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She tried hard to pass the exam.
Literal
She [topic-は] exam [target-に] let's-pass [quotative-と] made-an-effort.
The pattern [verb-volitional]+と+[verb of effort/thought] expresses purpose by packaging the volitional intention as the content of the second verb — '(intending) to X, did Y.' Here 合格しよう ('let's pass / will pass') is the volitional form, と marks it as the goal, and 努力した is what she actually did toward that goal. Functionally close to ~ために ('in order to') for stating purpose, but more about the inward intention guiding the effort — ~ために sounds more like a formal stated purpose, while volitional + と feels more like the will-to-act behind it. Both work, with subtle nuance differences.