In this longitudinal study, we investigate how demographic, cognitive and meta-cognitive variables affect students' success in chemistry and physics exams in two Science-Technology-Engineering-Mathematics undergraduate courses, biology and engineering. Independent variables include high school final examination performance, chemistry and physics marks, self-efficacy and accuracy of self-evaluation, namely the difference between the estimation of one's own performance in a specific task measured with a confidence rating scale and the actual performance score. We involved 81 biology and 125 engineering freshmen students in the study. Biology students were attending a General Chemistry course, while Engineering students were attending a General Physics course. Accuracy of self-evaluation scores were calculated through Rasch analysis of responses to an instrument that included chemistry and physics items, and a confidence tier. We found that for both courses, the likelihood of passing the exams of chemistry and physics was significantly predicted solely by their accuracy of self-evaluation accuracy score. We found the overconfident students had lower likelihood of passing the exam. Our results suggest that the perception of one's own ability is a relevant factor for predicting students' success at undergraduate level and can be a better predictor of academic success than high school performance and self-efficacy.