Is "Klassenarbeitsangst" a real word? Does it accord with general rules of compound noun formation?

At the end of a Duolingo story a question is presented to me:

Worum ging es in der Folge?

Italienisches Essen Mathematikprobleme Klassenarbeitsangst (correct answer)

It was easy to pick the right answer but having never seen the word Klassenarbeitsangst I looked it up. With quotation marks the exact word seems rare and doesn't yield a lot of hits on Google. Angst vor Klassenarbeiten seems to be the most common way to say the same thing. I have seen Prüfungsangst so I guess Klassenarbeitsangst makes sense, but is it a real word that people use?

This kind of thing is common in German, and as a learner one skill you need to pick up is how to decipher these compound words. English does pretty much the same thing, except instead of keeping the components as separate words or hyphenating them, German runs them together to make a single word. And this can be done even when the word is only used once. German has a reputation for extremely long words because of this habit, but many of the longest words are actually legal terms that aren't used in everyday conversation. Still, compound words do appear in everyday use and it's not uncommon to see see compounds that don't appear in any dictionary, or indeed have never been used before or since they were coined. (By the way, German is by no means the "worst offender" in this respect. There are many languages which allow words to be joined together ad infinitum. The Wikipedia article Longest words has many examples from other languages.)

In this example, it's easy to pick out three common words that might be components of this compound: "Klasse", "Arbeit" and "Angst", or "Class", "Work" and "Fear". Note that German may insert an 'n' or and 's' between words. There are three parts here and so there are two ways to group them into larger pieces. When there's a choice, the grouping is usually left to right, and it turns out this makes more sense here since "Klassenarbeit" can be found in a dictionary; in fact it has a specialized meaning that is related to, but hard to deduce from the component parts. In this case, even though the components might imply "class work", it's really a test or exam. (Note that the educational systems in German speaking countries are not the same as the ones in the US or UK, and indeed the US educational system is not the same as the UK educational system. So it may be difficult to find exact translations for the German words for different types of tests.) In cases where the meaning of the compound is not obvious from the meanings of the components, the compound will be found in dictionaries. So now we have, using context as an additional clue, "Klassenarbeit" + "Angst" which is "a (type of) test" + "fear or anxiety" and the result in English is "test anxiety". One way to verify this to look at the corresponding articles in German and English Wikipedias. English Test anxiety links to German Prüfungsangst and vice versa. "Prüfung" also means "test" so this makes sense.

Once you get the hang of this kind of thing it's actually very helpful for expanding your vocabulary. If you know of the meaning of each piece you can often use context to figure out the meaning of the whole word even if you've never heard it before, or even if the word can't be found in a dictionary. An example that appeared here recently is "Staatsanwalt". If you know Anwalt means "lawyer" or "attorney", and "Staat" means "state" or "government" then it's not hard to figure our that "Staatsanwalt" means "state attorney", or what we call a "district attorney" in the US. There's no need to look this up in a dictionary, though looking it up may be helpful in getting the exact meaning.

So is "Klassenarbeitsangst" a real word? It depends on what you mean by a word, and in German what counts as a word can be rather fuzzy. It is a word in the sense that it's written as a string of letters without any spaces or hyphens, but it's not a word in the sense that word is something you can look up in a dictionary. I would just call it a "compound" and leave the exact definition of "word" for students of linguistic philosophy.

Finally, does the word formation follow the general rules of compound noun formation? The problem here is that the general rules are kind of situational and hard to predict. You can argue that the "-n-" in "Klassenarbeit" comes from the fact that the plural of "Klasse" is "Klassen". But this seems random since I don't know why "classes work" would make any more sense than "class work". Similarly, you can argue that the "-s-" comes from the genitive case, so "fear of tests". But sometimes the "-s-" is what is called a "Fugen-s" or "join-s", added to make the word easier to pronounce, or perhaps just randomly. The "Compounds" section in Wikipedia's German nouns article has more details and examples if you're interested. Duden may have a long list of complex rules that tell you when to insert these interpolating letters and what they should be, but as a learner I don't think you need to sweat the details. It's enough to know that they do appear sometimes and they can be ignored if necessary. Instead of trying to create these words on your own I think your best bet is probably just to rephrase, at least until you become fluent in the language. I don't think anyone is going to correct you if you say "Angst vor Klassenarbeiten" instead of "Klassenarbeitsangst".

Two useful tools here are the DWDS usage database and Google Ngrams. If you try to look up "Klassenarbeitsangst" in DWDS there is no entry, but the site will automatically show you its guess for how to break down the word and gives you links to each of the parts. On the right side of the screen there is section called "Belege in Korpora" showing occurrences of the word in various text sources such as Wikipedia, Film subtitles, certain newspapers, etc. If the word has ever been used before then it will almost certainly show up in one of them, even if DWDS doesn't have an actual entry. Similarly, Google Books Ngram Viewer shows you usage of the word in books over a given time period. In both cases, 0 results show up for "Klassenarbeitsangst", so I think we can safely say that Duo just made up this word on the fly. But again, that's a perfectly normal and common thing to do in German.

I have never heard the word, and I agree it sounds like it was derived from Prüfungsangst. I can imagine Duolingo made this word up.

That being said, the German language is not "dead" yet. It is still productive, and new words are created continuously. The word is formed "correctly", i.e. according to existing lexical patterns for compounds. Competent speakers of German would easily understand its meaning, even when encountering it for the first time.

Maybe teaching this lesson -- that compound words can be made up and are made up all the time in German -- is actually the intention behind this example in Duolingo.