I think the sentence may be written incorrectly. I believe it should be, "The most common purpose for academic English is to provide answers to basic questions." The plural should be used only if the phrase "academic English" is referring to a group of people, and if so But this is only my opinion as a native speaker of the language. I am sure others will have opinions which either agree with me or disagree. It will be interesting to see what others may write.

The reason purposes was used here is because there is more than one purpose. You can use the short version of this sentence and say "The purposes for English are to provide answers". This is my humble opinion. Hope this makes sense.

I agree, I don't understand why the plural was used here. It doesn't make any sense.