Tertiary institutions are experiencing an increased number of enrolments, with students varying in their demographics, previous education, and academic achievement. This relative increase in undergraduate enrolments in Australia has not translated to an increase in student retention or graduate numbers. This prompts the need to explore predictors of academic performance for tertiary students to identify those most at risk of underperforming. This study aimed to investigate the relationship between secondary school subject completion and undergraduate grade point average (GPA). A cohort of 709 secondary school students entering undergraduate health science courses between 2012 and 2015 at an Australian university were investigated. Completion of Mathematics 3C3D, Physics, Chemistry and Physical Education Australian Tertiary Admission Rank (ATAR) subjects were significantly associated with GPA. In a subset of 458 students, longitudinal analysis revealed completion of secondary school Mathematics 3C3D was a significant predictor of academic performance over the duration of the tertiary health science courses. The results suggest that completion of advanced secondary school mathematics, but not physical sciences, is predictive of student achievement. This outcome further supports the need for improved uptake and completion of advanced mathematics in secondary school.