Thank you for your question.
I would advise you to share the information with the appeal panel because it could influence their decision.
Believe me, there is hardly anything that they won't have heard before!
There is no need to give written details in this instance, or to submit the evidence in advance. On the appeal form I suggest you write at the very end of your statement "There are some extenuating circumstances on the day of the Maths exam which we are considering bringing to the panel's attention, but it concerns a very private matter that we would rather not put in writing."
You should take 5 copies of the letter to the hearing (3 copies for the panel, 1 for the clerk, and 1 for the representative of the authority).
As you realise, you cannot prove exactly what happened on the day, but the fact that you have not rushed to use this information, and do have some previous evidence, should assist your case.
At the hearing I suggest that, rather than raise the issue yourselves, you wait for the panel to ask about it. Then turn to one another and say "Shall we go ahead?"
Hope this helps. Don't hesitate to ask if you have any further questions.