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 responds by shouting that he'll score higher if he defeats All Might.

Communication is proving difficult, but Izuku continues to talk to Katsuki. Katsuki smacks Izuku to the ground. He angrily demands Izuku stop speaking to him. As Katsuki walks away, Izuku asks him to wait and reconsider his plan. Irate, Katsuki yells at Izuku and says he doesn't need his power to pass the exam and can win it all by himself. Izuku yells back at him and tells him that shouting is why they never have normal conversations.

Battle
All Might destroys the entire main road of the city with a Texas Smash attack. The shockwave created by Texas Smash sends Izuku and Katsuki flying back as well. All Might menacingly walks through the dust towards his students. He warns them to take the exam seriously or else they'll be sorry. Izuku and Katsuki are both surprised at how intimidating their teacher can be.

Izuku runs and tells Katsuki to follow him. Katsuki refuses and All Might rushes towards him. Katsuki attacks with his Stun Grenade Ultimate Move and jumps at All Might. All Might manages to grab Katsuki's face, but Katsuki doesn't hold back and tries barraging him with his mini-explosions. The blast doesn't do that much damage and All Might slams Katsuki into the ground.

All Might turns his attention to Izuku and gets behind him. He taunts his young protégé and reminds him of the Hero Killer. Izuku activates Full Cowl and jumps away. Katsuki jumps at All Might at the same time and the tandem ends up running into each other in mid-air. Izuku wants to run while Katsuki only wants to defeat All Might. The latter admires All Might too much and the former is in a rush to win.

Katsuki recovers and walks towards All Might. He passes Izuku and his partner pleads with him not to fight. Katsuki replies that he must win because that is what a great hero does. Still trying to reason with Katsuki, Izuku grabs Katsuki's shoulder, but Katsuki angrily tells Izuku to let go of him, and suddenly All Might calls out to the pair. All Might uses a broken fence to pin down Izuku from above. He then gut-punches Katsuki to the extent that he goes flying and vomits while in the air. Katsuki slowly recovers and All Might realizes that Katsuki's angry about the improvement in Izuku's skills. All Might tries to advise him, that he still has much room to grow, and shouldn’t waste his potential, but Katsuki claims he'd rather lose than accept help from his former friend.

All Might prepares to crush Katsuki but Izuku runs in and angrily punches Katsuki. He yells at him not to give up and quickly carries him into an alleyway. All Might admits he let his guard down and complains about the heavyweights he's wearing. In an alleyway, Katsuki elbows Izuku in the back of the head, forcing Izuku to put him down. Izuku pleads again, admitting that he doesn't have a plan to run away from All Might or defeat him. He asks Katsuki not to give up because he's always been the type who wins no matter what. Izuku says the most amazing hero always wins as Katsuki always used to say.

Katsuki becomes enraged as he's being reminded of his own words, yells, and blasts the wall next to Izuku. He tells him that there is no way they can get away from All Might without fighting. Izuku starts to argue but Katsuki loudly demands he shut up. Katsuki comes up with a plan to use maximum firepower on All Might and then create distance between them. He runs out of an alleyway and distracts All Might. All Might is unimpressed and believes it's a sneak attack.

Furious about having to work with Izuku, Katsuki cries and yells to Izuku. Izuku suddenly appears behind All Might and is equipped with one of Katsuki's Grenadier Bracers. Izuku pulls the pin and unleashes a massive explosion on his idol. The recoil from the explosion injures Izuku's shoulder. This makes him question how Katsuki can use this weapon. Katsuki flies away and orders Izuku to run.

All Might recovers and admits he's impressed with the team's compromise between running and fighting. All Might also remembers that he taught them about damaging the city in their first combat training. They avoided doing so by using the explosion in part of the city that is already destroyed. Izuku and Katsuki are both clever, but they have so many complicated emotions about each other that they can't communicate. All Might knows that can't be solved in one fight, but he's determined to still teach them a lesson.

Izuku and Katsuki rush towards the escape gate. Izuku points out that the escape gate looks ridiculous but if they get through it, they pass the exam. Katsuki notices that All Might's attack was from somewhere near the gate and that it reached all the way to the middle of the replica city. Izuku wonders why All Might isn't pursuing them and Katsuki says when All Might catches up he'll blast him with the other Grenadier Bracer. All Might overhears this and instantly appears between them while mocking Katsuki. Then he breaks both of the Grenadier Bracers with two swift punches.

All Might knees Katsuki in the chin and sends him flying into a building. Then he grabs Izuku and slams him into Katsuki when he flies back out. All Might pins down Katsuki with his foot and pulls Izuku up by his arm. All Might congratulates them for working together but says that cooperation was a prerequisite and not an option.

Katsuki mulls over All Might's overwhelming strength. Katsuki silently admits All Might is the greatest hero on earth. All Might taunts Katsuki's strategy and the young man retaliates with a super explosion that blasts All Might away. Katsuki gets up and winces from the pain. He grabs Izuku's mask and tells Izuku to prepare to fly. Katsuki uses an explosion to send Izuku flying to the escape gate. All Might uses New Hampshire Smash to propel himself through the air and slams his back into Izuku. Izuku's back is injured and he's sent flying into the side of a bus.

Katsuki flies overusing his explosions and takes aim at his teacher. Katsuki tells All Might that he can't win unless he goes all out. He unleashes another super explosion on All Might and Izuku recognizes the attack from the Sports Festival. Katsuki gripes in pain and tells Izuku to run. Izuku's back is messed up and Katsuki yells at him to move. Katsuki uses more super explosions to keep All Might back and Izuku moves slowly towards the gate. Izuku knows that All Might will stop him and Katsuki can take advantage of that. However, All Might subdues Katsuki by slamming his head into the ground.

All Might asks Katsuki to stop fighting because his body is suffering. Katsuki replies by telling his opponent that he'll never stop fighting because he wants to win.

Inspired by Katsuki's resolve, Izuku activates Full Cowl and charges at All Might with nothing but his fist and a smile. He asks All Might to get out of the way and then hits him with a smash. Izuku gives it his all and then rushes Katsuki's unconscious body toward the escape gate.

All Might isn't surprised that Izuku saved Katsuki even though he could have just escaped. Izuku can't help his desire to save others and there's not an obstacle that can stop him when he does. He carries Katsuki through the escape gate and they pass their exam.

Aftermath
Izuku's friends cheer from the monitoring room. In Recovery Girl's office, Recovery Girl berates All Might for attacking the boys so hard. She says Izuku's back injury was especially bad.

Izuku thanks Recovery Girl for healing him. Katsuki remains unconscious and Recovery Girl says he won't wake for a while. All Might thinks about both Izuku and Katsuki's improvements. All Might admits he was impressed with how Katsuki smiles in the face of adversity. All Might desires to see how strong both of them get.

Anime and Manga Differences
In the manga version of this fight, Izuku and Katsuki's fight with All Might was depicted first out of all the final exams. The anime has this set in reverse, as their bout is the last of the tests. All Might was the one who told them the rules of the exam and not Shota Aizawa. The manga did not depict when All Might pinned down both Izuku and Katsuki. After finishing the test, Izuku watches his classmates' exams. In the anime version, Izuku watched all of his classmates before he took his own exam.