This coming Fall semester, I will have to organize a course to prepare high school students for the maths interview they will have before entering to university. This is my first time teaching this, so I am concerned about the organization of such a class.
My question: How such a class should be organized compared to a normal class?
Informations that may help to answer:
- The class will be only on the math part of the interview. Questions about motivation to apply to the university will be handle in the English course.
- The range covered by the interview is PreCalculus and single variable Calculus (roughly, AP examination curriculum). All students already covered this material in the previous years.
- Small group of students (about 10).
Any advice on references or textbooks is also welcomed.
Edit: Format of the interview: the interview is about 15-20 minutes long. It starts with a precise theoritical question like "State the Fundamental Theorem of Calculus", followed by a vague (in the sense: no single correct answer) theoretical question like "Why is it useful?", "Give an application" or "Which can of problem can you solve using this?". Finally, a problem has to be solved by the applicant. The focus is on the reasoning and methodical thinking of the applicant, its reaction to suggestion more than finding the exact numerical solution. There is no preparation time for the interview.