Given the policy goals of course graduation requirements (CGRs), this study first tests the hypothesis that CGRs promote academic excellence and equity by both improving student performance ("productivity hypothesis") and reducing the gap between student groups as defined by academic ability, race/ethnicity, and socioeconomic status ("equality hypothesis"). This study also assesses whether and how schools differ in CGRs' effects by testing the following hypotheses that CGRs affect student outcomes more positively in schools with (1) higher concentration of advantaged peers ("school structure hypothesis"), (2) greater academic/instructional capacity ("academic organization hypothesis"), and (3) stronger academic norms/climate ("social organization hypothesis"). This study analyzes the data from the High School Longitudinal Study of 2009 (HSLS:09) that provide the information on high school CGRs in several academic subjects at the school level and rich survey data on students, teachers, and schools. The analytic sample is limited to those respondents who were first-time ninth graders in fall 2009 and participated in both 2009 base-year and 2012 follow-up survey and with valid information on their high school CGRs. The empirical findings show that (1) higher math CGRs had positive effect on student math cognitive improvement, and (2) higher CGRs both in math and science had no impact on student test scores yet decreased the likelihood of students attending a four-year college in the semester after high school senior year. The second set of key findings indicates that students who are multiracial, lowest- and highest-achieving benefited the most by enrolling in schools with higher math and science CGRs while high-middle socio-economic status (SES) students who attended higher math and science schools had significantly lower math scores and lower probability of enrolling in a four-year college. The third set of key findings identifies two key school moderators, advanced course offering and student engagement in school, could optimize the CGR effects. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]