have you done one of these type of books from amazon?
Is it a live case study or just a presentation/powerpoint?
either way be sure to have a good narrative, be communicative, and invite their participation.
Here's a Bain video with rehearsed interviews that I think does a really good job of showing how a perfect interview goes: https://www.youtube.com/watch?v=qbP8QKlXjKg
This is a BCG case they have online that shows a "transcript" of a pretend interview (they also have more practice cases on their site) that also shows how an excellent interview candidate performs:
https://www.bcg.com/en-us/careers/path/consulting/driving-revenue-growth.aspx
I would read, at a minimum Part 3 and Part 4 of this book:
Here's a preplounge math tool to get better at math:
https://www.preplounge.com/en/mental-math.php
For business background, start reading Bloomberg Businessweek. A lot of their articles are very case-like scenarios.
You could also read through cases (without a practice partner) and absorb the kinds of problems/solutions being implemented to get more business sense.
Gotcha.
Another good resource to start thinking like a consultant is here: https://www.amazon.com/Case-Interview-Secrets-Interviewer-Consulting/dp/0984183523
Victor has a lot of stuff for free online.