The study aimed to determine if any of the entry requirements such as Ordinary Level (OL) results, Unified Tertiary Matriculation Examination (UTME) scores or Post-UTME (PUTME) scores could predict an outstanding academic performance of first-year undergraduate students admitted into the Faculty of Science in the Kaduna State University, Kaduna. The study adopted the descriptive research design. A purposive sample of nine hundred and forty-three (943) first-year students constituted the population for the study were drawn from Computer Science, Mathematics and Physics undergraduate degree programmes from the Faculty of Science of the university who were admitted from the 2010/2011 to 2014/2015 academic sessions. The instruments for data collection were OL, UTME and first-year Cumulative Grade Point Average (CGPA) results, which were coded and analysed with the aid of Computational Statistical Package for Social Sciences (SPSS). Pearson Product Moment Correlation (PPMC) Coefficient and Multinomial Logistics Regression (MLR) were the statistics used to answer the four research questions used. The results revealed that with a weak correlation, OL is a good predictor on the CGPA, a dependent variable, for academic performance which holds true for students who are in the CGPA category of '1st class' and '2nd Class Lower' respectively. It concluded that the use of OL and UTME as instruments is not enough to select candidates for admission and therefore recommended that other instruments such as senior secondary school mock examinations need to be included as part of the entry requirements in the admission criteria.