If she ______ hard, she would have passed the exam.

Had worked is the correct answer. This sentence is in the third conditional, which is used to describe an unreal or hypothetical situation in the past. The structure is: If + had + past participle, would have + past participle.

• Has worked is incorrect because the present perfect tense is not used in third conditional sentences.
• Worked is incorrect because the simple past tense is used in the second conditional, not the third conditional.
• Had worked is correct because it is the past perfect tense required in the if-clause of a third conditional sentence.
• Had been worked is incorrect because it is an incorrect passive construction in this context.