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Am I missing something here? (Note: the circled notes aren't included so we just ignore that. I'm only trying to analyze the rest.) In measure 8 (the second measure in the below excerpt), after Em, I don't need to add a chord there (as told), so I was wondering if there's anything wrong with my answers here. This isn't a specific piece. Are there secondary dominants here?
The two eighth notes on the first beat are both uncircled, making the chord a C# half-diminished.
However, it's unclear whether the exercise is intended to include seventh chords. If it's triads only, then the analysis is fine. The ii chord is just linking the two I chord inversions. An alternative analysis would be to consider the B in the ii chord as an accented passing tone and instead analyze the chord as viio6. It's functionally the same, but might seem more intuitive to think of a vii chord leading back to I, since that's a more common situation than a ii chord operating the same way.
There are no secondary dominants.
Adding to Aaron's answer - there are no secondary dominants. The reason being a secondary dominant essentially, is the V of any of the chords diatonic to that key - not including the V of the tonic itself, of course - that's simply the dominant.
So, in key D, F♯7 (V of Bm), B7, (V of Em), C♯7 (V of F♯m), E7 (V of A), would be examples.
