Maybe the opposite approach is the solution.
Instead of stating the required knowledge, use the average score for standardized exams in relevant courses/admissions exams as a starting point. Look at the exams in detail. Try and find out (if available) what types of problems most people get right. Then compile the content of those questions into a reference for yourself to use when preparing lectures for that particular group. (I don't know if this information is available.)
Stating a required body of information for mathematicians to know is rather pointless, since the term mathematician is much too broad. If you wished to define a certain type of mathematician, who is proficient in X, Y, and Z, then that would make a lot more sense.