AP Calculus BC is roughly equivalent to a first semester college calculus course devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these representations.

Here is a link to the Mathematical Practices for AP Calculus: https://advancesinap.collegeboard.org/stem/calculus/mathematical-practices There you will be able to download the Curriculum Framework document as well as find additional resources.

Day 1:

• Introductions
• MPACs & The Curriculum Framework
• Riemann Sums & Slouching Towards the Definite Integral
• Major Theorems and Big Ideas: What is the place for proofs?
• Consequences of Limits and Continuity
• L’Hopital’s Rule
• Slopes and Arclength of Parametric Curves
• What to know about Parametrics for the AP Exam?

Day 2:

• Polar Explorations
• Slops and Areas of Polar Curves
• Integration Techniques
  • • Partial Fractions
    • Integration by Parts LIATE or ILATE?
• Improper Intergrals
  • • Cool Applications
    • A Pair of Ducks
• Pacing and Resources
• Differential Equations and Slope Fields
• Euler’s Method
• The Logistic Model

Day 3:

•  Sequences
  • • The BMCT
    • Some important sequences
• Series
  • • What does it mean for a sequence to converge
    • Some important series
    • Absolute and Conditional Convergence
    • Tests for Convergence
•  Infinite Series
• Power Series
• Interval and Radius of Convergence
• Resources for making an exceptional BC course

•  MacLaurin and Taylor Polynomials
• Important Taylor Series
• Error Bounds
• Reviewing for the AP* Calculus Exam; planning and pacing 
• The AP* Reading – organization and process
• A Mock AP Reading

My name is Gerald Gillis and I have been teaching over 26 years at James M. Coughlin High School in Wilkes – Barre, PA.   I have taught AP Calculus for thirteen years.   I have written a successful AP Calculus course at my school where all of my students have earned a 4 or 5 so far.  Each year, I implement new teaching strategies so that my course stays fresh and current with the practices of AP Calculus and the AP Calculus Course and Exam Description.  I do not use a particular textbook; instead, I use a collection of assignments and activities that I have personally written for my students tailored to their specific needs.  During the workshop, I will share samples of my assignments, activities, and exams I have written.  I would definitely say that these assignments and activities are one of a few reasons why my students are successful on the AP Exam. 

My experience with the College Board includes conducting one and multi-day workshops, presenter at the AP Annual Conference in Washington, D.C., and several years as an AP Exam Reader.  I am the author of Module 3 for the Online Teaching and Assessing Modules for the College Board.  In the fall of 2019,  I conducted an online College Board workshop  called Using Existence Theorems to Justify Answer.  Most recently in October 2020, I conducted an online College Board Workshop under a new format consisting of five modules.