  We present approaches to quickly simulate systematics affecting CMB
observations, including the effects of the scanning strategy. Using summary
properties of the scan we capture features of full time ordered data (TOD)
simulations, allowing maps and power spectra to be generated at much improved
speed for a number of systematics - the cases we present experienced speed ups
of 3-4 orders of magnitude when implementing the map-based approaches. We
demonstrate the effectiveness of the approaches at capturing the salient
features of the scan by directly comparing to full TOD simulations - seeing
agreement at sub-percent levels of accuracy. We simulate the effects of
differential gain, pointing, and ellipticity to show the effectiveness of the
approaches, but note that one could extend these techniques to other
systematics. We finally show how to apply these fast map-based simulations of
systematic effects to a full focal plane showing their ability to incorporate
thousands of detectors as seen in modern CMB experiments.
