This may be two dumb questions but how can you take BC without taking A? Also if you had A before why would you repeat it ?
Go to the College Board Web site.
AP Calculus AB - One Semester/Quarter of college calculus. taught over one year of H.S.
AP Calculus BC Two Semesters/Quarters of college calculus. taught over one year of H.S.
This is the way college board expects them to be taken. The BC test has two parts and one gets two grades, one for the AP part and one for the BC part.
Wow - it often amazes me that it's so easy to interpret fairly simply statements differently. Both my old school district (at least as of a couple of decades ago) and my kids' school district, which are located in different parts of the country interpret College Board's statement to mean consecutive semesters rather than overlapping semesters, thereby allowing AP Calculus BC to follow AP Calculus AB without any repetition of topics and to include multivariate calculus, which is typically covered in a 3rd semester calculus course in college.
Back to your original question, I lean towards the challenge side of the scale but could imagine sacrificing that in some instances if the damage to his GPA would preclude admission to desirable college options. In general, I also would take it on a case by case basis under a cost-benefit analysis. For example, if your DS might benefit more from developing strong writing skills then it may be worth it to risk a B in history to get them, particularly as that does not appear to his career path. Ultimately though, since it is his choice, the most you can do is lay out all the considerations in each instance where he has to choose.
