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, All Might during the First Term Final Exam.

Prologue
Izuku runs to the escape gate, inspired by his classmates' performances from the nine previous matches. He reaches the entrance to the arena and he meets Katsuki's cold glare. Katsuki gets angry as he recalls calling out Izuku for stealing his moves.

Izuku follows Katsuki down the street and nervously suggests that their team try to escape and avoid fighting All Might. Katsuki orders Izuku to stop following him but Izuku continues pleading with his teammate to take a different route to the escape gate. Katsuki replies that he'll score higher if he defeats All Might.

Although communication is proving difficult, Izuku presses on. His pleading gets him a hard right hook from Katsuki. Katsuki demands Izuku stop speaking to him. Katsuki walks away and Izuku asks him to wait and reconsider his plan. Irate, Katsuki yells at Izuku and Izuku yells back at him.

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 cannot 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 cannot 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 should not 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 Might's 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 everything they have.

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.