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bent on (doing something)
Very determined to do something, perhaps aggravatingly so. She's bent on coming here for the weekend, so we better clean the guest room. I'm bent on getting an A on this exam, so I've been studying all week.
Also, bent upon. Determined, resolved, as in Jamie is bent on winning the math prize. This phrase, first recorded in 1762, always uses the past participle of the verb bend in the sense of "tend toward."