Plots of the first-order reversal curve (FORC) function are used to characterize ferromagnetic particles in rocks. The function is based on classical Preisach theory, which represents magnetic hysteresis by elementary loops with displacement Hu and half width Hc. Using analytical and numerical integration of single-particle magnetization curves, a high-precision FORC function is calculated for a sample with randomly oriented, noninteracting, elongated single-domain (SD) particles. Some properties of the FORC function are independent of the distribution of particle orientations and shapes. There is a negative peak near the Hu axis, and the FORC function is identically zero for Hu > 0. The negative peak, previously attributed to particle interactions, is due to the increasing slope of a reversible magnetization curve near a jump. This peak is seen in experimental FORC functions of SD samples but not of samples with larger particles, probably because of Barkhausen jumps. The second feature is not seen in any experimental FORC function. A spread of the function to Hu > 0 can be caused by particle interactions or nonuniform magnetization.