数学の問題は解けましたか。

mathematics; arithmetic

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

question (e.g. on a test); problem; problem (e.g. societal, political); question; issue; subject (e.g. of research); case; matter; question (i.e. doubt); public discussion; controversy; trouble; problem; inconvenience; difficulty

topic marker particle; indicates contrast with another option (stated or unstated); adds emphasis

to be solved; to loosen; to come untied; to be removed (e.g. restrictions); to be cleared (e.g. misunderstandings); to be broken (e.g. spells, curses); to melt

indicates a question (sometimes rhetorical); or; whether or not; some- (e.g. something, someone); indicates doubt, uncertainty, etc.; emphatic prefix; suffix forming adjectives or adverbs; in that way