why the verb in this sentence is conjugated singular?

Question

Книги не читаются сами! Завтра вам придется учить больше, если вы хотите сдать экзамен.

Why, if the person is вы (so second plural), the verb приходиться is put into the third singular?

Answer 1

Приходиться + dat. is an impersonal construct which means "smbd./smth. has to".

Завтра вам придётся учить больше means "tomorrow you'll have to learn more" or, if I may, "tomorrow it will fare with you that you learn more".

It is similar in construction to English "it seems to me", "it occurs to me" (which also have parallels in Russian: мне кажется, мне думается etc.).

Here, you put the agent ("I") into an oblique case (replace "I" with "me"), and insert the expletive subject "it" (expletive here means that the word means nothing by itself, but is just placed there because the grammar requires something to be there).

In Russian you don't normally use expletive subjects, except than in edge cases (— Тебе не кажется, что он жулик? — Казаться-то оно кажется…), but otherwise the sentence has exactly same structure as the English one.