I have a question concerning an online articles quiz: http://www.englishpage.com/grammar/Articles/Exercises/.

According to this quiz, question no. 9, sentence "I can't believe I failed ___ yesterday's test!" should not include any article before "yesterday's test". I would like to know why? In my opinion, since we are talking about the particular test which took place yesterday, we shoud use 'the'. Even if there would be couple tests and this is a first mention of one of them why not to use 'a'?

Thank you in advance for your reply.

Kind regards,
When you have a possessive of a time unit, you almost never have an article before it.

tomorrow's questions
yesterday's exam
this morning's newspaper

Adding "the" would be simply wrong. You don't need the article with the possessive form of "yesterday". The 's at the and does the job just fine.
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 CalifJim's reply was promoted to an answer.
Thank your both, ozzourti and CalifJim, for your replies. I didn't realize that this rule exists(or maybe I just forgot about it). Take care.