The role of emotions in learning settings such as schools has been widely acknowledged in research and practice. Prior research predominantly follows a variable-centred approach to investigate students’ emotions while person-centred analyses are still scarce. Based on a representative sample of N = 11 131 Swiss students in grade 9, this cross-sectional large-scale study investigates how four trait mathematics emotions (enjoyment, anger, anxiety and boredom) are related to students’ perception of mathematics instruction quality (cognitive activation, lack of classroom management, teacher support) and their mathematics test achievement. Results from structural equation modelling (variable-centred approach) revealed that enjoyment and all three negative emotions are related to two dimensions of instructional quality: cognitive activation and lack of classroom management. Association of emotions with teacher support differed, as associations were not confirmed for enjoyment and anxiety. Enjoyment was not related to achievement, whereas boredom showed positive associations. The results from mediation analyses suggest that the direct associations of perceived cognitive activation and perceived lack of classroom management with mathematics achievement are stronger compared to the indirect associations mediated by student emotions. Latent profile analysis identified four profiles: happy, unhappy, bored, and ambivalent. Students in the happy profile had the highest perception of instructional quality and outperformed the other profiles. Results are discussed in relation to the added value of a person-centred approach to better understand students’ emotions in mathematics education.