Background: Student persistence in undergraduate engineering majors often depends on how they perform in foundational engineering courses. Although mastery of prerequisite knowledge affects how students perform in these courses, research suggests that achievement goal orientations and task-value and self-efficacy beliefs play prominent roles in predicting students' achievement. Purpose/Hypothesis: Drawing on achievement goal, expectancy-value, and self-efficacy theories, this study explores the relationships and relative predictive significance of students' achievement goal orientations and task-value and self-efficacy beliefs on academic achievement when prior knowledge and class attendance in a foundational engineering course were accounted for. Design/Method: Participants were students enrolled in engineering statics at a primarily White institution. A multiple regression analysis was conducted using achievement goals, self-efficacy for learning performance, task value, absence, and prior knowledge as predictor variables, and participants' achievement scores as the outcome variable. Results: Positive relationships were observed between the different achievement goal constructs. The final regression model explained 50% of the variance in participants' achievement scores. Self-efficacy and task-value belief effects remained significant predictors of achievement, even after prior knowledge and regular class attendance were considered. Further, the combined effect of self-efficacy and task-value beliefs on achievement was larger than that of prior knowledge alone. Conclusions: Pedagogical approaches that seek to improve engineering students' task-value and self-efficacy beliefs may be more efficacious at promoting achievement than those that focus on fostering achievement goal orientations. Instructors should consider such approaches along with those that effectively address differences in prior knowledge in foundational engineering courses.