No. Depending on what you mean, you might say: She hopes that she will pass her exam. She is determined to pass her exam.

DavidK is right. To "be determined (to do something)" is different from "to determine (something)." When you determine something, it means you figure it out, or you reach a conclusion based on facts. "By counting the number of students in each classroom, we can determine the total number of students in the school." "Has your boss determined which person we should hire?" If you're "determined to" do something, it means you very strongly intend to make it happen. "She was determined to get a better job." "I'm determined to finish reading this book today." "He was determined to never call her again."

No, you would need to change "determines" to "is determined" as David suggests. "She is determined that she will pass her exam"