Admissions policy routinely converts a continuous school-leaving mark into a binary threshold. This study asks whether such a threshold is a defensible admissions rule for first-year mathematics-intensive Bachelor of Science pathways, taking a proposed 80% school-leaving Mathematics cut-off at a research-intensive South African university as the worked case. Using institutional data from first-time entrants in the 2024u20132026 cohorts, the study examined school-leaving Mathematics, National Benchmark Test (NBT) in mathematics, and broader pre-university academic measures as predictors of first-semester university mathematics outcomes. Predictive models, threshold analyses, matched-volume admission simulations, differential-prediction tests, and placement analyses were used to distinguish predictive validity from policy usefulness. Within the admitted range, school-leaving Mathematics and NBT Mathematics were related but not interchangeable, and each added information beyond the other. The analyses did not detect a discontinuity at the proposed 80% threshold, and a smooth curve fitted the data better than the binary cut-off models examined. These findings describe the predictive relationship but do not determine the preferred administrative threshold. At the volume implied by the proposed 80% rule, which selected 84.2% of the already-admitted outcome sample, additional pre-university information did not demonstrate a clear increase in passers selected. This finding is specific to that operating point and does not establish the absence of benefit at more selective admission volumes. Differential-prediction analyses also showed that school-leaving Mathematics did not carry the same predictive meaning across population groups. The findings support the predictive relevance of school-leaving Mathematics but do not establish 80% as a uniquely justified admissions threshold. Its policy justification requires explicit consideration of capacity, access, and the consequences of selection errors.