My Hero Academia/Recap/Quirk Apprehension Test Arc

The Quirk Apprehension Test arc encompasses chapters 5 to 7 of the manga and episodes 5 and 6 (the first half) of the anime.

Having passed the U.A. Hero Course's entrance exam, Midoriya meets with All Might at Dagobah beach the night after. All Might congratulates him and later advises Midoriya to hone his use of One For All better to avoid grievous injuries.

Midoriya is wished well by his mother, Inko, before he departs for his first day of school. He eventually finds that his class - 1-A - is shared by childhood bully Bakugo, a particularly strict young man who introduces himself as Tenya Iida and Ochako Uraraka, the friendly young lady whom he saved from the zero-point villain. Before they can properly acquaint one another, they're interrupted by their homeroom teacher - Shota Aizawa - who's introduced climbing out of a sleeping bag. Right on the first day, he puts them through a Quirk apprehension test and stipulates that whoever scores the least points will be expelled.

Midoriya is hesitant to use his Quirk and consequently, he's lagging behind by the time they get to the fifth test - a softball throw. Just as Midoriya winds up to use One For All to get a good score at least on this one test, his Quirk is suddenly cancelled out. It turns out that this is the Quirk of his teacher, Aizawa (actually the obscure pro Hero Eraser Head) - the power to nullify emitter Quirks. Aizawa scolds Midoriya for his plan and states that if he's constantly going to make himself a liability to others by grievously injuring himself, he won't be able to become a Hero. Unbeknownst to him, a concerned All Might watches from behind. Understanding his teacher's words, Midoriya winds up once again. He channels One For All only through his fingertip and scores an excellent throw. Even though his finger is broken, he can still move. Aizawa is impressed by the young man's quick thinking, whereas All Might is elated.

While the rest of the class cheers, Bakugo is completely flabbergasted. In a fit of rage and feeling lied to, he bays at Izuku for answers as he attacks, before he's restrained by Aizawa. As a consequence of his finger injury, Midoriya ends up last. Just as he fears for the worst, Aizawa declares that he lied about the expulsion stipulation to better motivate the class to do their best. After he gives Midoriya a tip to Recovery Girl's clinic, he leaves. Close by, All Might calls him out for lying, knowing he's actually expelled students this way. Aizawa backtracks and notes that he only expels students he feels have no potential and notes that this simply wasn't the case with Midoriya.

As Midoriya prepares to head home, he's greeted by Iida and Uraraka, from he quickly befriends for their kindness and honesty.

This arc contains examples of:

Adults Are Useless: Inverted with Aizawa; the instant Bakugo tries to attack Midoriya, he ties him up with his capture weapon and nullifies his Quirk to prevent a brawl.
Cassandra Truth: When Bakugo dismisses Midoriya as a "Quirkless loser", Iida counters because he's seen his Quirk in action. Bakugo doesn't believe it until he sees it for himself.
Cast From Life Force: Recovery Girl's Quirk heals others not through undoing their injuries, but by stimulating the natural healing process, which drains her patient's stamina for a while. Therefore, Midoriya feels rather tired when his broken finger is fixed.
Cheshire Cat Grin: Aizawa has a very awkward one on his face when he declares that he lied about expelling the worst performer.
Color Failure: Midoriya's reaction to finding out the expulsion stipulation was a lie.
Explosion Propulsion: Bakugo uses this to pitch his softball and manages to score over 700 meters with it.
Fingore: Predictably, using One For All during the softball throw shatters Izuku's right index finger.
I Lied: Right at the end of the test, Aizawa claims that his stipulation of expulsion was a lie meant to stimulate the students to do their best.
Jaw Drop: Bakugo is completely gobsmacked when he sees that not only does Midoriya have a Quirk, but a very powerful one at that.
Jerkass Has a Point: Cruel as he might seem to his students, Aizawa's criticism of Midoriya's reckless Quirk usage is completely on-point and acknowledged by the latter. Heroes who turn themselves into a liability through misuse of their Quirks are no good on the field.
Oh Crap: Midoriya makes a very comical face of horror when Bakugo comes charging at him.
Power Nullifier: Aizawa's Erasure Quirk prevents the effects of emitter and transformation Quirks, but not mutant Quirks.
Readings Are Off the Scale: When Uraraka throws the softball, her Zero Gravity Quirk allows her to have it float for as long as she wants. Her score ends up being an "infinite" one, shocking all of her classmates.
Take a Third Option: Seeing how a Quirkless throw won't get him anywhere near a good enough score to pass the test, and how using One For All on his whole arm would render it completely useless for the rest of the test, Midoriya opts to flick the softball using only one finger. While he breaks it in the process, he's still capable enough to power through the rest of the test.
Three Amigos: By the end of this arc, it's readily apparent that Midoriya, Uraraka and Iida have started to become friends. They've stayed together since.
Wacky Homeroom: How many of the students are introduced, and it's clear it's just going to get wackier.
Was It All a Lie?: A rather extreme variation, as Bakugo seems to assume in these episodes that Midoriya was lying about being Quirkless, and keeping his powers a secret for years. He doesn't take it very well.
Weaksauce Weakness: Aizawa's Erasure Quirk is a very potent power for dealing with opponents, but according to him, it's hindered by a major nuisance - he has dry eye and has to use it for a limited time, which is why he complains about using it in class.