The article describes the development and evaluation of a web-based pre-course in mathematics, delivered to four cohorts of engineering students at a German university. Based on demographic, personal, and learning-related data relationships between students' preconditions, their learning gains in the pre-course, and study success in the degree programme were analysed. The results support the existing literature in that domain-related prior knowledge and secondary school achievement play a dominant role regarding study success in engineering. The analyses also showed that the influence of cognitive predictors could only be compensated for by a strong learner engagement. At-risk students with high pre-course learning gains showed significantly better first-year performance. The number of self-tests a student attempted was positively related to pre-course learning gains and even to first-year performance, suggesting that this variable is a good indicator of student engagement.