The relation between academic achievement and various measurements of cognitive abilities, problem-solving skills and self-managed learning has been established in the research before the COVID-19 pandemic and distance learning. The aim of the current research was to analyze the extent to which these aspects predicted the educational achievement of 9th grade students (mean age 15.4 years) during distance learning, when students had to do relatively more tasks independently, organize their daily learning and deal with problems on their own. Relations between self-assessed problem-solving skills, self-management skills, tests of reasoning abilities and the results of diagnostic tests in Mathematics and Latvian were analyzed for n = 256 and n = 244 students, respectively. The results show that: (1) diagnostic test results in Mathematics are best predicted by the parental education level, fluid nonverbal reasoning and verbal reasoning; (2) the best predictors for the results in the diagnostic test in Latvian are parental education, flexibility to change the solution, fluid nonverbal reasoning and verbal reasoning; (3) self-management cannot significantly predict the results of either of the two tests, although it correlates to the results of the tests in both Mathematics and Latvian; (4) only one of the aspects of problem-solving, flexibility to change the solution, can significantly predict results in diagnostic tests. The results confirm the significance of cognitive abilities as an important predictor of academic achievement, as well as the role of parents’ education level. The results also suggest that the flexibility to change the solution, an aspect of problem-solving, might play a role in students’ success in academic tests.