For most of human history, the nature of assessment in formal education can best be described as "recitation." A student would listen to a more knowledgeable person or recognized expert (typically a person from the group that held power - i.e. men) talk, discuss or practice what was said, and repeat (or recite) back when asked. There were generally two types of recitations. The more knowledgeable person would expect the learner to repeat back verbatim what they heard (what we think of as memorization) or repeat back and comment on what was learned by adding a personal opinion. For men like Socrates and Aristotle, the nature of this interaction was less about knowledge transmission and more about helping the student uncover "true" knowledge. This meant that, yes, Aristotle quizzed Alexander in the way we think of the word today; Aristotle would ask Alexander a question based on something the boy had studied and would respond based on the nature of his response.

To clarify something in your question - you asked about the "days of tutors" and referenced Greek scholars. The notion of a "tutor", though, endured until the late 1800's, even longer in some cases. Harvard professors were typically known as "tutors" until the mid-1800's and some American schools and colleges kept the moniker until the mid-1900's. The name was generally used in places that followed a classical curriculum - Latin and/or Greek, some maths, some sciences, rhetoric, and logic. The title faded in use as teaching developed into a profession, losing prestige as the person in charge of children's learning was more likely to be a woman than a man. At the same time, the curriculum moved from classical to liberal arts (science, history, literature, math, physical education, music, art.) or "modern" curriculum. Shifting from "tutor" to "teacher" reflected a school's commitment to educating children for their future. Finally, when formal education was mostly about the sons of men with means and access to power, the title of "tutor" implied an intimacy in the relationship between knowledgeable person and learner, as well as an exclusivity. The adult was usually working with one on one with a boy or perhaps a larger group, but typically not a class of 20-30. As populations increased and education became something for all children, that intimacy, and exclusivity, shifted. And as such, language followed.

Regarding the notion of pass/fail, school didn't become a thing young people did with any degree of consistency until well into the 20th century. This mean there wasn't really a need to summarize learning via a symbol (i.e. a grade) until long after Socrates' time. Some tutors had methods of evaluating student performance that involved awarding points or assigning a letter and those method include a notion of failure. It was more common, though, for a young person who worked with a tutor to work with them until the adults around them felt they had learned what they needed to learn or it became time for the young person to take on adult responsibilities. For Alexander, that meant ascension to the throne (source).