"He is satisfied, because the students are able to answer everything."
Translation:Er ist zufrieden, weil die Schüler alles beantworten können.
Had the same question. From the info below, it appears that "antworten auf" is not correct for this context.
English reply to something is the equivalent to German auf etwas antworten while English answer something is the equivalent to German etwas beantworten. If you reply to a question or answer someone then you go with antworten which means to respond, to be responsive. If you answer a question or a request then you go with beantworten which means to give an answer. Additionally if you response to a letter you also use beantworten which now means to give a written response.
Note that beantworten carries the connotation of fully or, at the very least, sufficiently answering the question, antworten auf only suggest that you reply but this response may not be satisfying.