"A year ago" versus "a year back"
I would think that "a year ago" is the phrase normally used. Looking at the data reported by the Corpus of Contemporary American, I can create the following chart.
"Year ago" and "years ago" are the most used phrases, at least in American English.
Looking at what reported by the British National Corpus, I obtain the following data.
"Year ago" and "years ago" are still the most used phrases, compared to "year back" and "years back".
Differently from what reported from the Corpus of Contemporary American, "year back" and "years back" are not used in academic contexts.
A year ago would be the regular way to say it; a year back is a colloquial way of saying the same.
"I studied that a year ago" sounds better.