Every student must remember to bring his book.I believe that it is inappropriate to use his if some of the students are female, so I recommend avoidance of usage like that.
So what should you do? Some people suggest his or her. While that is certainly non-sexist, it is rather ugly.
How about the following?
Every student must remember to bring their book.Traditionally, this would be regarded as wrong, as their should refer to a plural noun, and student is singular. But the use of their and they to refer to a gender-neutral singular noun is becoming increasingly acceptable.
In the on-line Guardian (here), I saw the following, quoting a medical specialist:
But if any woman is worried, then they should contact their surgeon or GP.Here, they is used even though we know that the referrent must be female and so she would seem to be perfectly OK.
It seems that they really is becoming more acceptable for referring to indeterminate singular nouns; and I believe it is no longer appropriate for English teachers to mark it as wrong.