Approaches to learning have been identified as crucial factors that influence students' mathematics performance. However, there have been mixed findings on which of the different approaches improve performance in undergraduate mathematics. Thus, this study aimed to unravel the specific effects of prior mathematics knowledge and approaches to learning on performance in mathematics among first-year engineering students. The design is cross-sectional, and the data are analysed with some structural equation modelling techniques. The findings show a positive effect of prior mathematics knowledge on performance. The effect of surface approaches to learning on performance is significant, negative, and surface approaches to learning mediate the effect of prior mathematics knowledge on performance. There are no substantial relations between prior mathematics knowledge, deep approaches to learning, and performance. Students who adopt surface approaches performed poorly but we found no evidence to claim that students who adopt deep approaches perform better in the course. By implication, our findings underscore the importance of discouraging engineering students from capitalizing on surface approaches to learning mathematics.