There are three kinds of examinations that you will encounter during your time at Hertford.
First, there are College-only examinations called Collections that you normally sit at the beginning of Hilary and Trinity term. These examinations relate to work you have done in the preceding term. They do not form part of your final degree classification. They are, however, important opportunities to gain valuable practice in examinations. They also provide material upon which your tutors can gauge academic progress when writing references.
Secondly, there are First Public Examinations that students sit at the end of Trinity Term of the first year. You are required to pass these examinations to proceed in your degree.
Finally, your eventual degree classification will be determined by your Finals examinations that are sat in the final term of your second and third year, and also your fourth year if you carry on to the M.Math.. (During the third and fourth year you may also write a dissertation to be counted towards your degree classification, in place of some written examination.)
More detailed information on examinations can be found on the Mathematical Institute webpages.