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Using the capabilities of the knowledge structure theory, the researcher prepared a model for the experts’ knowledge structure of the valid test items of the university Calculus topic “trigonometric substitution of indefinite integral about integrands involving quadratic square root”. After the Calculus course was taught and tested, this knowledge structure model was combined with Bayesian network analysis to find the best recognition rate of Bayesian network and to identify easily the error types that students might make in learning “trigonometric substitution” unit. Then, the statistical information was analyzed using the Bayesian probability analysis methods to establish the “trigonometric substitution” unit model as an example of a Bayesian network adaptive diagnostic test system, to determine four established Bayesian network models to compare their recognition rates, and to establish this structure could be used as the foundation for developing remedial teaching approaches. [ABSTRACT FROM AUTHOR]