Associations Between State Examination Scores and Performance in Mathematics and Calculus Among Engineering and Technology Undergraduates

The purpose of the article is to evaluate the predictive validity of the ICFES Saber 11 Mathematics and Critical Reading scores for first-semester achievement in Differential Calculus and Fundamental Mathematics among engineering and technology undergraduates. The article describes an empirical evaluation framework descriptive correlational analysis complemented by discriminant analysis based on administrative cohort data, enabling universities to quantify how much variance in course outcomes is explained by pre-admission test scores. Using records for 846 students at the Technological University of Pereira (2019-I and 2019-II cohorts), the authors estimate associations and classification performance to assess the tests’ predictive capacity. The results show that Saber 11 Mathematics accounts for 8.30% of the variance in Differential Calculus performance and 10.24% in Fundamental Mathematics, indicating limited predictive power for these foundational courses. As an example, we illustrate how the evaluation can inform admission policies and early diagnostic placement in basic mathematics. Our proposal allows institutions to complement exam-based entry with targeted learning supports aimed at reducing course repetition and student dropout. The effectiveness of the evaluation is confirmed by variance-explained metrics (R² ≈ 0.083 and 0.102) and discriminant-analysis diagnostics. New research results supplement the literature on state exam predictive validity in higher education and can be used for admissions design and early-warning/academic-support systems. This paper is novel because it provides cohort-level, program-specific evidence from a Colombian university showing the limited predictive capacity of Saber 11 Mathematics for first-semester performance in engineering and technology programs. Keywords: Academic performance, discriminant analysis, correlation analysis, mathematics. DOI： https://doi.org/10.35741/issn.0258-2724.59.6.25