Approximate analytic solutions exist for particle motion in a one-dimensionl current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn-dusk electric field of 0.1--1 m V/m, lobe field of 10--40 n, and sheet thickness of 1000 km, the analytic solutions as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.