Results from PISA 2003 for Germany show considerable differences between students' comparably high problem-solving competence and their average mathematical competence. According to the cognitive potential application hypothesis, this difference can partly be ascribed to students not applying their competencies effectively in the specific test situation. To investigate this hypothesis, effects of test context and moderator effects of mathematical self-concept and mathematics anxiety on achievements in mathematics (Study 1, n = 256) and problem-solving (Study 2, n = 259) were investigated in an experimental design. Both studies showed a negative effect of the mathematical context, especially for students with low mathematical self-concept and for students with high mathematics anxiety. Implications of these results for the assessment as well as the training of cross-curricular and domain-specific problem-solving competencies are discussed.