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A method is described to determine if a constructed mathematical response is equivalent to the correct answer specified by the course author. Based on a combination of random evaluation and operator analysis, the method is theoretically justified for a general class of functions.Possible breakdowns due to computer arithmetic are discussed as well as the difficulties encountered when a function fails to fall in the general class.For CAI applications where a response is considered correct if it is equivalent to the correct answer, the method offers two possible advantages:(I) Only one form of the correct answer is specified.(2) Extensive and time consuming manipulation of expressions is avoided.

A simple analysis of some computer-economic factors involved in comparing multimachine installations versus large single machine installations is given, and a mathematical model is derived to assist policy decisions.