This paper uses an item response model to analyse a set of response data in a test consisting of a mixture of one-component items and two-component items. The items are measuring quantitative reasoning and numerical facility. In each of the two-component items, the second component is dependent upon the first so that the condition of local independence is violated at the component level. A multicomponent model based on conditional probabilities expressed in a modified form of the logistic function is fitted to the data. Ability estimates of the students and diffculty esimates of the items along the teo dimensions of abilities are obtained.