A first-year introductory course on mathematics has been the norm in engineering education. These courses create a solid mathematical background for learning engineering courses. The students who are admitted as a lateral entry in the second year as per norms are deprived of learning these fundamental courses. Instructing mathematics to these students is a challenge because of their limited knowledge of prerequisite mathematical concepts. Hence, a new approach has been considered in the curriculum of an autonomous self-financed college in the University of Mumbai. An audit course is designed, in addition to regular mathematics classes in semester III, which makes the students familiar with the concepts required to achieve mathematical competencies in the Second year. This audit course is compulsory for the Direct Second Year (DSE) students. The author presents some observations concerning the performance of DSE students in Mathematics courses before and after the introduction of the audit course.