Questions about Jazz improvisation for Saxophone?

I'm planning to be a jazz studies major in college and I have an audition with the college's music department next week. I started playing alto saxophone in grade school but didn't really have proper teaching until I reached high school. I'm able to get a pretty decent sound despite my set up (cheap mouth piece;student saxophone). My only worry is the college requires me to improvise on the two jazz tunes I have to play. I just wanted to know if it is absolutely necessary to improvise using the given chords on the sheet music? I know it would be better to stick with what's on the page but with my level of knowledge with chord progression, it's difficult. I find myself "thinking" too much about what notes to play. Do you think with my current knowledge of jazz, I should just play how I feel and see how I can make it work? Also, is there any nice simple patterns I could lean quickly? (By the way, I plan on getting a proper saxophone upon beginning college and I've recently been listening to jazz every single day).