Izuku Midoriya & Katsuki Bakugo vs. Toshinori Yagi

Izuku Midoriya & Katsuki Bakugo vs. Toshinori Yagi is a battle fought between Class 1-A students Izuku Midoriya and Katsuki Bakugo against their teacher, the Pro Hero All Might during the Final Exams Arc.

Battle
The battle begins with Izuku and Katsuki walking towards All Mights position near the escape gate. Izuku tries to reason with Katsuki and to convince him that they can't take on All Might and so they should try and hide in order to escape, but to no avail as Katsuki is dead set on defeating All Might. Izuku tries one more time to get Katsuki to listen to him and understand that they can't defeat All Might even with with the handicaps but before he finishes speaking Katsuki hits him with his gauntlet, telling that even though he is doing decently he shouldn't say another word. They then start shouting at each other shortly before All Might punches the air and sends them flying, causing major damage to the mock city itself and starting the fight properly.

Izuku is surprised by the amount of damage caused by All Mights punch, even though he has a sever handicap holding him back, and when All Might warns them that thinking of their fight as a test will only land them in a world of hurt, and to come at him with with everything they've got.

Despite Izuku's insistence on running away, Katsuki runs in and tries to attack All Might after blinding him temporarily with a stun grenade. Unfortunately he is grabbed by All Might in mid air and the attacks he manages to land on All Might seem to have little to no effect, with All Might remarking that the blast were "weak, hardly more than a sting".

Aftermath
After Izuku escapes the arena with Katsuki and passes the final exam he and Katsuki are taken by All Might to Recovery Girl tent to get them healed up. Here Recovery Girl chastises All Might for not holding back and says that he could have done permanent damage, especially to Izuku's spine which she was barely able to heal.

The fight lays the foundation for the improvement of tensions between Katsuki and Izuku by forcing them to work together for the first time.