noun
problem child
Refers to a child who causes trouble or is difficult to manage, often in a school or family context. Can also be used figuratively for a person or entity that is a source of trouble.
彼はクラスの問題児だ。
He is the problem child of the class.
あの子は問題児扱いされている。
That kid is treated as a problem child.
優等生 means 'honor student' or 'model student', the opposite of a problem child.
Compound of 問題 (problem) and 児 (child). The exact historical derivation is straightforward; the word has been in use since at least the early 20th century.