The purpose of this study is to analyse relations between students' attitude towards mathematics, prior knowledge, self-efficacy, expected grades, and performance in mathematics among 115 firstyear engineering students. We combine two statistical techniques to analyse the data we generated by questionnaires and two tests. First, item-level modeling, in terms of confirmatory factor analysis, which we use to compute the factor scores of construct-validated measures, and to control for measurement errors. Second, composite modeling, in terms of path analysis, which we use to test the research hypotheses. The findings show that both self-efficacy and expected grades have substantial effects on students' performance. Prior knowledge has a non-trivial effect on self-efficacy which, in turn, plays a significant role in students' grade expectations. All other hypothesised relations are not significant. We argue that these findings confirm some basic tenets of social cognitive theory.