Is the word 'across' a compound preposition?

Hi

I am doing A Level English language. As part of my Easter holiday homework/revision I have been asked to focus on word classes but also types of these classes (proper and concrete nouns etc.) I was just wondering, is across a compound preposition? All of the websites I've looked at define a compound preposition as being ones which 'are generally formed by prefixing a Preposition to a Noun, an Adjective or an Adverb.'

I don't think so. I might be wrong, but I was under the impression that compound prepositions are formed using two or more words (like, due to or in addition to or because of), so I think that definition might be wrong. In my grammar book, 'across' is listed as a simple preposition and 'because of' (for example) as a complex/compound preposition (complex might be the better word as it avoids confusion; I've also come across it a lot more than compound).