Research has identified several aspects that influence students' transition to mathematics studies at university, but these aspects have often been studied separately. Our study contributes to the field's understanding of the transition between upper secondary and university mathematics by taking a multifaceted perspective not previously explored. We analyse experiences and attainment in mathematics of 154 engineering students with respect to known aspects of this transition, and our results show that it is important to consider several aspects together in order to understand the full complexity of the transition. It is revealed that students with previous experiences of university studies, when compared with new first year undergraduates, perceive a larger difference between studying mathematics at the upper secondary level and university. Our results also show that the engineering students enrolled in distance programmes experience larger differences between secondary and tertiary levels than engineering students enrolled in campus programmes. Furthermore, our analyses show that students' success in mathematics is related to their perceptions of the rift experienced in the transition. In all, our results highlight the importance of taking a student perspective in the development of explanatory and useful models of students' transition between upper secondary and university mathematics.