This study introduces procedures for constructing a proficiency scale for a large-scale test by applying Tatsuoka's Rule Space Model. The SAT Mathematics (SAT M) Section 2 is used for illustrating the process and the results. A task analysis is summarized in a mapping sentence, and then 14 processes and content attributes are identified for explaining the underlying cognitive aspects of the examinees' performance on the SAT M. Analysis results show that almost 98 percent of 2,334 examinees are successfully classified into one of 468 cognitive states. The cognitive states are characterized by mastery or non-mastery of the 14 attributes. Attribute Characteristic Curves, which are conditional probability functions defined on the SAT Scale, are introduced and used for interpreting an examinee's proficiency. Prototypes of a student's performance report and a group performance report are given as examples of possible ways for summarizing the analysis results. The study contains 19 tables and 1 figure. One appendix (two tables) introduces the Rule Space Model. (Contains 38 references.) (Author)