There were conflicting definitions and misrepresentations of turnover frequency (TOF), catalytic cycle frequency (CCF), and catalytic first-order rate constant (k_cat) in the literature. Based on the Benfield and Lineweaver-Burk methods, data were generated. The results indicated that the CCFs for the forward (~ 0.0025-1.58 exp. (+17)/s) and reverse (~ 0.0003-5.4 exp. (+18)/s) directions showed an increasing trend with higher concentrations of the enzyme; this was applicable to the TOF. The number of fragments per molecule of an enzyme in the forward direction was 0.19-1.23 exp. (+5). In conclusion, TOF and CCF are different parameters, and the former in particular was not the same as k_cat, while the latter was a constant; TOF and CCF vary. Strictly speaking, TOF was equal to f(M_3). Besides, CCF per molecule (> 1) of the enzyme is greater than TOF (< 1). This can be verified using sucrase in a future study; a larger data set is needed if starch is a substrate in order to reevaluate the models and address statistical concerns. PACS: 87.15.RJ; 87.14.ejKeywords: Aspergillus oryzae alpha-amylase; Catalytic cycle frequency; First-order catalytic rate constant; Gelatinized insoluble potato starch; Turnover number; Turnover number frequency.