"Was determined" - decided that nothing could stop me from doing something: "I was determined to get to the movie theater despite the horrible weather."
"Determined" - made an observation: "I determined that the green jelly beans tasted terrible."
"Was exhausted" - tired: "I was exhausted after running 10 km."
"Exhausted" - used up: "I exhausted my supply of jelly beans
"I determined (to do sth)" means that you decided to do that thing. This pattern has a formal or official feel and is mostly used in written English.
"I was determined (to do sth)" means that you were fully resolved or committed to doing that thing, even in the face of obstacles or setbacks. This pattern is more common in everyday English.