An ability-based guessing model is formulated and applied to several data sets regarding educational tests ill language and in mathematics. The formulation of the model is such that the probability of a correct guess does not only depend on the item but also oil the ability of the individual, weighted with a general discrimination parameter. By so doing, the possibility that the individual uses his or her ability to some extent for differentiating among responses while guessing is also considered. Some important properties of the model are described and compared with analogous properties of related models. After simulation studies, the model is applied to different data sets of the Chilean Sistema de Medicion de la Calidad de la Educacion (SIMCE) tests of mathematics and language. The conclusion of this analysis seems relevant-namely, that the examinees use their ability to guess in the language test but not in the mathematics test.