  We present the first short time-scale ($\sim$hours to days) optical
variability study of a large sample of Active Galactic Nuclei (AGN) observed
with the Kepler/K2 mission. The sample contains 252 AGN observed over four
campaigns with $\sim 30$ minute cadence selected from the Million Quasar
Catalogue with R magnitude $< 19$. We performed time series analysis to
determine their variability properties by means of the power spectral densities
(PSDs) and applied Monte Carlo techniques to find the best model parameters
that fit the observed power spectra. A power-law model is sufficient to
describe all the PSDs of our sample. A variety of power-law slopes were found
indicating that there is not a universal slope for all AGN. We find that the
rest-frame amplitude variability in the frequency range of
$6\times10^{-6}-10^{-4}$ Hz varies from $1-10$ % with an average of 1.7 %. We
explore correlations between the variability amplitude and key parameters of
the AGN, finding a significant correlation of rest-frame short-term variability
amplitude with redshift. We attribute this effect to the known "bluer when
brighter" variability of quasars combined with the fixed bandpass of Kepler
data. This study also enables us to distinguish between Seyferts and Blazars
and confirm AGN candidates. For our study we have compared results obtained
from light curves extracted using different aperture sizes and with and without
de-trending. We find that limited de-trending of the optimal photometric
precision light curve is the best approach, although some systematic effects
still remain present.
