculus BC

AP Calculus BC- Link to the Calculus BC curriculum map

This course continues the exploration of Calculus started in AB Calculus. It develops many of the concepts introduced in AB Calculus providing more depth and rigor, and introduces new more abstract concepts. The course investigates how Calculus can be applied in real-world situations, while providing a rich theoretical frame work. BC Calculus is equivalent to Calculus II at the college level for which credit will be earned if students score a 3, 4, or 5 on the AP test depending on the university attended.

Students will develop their understanding of Calculus while formulating analytical arguments and justifications. The instructional approach is student-centered. Students will actively participate in class on a daily basis, solving problems in a cooperative learning environment. Students are expected to construct conclusions and argue their validity with proper mathematical notation. Generally speaking, the students are the workers while the teacher acts as a coach guiding students along their mathematical journey.

Topics covered in the course:

• All AB Calculus concepts.
• Solving differential equations both numerically and analytically.
• Using Shell method to find the volume of various solids generated through rotation.
• Finding the length of a curve.
• Integration techniques.
• Improper Integrals.
• Finding limits of various indeterminate forms.
• Determine convergence of infinite series.
• Infinite power series.
• Maclaurin and Taylor polynomials.
• Finding error of approximations using multiple methods.
• The Calculus of polar and parametric equations.
• Two dimensional motion using vector-defined functions.