Educational inequalities in access to higher education are constituted by multiple intersecting factors that impact equity and the pursuit of tertiary studies. This study seeks to explore the disparities related to gender, socioeconomic level, rurality or urbanicity, and academic trajectory of 202,688 Chilean students who graduated from high school in 2016, to elucidate how these variables generate intersections that impact access to higher education. To carry out the analysis, an intersectionality approach was considered and an innovative quantitative model called the Multilevel Analysis of Individual Heterogeneity and Discriminant Accuracy (MAIHDA) model was applied, which allows for entering multiple variables to generate a complex analysis of their interactions. The results showed that a large amount of variance (20%) in math scores is explained by the aforementioned variables. These are socio-demographic variables, which ideally should not be indicative of one's academic performance. It was also found that males, students of higher socioeconomic status, those from urban areas, and those with more favorable academic trajectories tend to have higher test scores. In addition, relevant interactions and mutual reinforcement between variables were identified. These results highlight the need to address the barriers and inequalities certain groups face in accessing higher education.