Students' self-efficacy expectations (SEE) in mathematics are associated with their engagement and learning experiences. Going beyond previous operationalisations of SEE we propose a new instrument that takes into account not only "facet-specificity" (expectations related to particular competences or skills) and "strength" (confidence of the expectations), but also "level" (perceived task difficulty) of these expectations as proposed by Bandura ("Self-efficacy: The exercise of control," W. H. Freeman & Co, New York, 1997; "Self-efficacy beliefs of adolescents," Information Age Publishing, Greenwich, 2006). In particular, we included level-specific items referring to perceived difficulty on a subsequent national test in mathematics. In total 756 Norwegian grade 5, 8, and 9 students completed the "Self-Efficacy Gradations of Difficulty Questionnaire." We fitted plausible multitrait-multimethod models using structural equation models. The best fitting model included three factors representing levels of perceived difficulty, and a-priori specified correlated uniquenesses representing four facets. The facets related to problem solving or students' self-regulation skills during the test in order to accomplish the following: (1) complete a certain number of problems, (2) solve tasks of a certain challenge, (3) concentrate, and (4) not give up for a certain amount of time. The results indicated that three correlated constructs representing levels of SEE are associated with scores on national tests in mathematics, and that the strongest association is between national test scores and medium level SEE. Taking level (difficulty) into account broadens our understanding of the self-efficacy construct, and allows investigation into differential relationships between SEE and performance.