Sending positive energy your way. Take a deep breath. First semester freshman year can be a tough transition for some kids. It seems that Honor Algebra II is the only issue requiring your actions at this point. History and English are what they are and the current directiom might help free up more time/energy for math/science in the coming years.
While I generally think that parents need to step back, in this case, I think you should make a conference for you and your son to meet with the algebra teacher. You need to look at his test and see why he received an F because your DS has not been able to figure it out.
If your DS has an IEP or 504, then you have far more leverage, but regardless, there should be procedures/support in place. At my DS' high school, there are weekly coach classes for all core subjects for anyone who needs extra help. Each student is assigned a counselor and assistant principal, who should be able to assist if there are issues with a teacher.
It is okay for you to help because your DS needs it. This is not a situation of you helicoptering because you don't like grades lower than an A, but a genuine confusion why he is failing a test he appears to otherwise understand.
Thanks, I kind of needed this perspective.
Since the final is a multiple choice standardized test that all algebra II classes take my current plan is to leaving this discussion with the teacher till after finals. My logic goes as follows. Figuring out why he is failing her "honors" tests is not necessary for doing well on the final, and doing well on the final is this weeks emphasis. And second when/if he does well on the final we have another data point to show that while he does understand the "standard" material what we need to figure out what he is having problem with on her tests. And if he doesn't do well on the final, than it's moot and he might as well move to the regular class.
Edited to add, he did "solve" his own problem with the English & Social Studies teacher. I was needed for input because the school likes a parent to be involved in a change of class for freshman.
