<p>Mathematics self-efficacy (MSE), that is students’ beliefs about their ability to be&#xa0;successful in mathematics, is important because it can predict future academic and career achievement, effort, and success on difficult tasks. However, sometimes there students’ self-efficacy may not match their performance, which we call incongruous mathematics self-efficacy (IMSE). Little previous work has examined IMSE and none has examined it at the level of specific mathematics tasks in university intermediate algebra. In this study, fifteen participants were interviewed and asked about their task-specific MSE for three problems, two purely algebraic and one word problem, that they were then asked to solve. We compared participants’ MSE and their solutions to identify instances of incongruous task-specific MSE, finding them for eleven of the fifteen participants. For example, on the word problem, one participant rated the problem as difficult and expressed low confidence in her work but solved the problem correctly. We describe 12 total instances of task-specific IMSE in qualitative detail. Our results have implications for the measurement of MSE as well as for university educators who strive to better support students’ education.</p>