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Regular Common Core Algebra II should be uniform in theory. In reality different districts & states uses different materials & books so aren't precisely the same. The highest level of math common core defines standards for in Algebra II. Some level of Trig is supposed to be spread out and part of Geometry & Algebra II. Math higher than "Algebra II" is not defined by common core.

What isn't defined in Common Core is what what to do with "honors", "pre-ap" or in common core language compressed classes. Basically how to get kids through math faster and into Calculus in High School. I was involved in a committee through my school district who's task was to try and figure out what we called all the "pathways' through the program. Most "honors" classes in the new system are "compressed classes". Basically three years of Common Core math squished into 2 years. This "compression" is the recommendation method.. This is learn math faster not necessarily to more depth.

My guess is this is what's your school means by "pre ap geometry" and "pre ap alegbra II". The reason the school may be reluctant despite the A to jump your kid from regular Geometry to this "pre AP" Algebra II is there very well might be topics he would miss. In our district the new pathway offers a two year "Geometry/AlgebraII/Trig/Pre-Calc" class, that leads a student straight to Calculus the following year.

As the parents of a rising Senior who has low processing speed, I'd jump your son to this faster paced class with caution. Because my son didn't get the grades in H. Algebra II (**) as a freshman he was dropped down to regular Pre-Calculus. (THIS IS BEFORE COMMON CORE CHANGES) This has ended up being a good pathway for him, although I was frustrated at the time. Like your son he picks up new topics easily but he can take a longer time to do the homework than other kids in the class. And the honors class did go faster and had more homework. This happens for him x5 for all his academic classes. The added stress of all that homework has caused extreme anxiety. So while my son really missed doing proofs in Pre-Calc. He received good grades in regular Pre-Calc, good grades this year, a top score on both the SAT Math Subject test & (just found out day) SAT Math section. He took AB Calc rather than BC Calc. Our school teaches AB Calc with the same rigor as BC it just covers 1/3 less of the material. It's been a success for him. He likes math again after Algebra II. And I believe he has gotten a very solid math background.

If you do get the approval to move him math class. Do make sure you find out what topics he might have missed and have him work on them this summer. IF my son had been approved to move to B.C. Calc from non honors pre-Calc he would have had to do a large amount of summer homework.

** Don't get me started on his teacher. She expected that all the kids spend the summer taking a summer prep class, and she tested material she never taught.