We examine how student aptitudes impact how much students learn from doing graded online and written homework in an introductory electricity and magnetism course. Our analysis examines the correlation between successful homework completion rates and exam performance as well as how changes in homework completion correlate with changes in exam scores for students with different physics aptitudes. On average, successfully completing many homework problems correlated to better exam scores only for students with high physics aptitude. On the other hand, all other students showed zero or even a negative correlation between successful homework completion and exam performance. Low-and medium-aptitude students who did more homework did no better and sometimes scored lower on exams than their low-and medium-aptitude peers who did less homework. Our work also shows that long-term changes in homework completion correlated to long-term changes in exam scores only for students with high physics aptitude, but not for students with medium or low aptitude. We offer several explanations for the disparity in homework learning gains, including cognitive load theory, ineffective homework strategies, and various mismatches between homework and exams. Several solutions are proposed to address these possible deficiencies in graded online and written homework.