This was an impressively worthless chapter. Nothing at all to do with taming, MC doesn't actually show or explain any of the knowledge they were working with, and the payoff just sets up a repeating gag with no resolution. It would have been much better if he wrote about taming magic for the essay and when confronted by the girl started preaching about how great taming magic is, and people are impressed by his depth of knowledge in it or something. That's what this manga is about, not generic "I'm super smart and know all the magic so I'm going to impress everyone with the power of mayo beauty magic" nonsense and school "drama".