The main purpose of this study was to determine the direct and indirect effects of mathematics anxiety on achievement in mathematics of first year science and engineering students. Data were obtained from a descriptive survey from 245 (201 male, 44 female) students from five departments of two faculties. Instruments used for data collection were standard scales of mathematics self-efficacy and mathematics anxiety adopted from MSES-R and RMARS for self-efficacy and anxiety, respectively. Factor analysis was used for data reduction and Cronbach's a was obtained to check reliability of each factors. The independent samples t-test was conducted to compare means. Finally, path analyses were done to determine the direct and indirect effects of anxiety factors on mathematics achievement. The results indicate that the anxiety and self-efficacy scales yielded three factors each; the level of prevalence of mathematics anxiety among the gender groups was high for test- and task-related anxieties and moderate for course-related anxiety; no significant gender difference in anxiety was observed; gender difference was significant in only mathematics capability and engagement in mathematics self-efficacy; all the anxiety factors and only two of the self-efficacy factors have significant direct effects on mathematics achievement; and the mathematics test anxiety has significant indirect effect as well through mathematics capability self-efficacy. Recommendations were forwarded that mathematics instructors should support female and mathematics test-anxious students by decreasing mathematics test anxiety and enhancing mathematics self-efficacy to do test. Specifically, teachers can cut students' test anxiety in test taking situations through planned strategies of both teaching as well as preparing students for tests.