Like most crap you've read on the forums, there is little rules supporting the concept of it.
"
A specialist wizard can prepare one additional spell of her specialty school per spell level each day."
Prepare is a strong word to toss around. It goes beyond having a spell slot and includes things like validating your class level, ability to cast spells, spells in your spell book, and so on. If you read
Precocious Apprentice closely, the first stage of the feat skips the Spell Preparation process, for instance you don't have to know the Spell to cast it even as a Sorcerer or have it in your Spellbook as a Wizard and certainly don't have to meet level requirements obviously.
The other part, Focused Specialist, also rams head on with the rules.
A. "You lose one spell slot from each level of wizard spells you can cast."
PA it's self clearly indicates it is not granting you the ability to cast 2nd level spells in the game term of requirements & prerequisites, FS's Replaces part does in fact check what you can and cannot cast so the Replaces is never validated.B. "Benefit: You can prepare two additional spells of your specialty school per spell level each day."
There is that prepare word again which intent goes far beyond simply having a spell slot.So no, it's not exactly a clear "win" for this combo there. In fact, you know how the general opinion of the forums says no to things like "UMD a Wand, I can cast 3rd level spells!" as you don't have a
real ability to cast 3rd level spells? Or even prerequisites using the term "caster level" and such mean levels in a class and not that easily modified total (per dmg)? It's of no surprise that the FAQ contains the following:
If a 1st-level character takes the Precocious Apprentice feat, can he cast 2nd-level spells for the purposes of qualifying for a prestige class or meeting the prerequisites of a feat?
In the Sage’s opinion, the Precocious Apprentice feat would not help you qualify for a prestige class or feat because it gives you a chance at casting a 2nd-level spell, not the inherent ability to cast 2nd-level spells.
Which is the same thing, but official rules interpretation that can be quoted as saying PA is a shitty feat and people really need to stop trying to use it in stupid ways.
P.S. PA doesn't meet Fiery Burst's Prerequisite under intent or by the clause of PA either.