Dan Smith gave a great answer as usual. Offhand, I’m fairly sure that the 20000 words represent passive vocabulary, with only a third to a half of that active vocabulary. Note that that number is an average — some students would have a much larger vocabulary, others a much smaller one. And as Dan says, American high school students learn vocabulary in context, with very little time dedicated to “memorizing” lists of words. One suggestion would be to learn a bit about Latin (and Greek) roots, prefixes, and suffixes, as this will allow you to analyze a lot of academic vocabulary.

High-school-age students--if they are native English speakers--are said to have a vocabulary of about 20,000 words, on average. It is probably best to acquire vocabulary by using it. A good way is to find material you really want to read, about something you enjoy, that is "hard" but not "too hard."