When is zero article used for a noun denoting known subbject?

The penultimate question of "EXERCISE 2" in world-english(dot)org(slash)articles.htm
- "I can't believe I failed ___ yesterday's test!"
has the correct answer for (asked in __) article as NOTHING.

Why?
My answer would have been "the"
The person seems to be speaking with himself and both participating in this dialogue knows about which test one of them told to another.

***Neither a teacher nor a native speaker.***

What exactly do you mean?
So the correct answer (according to the test is):
I can't believe I failed yesterday's test!
:?:

I would have said:
I can't believe I failed at yesterday's test!

And you say it should be:
I can't believe I failed the yesterday's test!
:?:

In my opinion you don't need the here because yesterday already tells us which test you mean.
If there were several tests yesterday, it could make sense to use the, in order to refer to a specific one.

Cheers!

You wouldn't use "the" with yesterday's no matter what. Compare these sets of sentences.

I can't believe I lost Laura's book.
*I can't believe I lost the Laura's book.
I can't believe I lost the book that belongs to Laura.

I can't believe I failed yesterday's test.
*I can't believe I failed the yesterday's test.
I can't believe I failed the test yesterday.

Barb_D and Nightmare85, thanks!
Can you indicate me a rule for omission of an article (for zero one).
I cannot find any, for example in "EXCEPTIONS TO USING THE DEFINITE ARTICLE"
while "4. THE DEFINITE ARTICLE" of "UNDERSTANDING THE ARTICLE AND OTHER WORD CLASSES" (pdf)tells that "THE" is used with genitives(Examples: "The girl’s friends, the butcher’s shop"

As far as I cannot hook to a rule or some mnemonics the examples are quite useless to me.
Or to overdiscuss it to death

Nightmare85 said:

In my opinion you don't need the here because yesterday already tells us which test you mean.
If there were several tests yesterday, it could make sense to use the, in order to refer to a specific one.

Click to expand...

I thought that the rules are that either "THE" :
or "A" :

vgv8 said:

"THE" is used with genitives (Examples: "The girl’s friends, the butcher’s shop"

Click to expand...

The pattern is as follows:

• the girl's friends
  • the girl has friends / the friends of the girl's

• the butcher's shop
  • the butcher has a shop / the shop of the butcher's

• the yesterday's test :cross:
  • the yesterday has a test :cross:
  • the test of the yesterday's :cross:
    • the meaning we want is there was a test yesterday
• yesterday's test :tick:

Nightmare85 said:

***Neither a teacher nor a native speaker.***

In my opinion you don't need the here because yesterday already tells us which test you mean.

Click to expand...

That's correct. In other words, use 'the'—unless there's possessive adjective:

• Go get the paper. <no adjective>
• Go get the Monday paper. <adjective>
• Go get Monday's paper. <possessive adjective>

Possessive adjectives and articles hold the same structural position, which is why they cannot co-occur. You have to choose one, not both:

• the papers
• my papers
• the my papers :cross:
• my the papers :cross:
• the test
• yesterday's test
• the yesterday's test :cross:
• yesterday's the test :cross: