Determining how to provide good tutoring functions is an important research direction of intelligent tutoring systems. In this study, the authors develop an intelligent tutoring system with good tutoring functions, called "FUDAOWANG." The research domain that FUDAOWANG treats is junior middle school mathematics, which belongs to the objective mature domain. Its characteristic is that the knowledge employed is the mature knowledge accepted by most people. FUDAOWANG uses automatic reasoning technology about objective mature problems to realize its intelligence. Based on the results of the automatic reasoning, FUDAOWANG synthetically applies the problem-based tutoring and advanced education concepts to achieve the tutoring functions of stepwise prompt, detailed answers, rethinking after solution, consolidated exercise, etc. The evaluation of FUDAOWANG shows that it is helpful to students in improving learning achievements and cultivating good learning habits. (Contains 1 table, 1 box and 11 figures.)