Take another look at the sentence:

Because Tran knew that a strong chemistry background was essential for a future pharmacist, she rose from her warm bed and begun studying her notes for another test.

The third verb, begun, is incorrect. This sentence requires the simple past. Began is the right form.

Verb Simple Present Simple Past Past Participle
begin begin(s) began begun

Knew, the verb you chose, is perfectly correct. Before you continue, review the rules for irregular verbs.

Try again to become a champion!

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