University Malaya enrolls students from all states in Malaysia as well as a small number of students from overseas. The objective of this paper is to investigate the effect of past performance on students at three faculties, namely, Faculty of Economics and Administration(FEA), Faculty of Business and Accounting(FBA) and Faculty of Arts and Social Sciences(FASS). Students' prior achievements include their entry scores or points in English language proficiency and mathematics at the Malaysian Certificate of Education (MCE) level. Other factors taken into consideration are gender of students and their ethnic origins. Research results show that entry points are an important factor in influencing students' achievement in all three faculties. Apart from this, female students are found to have better results than their male counterparts in FBA and FASS. It was also found that mathematics performance at the MCE level is one of the influential factors for academic achievement in FBA. (Contains 1 table and 4 figures.)