Students are admitted into higher education based on their past performance. This paper compares two measures of past cognitive skills: teacher and national exam scores. By using a nationwide dataset, we look at how the predictive power of teacher assessment and exam scores for selecting successful students may vary with the degree of selectivity of higher education programmes. We find that teacher scores predict students' performance in higher education more accurately, and its predictive power remains the same independently of the selectivity programme indicator considered. We found that national exam scores are noisier and only gain relevance for highly selective programmes. Furthermore, we explore national exams' volatility and institutional selectivity as potential mechanisms to justify the results. Our results provide solid policy hints on the role that high school scores and admission exams should have for access and performance in higher education.