Computer-based testing--is an effective teacher's tool, intended to optimize course goals and assessment techniques in a comparatively short time. However, this is accomplished only if we deal with high-quality tests. It is strange, but despite the 100-year history of Testing Theory (see, Anastasi, A., Urbina, S. (1997). Psychological testing. Upper Saddle River, NJ: Prentice-Hall) there still exist some misconceptions. Modern wide-spread systems for computer based course management and testing reveal a set of problems corresponding to certain features of testing methods. This article is devoted to some omissions typical to several course management systems (e.g., Moodle and Blackboard). These omissions and the ways of avoiding them are shown in a simple test intended to verify student knowledge. We suggest a special test description language dedicated to drawing your attention to the mathematical aspects of test quality. The language can also be realized in computer software. We provide an example of such software in this article.