。
She is convinced that she'll pass the exam.
Literal
She [topic-は] exam [target-に] will-pass [quotative-と] is-convinced.
確信する ('to be convinced of') is one of many Japanese verbs of cognition that take their content with the quotative と — joining 思う ('think'), 信じる ('believe'), 言う ('say'), 感じる ('feel'). The と packages the preceding clause as the content of the conviction. Note that the embedded clause uses plain non-past 合格する, not the volitional or future-marked form — Japanese doesn't grammatically distinguish present from future, so plain non-past covers both 'will pass' and 'is passing' depending on context. The progressive ~ている marks an ongoing mental state.