Background: Various findings regarding the relationship between math anxiety and engagement have been identified in the literature, with many focusing on general math anxiety and overall math engagement. Objectives: Based on the control-value theory, this study examined the relationships between trait- and state-math anxiety and behavioural and cognitive engagement in math under daily practice and exam preparation conditions across math tasks of varying difficulty levels. Methods: A survey study with 449 high school students and an experimental study with 33 freshmen were conducted. Students' trait- and state-math anxiety, as well as behavioural and cognitive engagement in math, were measured under daily practice and exam preparation conditions across easy and difficult math tasks. Results: A two-level latent variable model was built in the survey study, and two-way ANOVAs and regressions were used in the experimental study. Students exhibited greater state anxiety under exam preparation conditions in the survey study and showed differences in state-math anxiety and engagement across learning contexts and math tasks in the experimental study. Students with higher trait-math anxiety displayed less engagement in both studies, while those with higher state-math anxiety when facing difficult tasks tended to engage more cognitively in the experiment. Conclusions: These findings demonstrated discrepancies in the relationships between trait- and state-math anxiety and math engagement, while accounting for learning context and task difficulty.