This study examined the mediation and moderation of membership in a demographic group underrepresented in physics classes on course outcomes measured by course grades and Force and Motion Conceptual Evaluation (FMCE) post-test scores. The study used a large dataset (N = 4490) of course grades, SAT and ACT mathematics scores (ACTM), and matched FMCE pretest and post-test scores to investigate differences by gender, underrepresented ethnic or racial minority (UERM) status, and status as a first-generation college student (FGCS). For UERM and FGCS students, ACTM and pretest scores significantly mediated the relation of membership in the demographic group and both course grade and post-test score. Differences between minority and majority members of these groups were largely removed by controlling for ACTM and pretest scores. The overwhelming majority of the effect acted through ACTM for course grade (60% and 45%, respectively), while more of the effect acted through pretest score for the post-test (36% and 48%, respectively). As such, for these groups prior preparation measures predict physics outcomes (course grades or post-test scores) differently. The mediational relations for gender were dramatically different. No mediation was detected for the relation of gender to course grade because no significant difference in course grade existed. Sixty percent of the effect of gender on post-test score was not explained by either ACTM or pretest score; pretest score accounted for 38% of the effect. As such, the majority of the difference in post-test scores between men and women was not explained by either ACTM or pretest scores. Significant moderation was also detected showing that the relation of these variables was not consistent for members of all demographic groups.