Some mathematical models for deciding the number of examination questions on computerized adaptive tests

The computerized adaptive test (CAT) was developed to obtain an efficient estimate of an examinee's ability. In traditional paper-and-pencil tests, all examinees had to answer the same number of questions. This kind of test was not fair for every examinee. Consequently, the CAT plays an important role in fair and adaptive examinations. However, the basic and necessary requirements in the CAT are the databases and computer operation rules of the examination system. This paper presents some mathematical algorithms dealing with the number of questions for the examination system. The algorithms are feasible and can determine the reasonable number of questions for a CAT system.