“I actually wrote a paper on this in college.”
You're watching a documentary on TV about a war in ancient Rome. You remember studying this and writing about it when you were a student. You tell your girlfriend about it.
I actually wrote a paper on this in college.
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(something) actually (is / does something)
"Actually" is a word that you use when you're saying something that you think will be surprising or new information to the listeners. For example:
You can use "actually" in several places in a sentence. One place is before a verb, like this:
write a paper on (a topic)
When you're in school, you have to "write papers" on different topics. A "paper" is something that you write about a certain topic. It's usually between 2-20 pages long.
You also write essays in school. An "essay" is shorter than a "paper".
(someone)(did something) in college
When Americans say that they did something "in college", they mean that they did it while they were a university student.
Here's a full explanation of the difference between "college" and "university".