The transitional phrase in <em>In the hope that I would get a better grade, I found myself studying much more often than I normally do</em> is a. In the hope that.
Explanation:
<u>Transitional words or phrases</u> are those used to create links between ideas, to connect one idea to the next one. These words or phrases are very useful in writing to establish different types of connections between ideas, such as time, exemplification, place, contrast or purpose, like in this case: the phrase <em>in the hope that</em> introduces the objective the writer had when studying much more than he usually did.