We discuss a study to evaluate the extent to which free-response questions could be approximated by multiple-choice equivalents. Two carefully designed research-based multiple-choice questions were transformed into a free-response format and administered on the final exam in a calculus-based introductory physics course. The original multiple-choice questions were administered in another similar introductory physics course on final exam. Findings suggest that carefully designed multiple-choice questions can reflect the relative performance of the free-response questions while maintaining the benefits of ease of grading and quantitative analysis, especially if the different choices in the multiple-choice questions are weighted to reflect the different levels of understanding that students display.