This paper presents the first test of the popular trajectory surface-hopping (TSH) method against accurate three-dimensional quantum mechanics for a reactive system. The system considered is a model system in which an excited atom with an excitation energy of 0.76 eV reacts with or is quenched by the H2 molecule. The electronically nonadiabatic collisions occur primarily near a conical intersection of an exciplex with a repulsive ground state. The accurate quantal results are calculated using the outgoing wave variational principle in an electronically diabatic representation. Four variants of the TSH method are tested, differing in the criteria for hopping and the component of momentum that is adjusted in order to conserve energy when a hop occurs. Coupling between the ground and excited surface occurs primarily in the vicinity of a conical intersection and is mediated by an exciplex found on the upper surface. We find that the overall TSH quenching probabilities are in good agreement with quantum mechanical results, but the branching ratios between reactive and nonreactive trajectories and many of the state-selected results are poorly reproduced by trajectory calculations. The agreement between trajectory surface hopping and quantal results is on average worse for the relatively more "quantum mechanical" j = 0 initial state and M + H2 quenching process and better for the relatively more "classical" j = 2 initial state and MH + H′ reactive process. We also perform a statistical calculation of overall quenching probability and unimolecular rate of the nonadiabatic decay of the exciplex. We find that only about 10 % of trajectories can be described as "statistical" and that statistical calculation overestimates the total quenching rate significantly.