Despite BC Calculus Being The Hardest Math Class

I would like to start this reflection by acknowledging that despite BC Calculus being the hardest math course I have taken, it was the most impactful on how I view and interact with mathematics. I remember the day of our infamous “Bull Run” invitational meet (one of the hardest cross country courses in the USA), I was complaining to Ebenezer about how hard the class had gotten despite it only being the first quarter. He reassured me that despite the challenge, this course shaped his love for mathematics and that after taking this class he would go through math problems — related to his running pace — as he was racing. Although I have not developed this degree of infatuation where I constantly think about math as I run, I do understand what

It is only near the end of this year that I appreciated why you would always exclaim “some ways of solving a problem are just so elegant!” My favorite Calculus topic was Integral Approximation. I value the simplicity in this topic and it is something that just makes so much sense to me. When we first learned the different ways of approximating the area under a curve, I was continually left telling myself “of course! That makes so much sense! I’m pretty sure I would have come up with this had it not been for those before me”. On the contrary, my least favorite topic was volumes of solids of revolution. I felt lost from the very start and felt as though I fell too far behind to understand the topic. By the time I thought I had a grasp, I was forced to go on to the next topic — without ever developing a concrete understanding of what I was really doing. In preparation for the AP exam, I spent a lot of my time reading the Princeton Review prep book. I found the tests we took in class really helpful, however, I wish we went through more in class lessons of pure review. I wish I had created “cheat sheets” for each lesson as we learned it throughout the year. This would have saved me so much time and helped me in studying for