As an upcoming sophomore at DA, I am excited to embark on the journey of taking AP Calculus BC. Since the AP Calc BC course at Deerfield began in the previous spring, I have been assigned to review the material that the students covered during that term. In light of this, I was wondering if you could recommend a resource that would help me prepare for the course effectively.

BTW, I am curious to know if it is common to take AP Calc BC as a sophomore.

Calculus in 10th grade is three grade levels ahead of the standard sequence (that completes precalculus in 12th grade).

Presumably, you are very good in math to be in that +3 math track.

However, if the school recommends you to review or self-study some material, the school should be able to provide recommended texts and other materials for you to review or self-study from. There are other outside resources like the MIT OCW 18.01 course materials that you can use as a supplement.

Not sure about Deerfield, but at Lawrenceville, I’d estimate ~20 students (out of 220) in my grade took Calc BC as sophomores.

Lawrenceville also does Calc BC in 4 trimesters (kind of; the class is called Precalc BC, but you start calculus in the spring), and we just learned basic limits, continuity, and some really basic derivative rules—think power rule.

I want to express my heartfelt appreciation for your valuable suggestions. As I’ve meticulously planned my summer schedule, I’ve realized that I’ll only have a compact timeframe of 10 days to fully immerse myself in AP Calc BC preparation. With that in mind, I’m eager to know which resources would be most effective for this short period. What about Khan Academy, Formal AP prep book…

Furthermore, I’ve been informed about the topics covered during the spring term, which include fundamental concepts such as limits, the definition of the derivative, derivative rules, and the derivative of trigonometric functions. Additionally, applications of the derivative such as tangent and normal lines, particle motion, related rates, curve sketching, and optimization were covered. Moreover, the theorems explored encompass the intermediate value theorem, extreme value theorem, mean value theorem, and Rolle’s theorem.

Considering this comprehensive list, I’d greatly appreciate any specific guidance you can provide regarding the aforementioned resources and these specific topics.

I don’t know your level of proficiency at math or how quickly you pick up new topics. You say you have 10 days available to you … is that 80 hours or 20 hours? It makes a big difference. Can you learn limits, continuity, what a derivative is, derive the power rule, product rule, etc, in the time you have available? Sure. It’s just memorization and there are plenty of online resources out there like Khan Academy that will help you. For example, Rolle’s theorem is simply about maxima and minima of continuous functions and any You Tube vid will demonstrate that.

Will you become fully proficient in the nuances of limits, continuity, differentiation, how to apply it to all kinds of interesting problems, etc? Probably not unless you are an exceptional math student - which you may be. Most people have to work a large number of problems and struggle with some proofs to internalize certain concepts.

But, given the time you have, you need to nail the basics. What do you need?

- Quick and easy tutorials. Khan Academy is fine for that, you can supplement with some You Tube videos
- A more formal walkthrough that ties concepts together and addresses common problems where differentiation comes into play such as kinematics. The MIT course referenced above can be a good starting point for that though I don’t know if the text is available free.
- A textbook for proofs and additional problem sets. There is no substitute for a
*well-written* calculus text. I’m a huge fan of the Thomas and Finney text but there are others. You can find it online in pdf format.

Good luck with your efforts.

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