Digital tests make it possible to identify student effort by means of response times, specifically, unrealistically fast responses that are defined as rapid-guessing behavior (RGB). In this study, we used latent class and growth curve models to examine (1) how student characteristics (i.e., gender, school type, general cognitive abilities, and working-memory capacity) are related to the onset point of RGB and its development over the course of a test session (i.e., item positions). Further, we examined (2) the extent to which repeated ratings of task enjoyment (i.e., intercept and slope parameters) are related to the onset and the development of RGB over the course of the test. For this purpose, we analyzed data from N = 401 students from fifth and sixth grades in Germany (n = 247 academic track; n = 154 non-academic track). All participants solved 36 science items under low-stakes conditions and rated their current task enjoyment after each science item, constituting a micro-longitudinal design that allowed students' motivational state to be tracked over the entire test session. In addition, they worked on tests that assessed their general cognitive abilities and working-memory capacity. The results show that students' gender was not significantly related to RGB but that students' school type (which is known to be closely related to academic abilities in the German school system), general cognitive abilities, and their working-memory capacity were significant predictors of an early RGB onset and a stronger RGB increase across testing time. Students' initial rating of task enjoyment was associated with RGB, but only a decline in students' task enjoyment was predictive of earlier RGB onset. Overall, non-academic-school attendance was the most powerful predictor of RGB, together with students' working-memory capacity. The present findings add to the concern that there is an unfortunate relation between students' test-effort investment and their academic and general cognitive abilities. This challenges basic assumptions about motivation-filtering procedures and may threaten a valid interpretation of results from large-scale testing programs that rely on school-type comparisons.