Separate tests of mathematics skills, proportions and translations between words, and mathematical expression given the first week of class were correlated with performance for students who completed a college physics course (completes) and students who dropped the course (drops). None of the measures used discriminated between completes and drops as groups. However, the correlations between score on the test of math skills and on both of the measures involving mathematical reasoning (proportions, and translations) were dramatically different for the two groups. For the completes, these correlations were slightly negative, but not significant. For the drops, the correlation was positive and signficant at the p < 0.01 level. This suggests the possibility that the students who complete the course tend to have independent cognitive skills for the “mechanical” mathematical operations and for questions requiring some degree of reasoning, while, in contrast, the same skills for students at high risk for dropping overlap significantly. The study also found that when students are given the results of mathematics skills tests in a diagnostic mode, with feedback on specific areas of weakness and time to remediate with self study, the correlation between mathematics and physics is lower than previously reported values.