Please help me figure out this two expressions:
"What do you expect to know?" and "What are you expected to know?"
What do you expect to know?
"What knowledge do you, personally, expect that you will have?" This is an unusual question because normally people don't "expect" to know something; they either know it or they don't. There are some legitimate uses of it, though; someone might ask this of a friend who's about to go to a pub quiz, for example, to ask which questions they think they might have the answers to.
What are you expected to know?
"What knowledge does an external entity (person, group etc.) who is not you expect that you will have?" Possible usage includes someone asking another about an impending job interview, if they want to know what knowledge the recruiter/interviewer will be expecting the interviewee to possess.
The difference is simply that What do you expect to know? poses a question in the "active" voice (for which the answer might be I expect to know X).
By contrast, What are you expected to know? is "passive" (a typical answer being I am expected to know X).
To clarify, in the first ("active") version, the explicitly-stated grammatical subject of the verb expect is you. You're being asked what you expect to know.
In the second ("passive") version, the grammatical subject isn't explicitly stated. You're being asked what someone else (your teacher, for example) expects you to know.