Physics instructors and education researchers use research-based assessments (RBAs) to evaluate students' preparation for physics courses. This preparation can cover a wide range of constructs including mathematics and physics content. Using separate mathematics and physics RBAs consumes course time. We are developing a new RBA for introductory mechanics as an online test using both computerized adaptive testing and cognitive diagnostic models. This design allows the adaptive RBA to assess mathematics and physics content knowledge within a single assessment. In this article, we used an evidence-centered design framework to inform the extent to which our models of skills students develop in physics courses fit the data from three mathematics RBAs. Our dataset came from the LASSO platform and includes 3,491 responses from the Calculus Concept Assessment, Calculus Concept Inventory, and Pre-calculus Concept Assessment. Our model included five skills: apply vectors, conceptual relationships, algebra, visualizations, and calculus. The "deterministic inputs, noisy 'and' gate'' (DINA) analyses demonstrated a good fit for the five skills. The classification accuracies for the skills were satisfactory. Including items from the three mathematics RBAs in the item bank for the adaptive RBA will provide a flexible assessment of these skills across mathematics and physics content areas that can adapt to instructors' needs.