"I hope tomorrow's examination is not hard."
Translation:Umarım yarınki sınav zor değildir.
A secondary use of the suffix "-dir" is at the end of predicates of sentences/clauses that involve hope, expectation or conjecture. Words like "umarım (hopefully)", "herhalde (probably)", "muhtemelen (probably)" often bring this -dir with them; especially in cases where the speaker does not know whether the core sentence (in this case, the exam not being difficult) is correct or not.
With "umarım" (unless I'm missing something), when the predicate is not a verb, it always takes -dir.
I hope my explanation is correct: ki here is not a conjunction. I am guessing this suffix -ki here has the role to turn a temporal adverb to an adjective (am I right?). see that -ki still preserves the role of connecting, but this time it is used to connect an adverb and a name to establish a specific connection. It is tomorrow's exam, not not next week's. You have to make that specific.
Ok, so I was happy with what -ki was doing on yarın, but I wondered whether ki as a standalone conjunction after umarım was also needed (e.g. umarın ki yarınki etc.), because what comes after "I hope" in English is definitely a subordinate clause (so a situation where that is optional in English but, according to the Tips & Notes, resquired in Turkish). My assumption was that the -ki on yarın can't do double duty (i.e. BOTH function as a conjunction AND turn yarın into an adjective), but maybe that's not the case.
BTW, thanks for your other comments, which are very helpful. Can I ask, is -ki meant to ignore vowel harmony here?
I am glad you were happy! But, apparently I was not much of help, totally explaining something else :D OK. ... ki as a standalone conjunction after umarım is not needed here at all. (I do not know what Tips and Notes are mentioning about, but) Think of umarım, as "hopfeully" here: like the "Hopefully" in English, Turkish sentence here does not need the "so that" structure. Just simply expressing a hope, there is no need to combine anything. ... Yes. you are right, -ki is ignoring the vowel harmony! Probably, it is because -ki is an Arabic origin suffix. And vowel harmony, I am guessing, is more of an authentic Turkish.