Mathematics is a language for expressing physical, chemical and engineering laws nevertheless engineering students often perform poorly in mathematics. Studying can be influenced by several different social, cognitive and non-cognitive factors which all can have an impact on students' academic performance. Many researches revealed positive effects of mathematics self-efficacy on mathematics achievement. Similar results can be found among learning approaches, students using deep-approach achieve better results. It is legitimate to question whether there is a relationship between self-efficacy and learning approaches. My research focused on the interrelationship between two aspects of mathematics self-efficacy (mastery experience, physiological state), learning approaches (deep strategy, deep motive, surface strategy, surface motive) and achievement. This research also examined the variance of self-efficacy, learning approaches and achievement in relation to the number of failed attempts. 306 undergraduate engineering students at a Hungarian university took part in the study. To examine the above mentioned question the study employed quantitative approach and data were collected using two questionnaires during the semester. The self-efficacy scale was adapted from a variety of sources and was modified to local conditions. To measure learning approaches the Revised Two Factor Study Process Questionnaire was rephrased to the domain of mathematics and to the local conditons. The data were analysed quantitatively using descriptive statistics, bivariate correlation, partial correlation, and regression analysis. The results show that self-efficacy, learning approaches and academic achievement were strongly correlated with each other. Students who have higher level self-efficacy use deep strategy in learning and have deep motives, while students classified as low in self-efficacy adopted surface learning approaches. A new variable was introduced which has not been investigated yet in other researches: the number of failed attempts. A significant correlation between the mentioned variables and the number of attempts was identified. My results demonstrate the importance of such kind of learning environment which fosters self-efficacy and deep learning approach.