This course is designed to prepare students for the Advanced Placement Examination in Calculus BC and covers the curriculum typical of two semesters of college level Calculus. This course includes a more extensive and in-depth coverage of all topics described in Calculus AB, plus additional topics including sequences and series, vectors, improper integrals, and functions in polar and parametric form.  This course assumes a higher level of understanding of mathematical concepts and incorporates nonroutine problems.

Students will develop a strong grasp of the Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout the high school years.

Units of Study

Semester 1:

Unit #1 = Review of Calc A
Unit #2 = Techniques of Antidifferentiation
Unit #3 = Applications of Derivatives (part I)
Unit #4 = Applications of Derivatives (part II)
Unit #5 = Differential Equations

Semester 2:

Unit #6 = Applications of Definite Integrals
Unit #7 = Parametric, Vector, and Polar Functions
Unit #8 = Infinite Topics (L’Hopital’s Rule / Improper Integrals / Sequences)
Unit #9 = Infinite Series
Unit #10 = Power (Taylor Series)