I'm faced with a dilemma and need a big dose of instrumental rationality. I'll describe the situation:
This fall, I'm entering my first semester of college. I'm aiming to graduate in 3-4 years with a Mathematics B.S. In order for my course progression to go smoothly, I need to take Calculus I Honors this fall and Calculus II in the spring. These two courses serve as a prerequisite bottleneck. They prevent me from taking higher level math courses.
My SAT scores have exempted me from all placement tests, including the math. But without taking a placement test, the highest any math SAT score can place me into is Pre-Calculus Honors, which is one level below what I want to take in the fall. The course progression goes Pre-Calculus Honors to Calc I Honors to Calc II Honors.
So in order to take Calc I Honors in the fall, I either need to:
(1) Score high enough on a College-Level Math placement test or
(2) Forgo the test and take Pre-Calc Honors for 9 weeks this summer
I've taken both pre-calculus and calculus in high school. I've also been studying precalculus material over the past few days, relearning a lot of what I've either forgotten or wasn't taught in class. If I decide to take the test, I'm pretty confident I'll place into Calculus I. I'd estimate that chance being within 0.8, plus or minus 0.1. If I pass the test, I'll save 9 weeks of studying in the summer and use them to prepare for classes I'll be taking in the fall. I'd also free me up to take another summer class worth 4 credits and fulfill a prerequisite.
But if I decide to forgo the test and take Precalc this summer, I'm also pretty confident I'll do very well in the class. I'd confidently wager above a 90%. The class would ensure I've got the material down better than the placement test and would also give me my first six credits.
The questions going through my mind right now include: How can I best decide between these two options? How can I compare the heterogeneous benefits/costs? Are there any other relevant factors that I'm leaving out?
Advice would be greatly appreciated.
Edit: Writing this post, as well as reading and responding to the comments, has clarified the situation for me. Unless there is something else important I've missed, I'll take the test, place into Calc I, spend the summer taking a different summer class and preparing for fall classes. Thanks to everyone who helped me out.