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I'm taking the university entrance exam next week.
Literal
Next-week, university [possessive-の] entrance-exam [object-を] receive.
入学試験 ('entrance exam') is a compound 入学 ('entering school') + 試験 ('exam'). Japanese university entrance exams are a cultural institution — the intense 受験 (exam-taking) period dominates the final year of high school. Worth noting the cultural weight behind this simple phrase.