This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior achievement with the Iowa Algebra Aptitude Test, students from these two paths performed comparably (F = 3.54, p = 0.063) on the PCA. Student errors on the three instruments revealed a lack of understanding of the interpretation or meaning of rate of change regardless of the curricular path. Students successfully calculated the rate of change of linear functions; however, when the function was not linear, students struggled to calculate it, model it on a graph, or interpret it in a real-world context. (Contains 9 tables and 9 figures.)