Numerical comparisons have been made between exact and approximate solutions to the two-group space-time diffusion equations. Two slab cores were studied, one 240-cm thick and the other 60-cm thick. Prompt critical bursts and limited ramp insertions of reactivity were simulated by imposing perturbations on the fission cross sections throughout the first quarter of the core. Feedback effects were neglected. Results were obtained using the conventional point kinetics equation, the adiabatic approximation and the space-time synthesis method. For one situation, two nodal methods were also examined. Comparisons with the exact space-time solutions suggest that, when the point kinetics equations are expected on qualitative grounds to be a poor approximation, the actual quantitative errors can be extremely large. Of the other approximations tested the space-time synthesis method gave the most accurate results.