When Izuku believes he failed the exam, Inasa promises that if Izuku doesn't get in, he won't enroll either. Instead, they'll both attend Shiketsu together.
While Iida believes Izuku figured out the true purpose of the entrance exam when the latter willingly gives up all his points to save Ochako, Izuku corrects him that he had no idea. Izuku destroyed the Zero Pointer (and seemingly forfeited his place in U.A.) because Ochako needed help.
After Momo loses against Izuku in the Heroes vs Villains exercise, she starts doubting herself, only for Izuku and All-Might to detail exactly how much she contributed to her side and that she kept fighting even when it seemed she had no chance at all. As a result, she and Izuku are both declared the MVPs of the match.
After Izuku loses his arm fighting the USJ Noumu, Setsuna "heals" him by detaching her own arm and sticking it on his stump. She then uses said arm to play with his hair, calling it illegally fluffy.
During rescue training, All Might apologizes to Izuku for saying he couldn't be a hero without a quirk.
All Might: You proved me wrong, you know? Izuku: W-what do you mean? All Might: All day you've been proving me wrong. No Quirk and one arm, and your performance was one of the best in the class. You showed natural leadership ability and didn't let your current state hinder you physically either. Izuku: A-All Might... All Might: Quirk or no Quirk, you were always meant to be a fantastic Hero, Midoriya-shōnen. You're going to be the best of us.
When Momo is hesitant to accept One for All, feeling unworthy, she brings up how she got her recommendation just because she offhandedly mentioned wanting to be a hero when she was eleven. The very next day her mother had secured her a recommendation for U.A., making her feel like she's only a hero student because of her family's money. Both Izuku and Toshinori insist that no amount of money could have gotten her a recommendation, nor could it have let her pass the recommendation exam if the teachers didn't think she was the best candidate. No matter what she thinks, Momo earned her spot in 1A.
Momo's reason for accepting One for All? She doesn't want Izuku to be forced to stand alone at the top like All Might was.
During her "The Reason You Suck" Speech to Shouto, Momo counters his claim that he'll be the top hero by saying Izuku will be, something she states with absolute certainty. Even though she has two of the most powerful quirks in the series: Creation and One for All (which also synergize well together), Momo has complete faith in Izuku that he'll one day become number one.
In chapter 9, when Nejire asks what the situation is between several of the girls and Izuku, Momo very bluntly states she loves him. The others are shocked by her being so certain, but Momo states her feelings were already more serious than she let on but what happened a few days after their talk (her taking One for All) cemented her feelings for him.
Chapter 9 ends with Nejire, Mina, Setsuna, Camie, and especially Momo declaring that Izuku's theirs now.
In chapter 10, Melissa is told by both Izuku and All Might separately that she would make an amazing hero. In Izuku's case, Melissa hugs him tight, resulting in a big Group Hug from everyone present. All Might's reassurance causes her to break down in Tears of Joy. The faith they have in her leads her to take a front-line role during the Battle of I-Island, ending with her dad and adoptive uncle whole-heartedly endorsing her desire to become a Hero student.
After telling the students that he'll be forced to retire within the next year, All Might insists he's not worried about the future... because they are here.
After having his class perform another QAT, Aizawa thinks to himself that any future classes would "have some big shoes to fill" to measure up to them.
