I would say that it depends on the nursing school. Many schools don't require an entrance test, but many will require that certain prereqs be done before entrance to the program. For example, for my ADN program (well, not mine yet but hopefully in the fall) requires college algebra and Anatomy and Physiology 1 be finished before entering the program. Many schools will also choose students that have completed the most amount of prereqs finished as the nursing program itself is quite intensive.
If you have been in school (college) within the past 5 to 10 years, you might be able to transfer some classes. I would check with the schools in your area for more specific information.