Fair question. One admissions personnel told us at the appointee visit to try and get it done before this Friday. Not a hard due date, but a reasonable goal.
As far as the Calculus, that is a good idea, but you're probably not going to make a huge difference with that extra quarter of learning. Unless the class structure is really weird (I'm assuming you're probably in AP Calc), you will have already learned everything about single-variable differential Calculus that you need to know for the second placement test. Likely you are just doing basic integrals now through the end of the class, and that's probably not going to get you enough to validate Calc 2 (integral Calculus). So, my suggestion: do a good bit of review of not only this year of Calculus but also from trig and algebra. Just really nail those two tests and hope to get placed into Calc 2.
Also, not only for this question but for life: PAUL'S ONLINE MATH NOTES.
Best. Math review. On the internet.
Everything makes so much sense, and his instruction is saving my butt in multivariable right now. Paul is my hero.