Determining the gender of "un professeur" requires knowing if the teacher is male or female. True or False?

True. In French, the word "un professeur" is masculine in form. However, it can refer to a teacher of any gender. In traditional French grammar, gender agreement relies on the gender of the person being described. If you know that the teacher is male, you would continue referring to him as "un professeur" and use masculine adjectives and participles. For a female teacher, historically, "un professeur" could also be used given that certain professions did not have a widely used feminine form, but nowadays, it is more and more common to see the term "une professeure" to specifically indicate that the teacher is female, in which case feminine adjectives and participles would be used.