Am I expected to remember certain figures/dates for my exam?

If you don't know it, don't include it. The examiner will not be impressed with your ability to memorise a date down to the exact day/month/year, but will instead award marks for you ability in showing how this information might be useful for your argument. For example, writing 'Kristallnacht occured on the 9th November 1938' only exemplifies an ability to memorise. However, writing 'it is clear to see that anti-semitism was a clear facet of the Nazi party prior to the outbreak of war, as Kristallnacht occured in the year 1938' shows the examiner you have thought critically about the information at hand.