Learn Turkish: Sınavdaki uzun paragrafları usanmaksızın okudu. - He read the long paragraphs in the exam without getting fed up.

It attaches to the verb root usan (from usanmak, meaning to get fed up or bored). The suffix -maksızın (or -meksizin) is a formal way to say "without doing [verb]." Here, it describes the state in which he read: without getting fed up.

Could I just say usanmadan instead of usanmaksızın?

Yes, absolutely! The suffix -madan / -meden means the exact same thing ("without doing") and is much more common in everyday spoken Turkish. The -maksızın suffix taught in this lesson is highly formal and mostly used in writing, literature, or formal speeches.

Can you break down the word Sınavdaki?

It consists of sınav (exam) + -da (the locative suffix meaning "in" or "at") + -ki (a suffix that turns the location into an adjective). Together, it means "the one(s) in the exam." It acts as an adjective describing exactly which long paragraphs he read.

Why does paragrafları have the accusative case suffix?

The accusative case suffix (-ı) is required because the paragraphs are a specific direct object. We aren't talking about reading paragraphs in general; we are talking about the specific long paragraphs in the exam, as pointed out by the word Sınavdaki.