"Cheistigh sé san áireamh mé, he put questions in arithmetic to me"; and "Cheistigh sé díom cá raibh mé, he asked me where I was":
these examples in the dictionary make it sound to me like there's a role reversal in Duolingo's classroom!
There's also fiafraigh for "ask", in the sense of "inquire" rather than of "request", but you can equally well use ceist a chur for that:
"To ask someone something, rud a fhiafraí de dhuine."
"To ask someone a question, ceist a chur ar dhuine."