Learn English – Is “At Worst” used only in the future context

'Scenario' and 'worst-case' in Merriam-Webster dictionaries

"Worst-case scenario" pretty clearly arose from the cobbling together of two terms that already existed in English: the noun scenario—which Merriam-Webster's Eleventh Collegiate Dictionary (2003) dates to 1875 in the sense of "an outline or synopsis of a play," but which seems not to have acquired the sense of "an account or synopsis of a possible course of action or events" until much later—and the adjective worst-case, which the Eleventh Collegiate dates to 1964:

worst-case adj (1964) : involving, projecting , or providing for the worst possible circumstances or outcome of a given situation {a worst-case scenario}

In fact, the "account or synopsis of a possible course of action or events" sense of scenario debuts in the Eighth Collegiate (1973), and the entry for worst-case first appears in the Ninth Collegiate (1983), suggesting that the new sense of scenario gained mainstream acceptance before the modifier worst-case did. This comports with my memory: I vividly recall first encountering scenario when I was in high school in Calgary, Alberta, in 1970–1971, in news reports noting that Prime Minister Pierre Trudeau had recently discovered the word and was now using it constantly to describe hypothetical situations and outcomes.

An early relevant match for 'scenario'

Scenario as "hypothetical setting" goes much farther back than 1973, however. From U.S. Department of the Army, Field Manual FM 21-5: Military Training (1957):

80. Scenario The fourth step in the development of a platoon sandtable [terrain model] exercise is the preparation of the scenario. The scenario tells the story of the exercise and answers the general questions of when, where, and how situations will occur, what the situations will be, and who will be affected by them. ... The entire scenario will not be made available to the platoon; but portions of it that concern the situations that must be solved are issued as orders or are portrayed on the sandtable.

Early relevant matches for 'worst-case'

As for worst-case as an adjective, Google Books searches find early instances of it in such phrases as "worst-case error" (going back to at least 1961), "worst-case analysis" (going back to at least 1961, as well), and "worst-case projection" (going back top at least 1971).

(I've tried to be cautious in identifying "confirmed" dates" for Google Books matches. The vast majority of matches Google Books returns for the searches I ran are snippet views that do not provide access to a publication date in the snippet window—and many are from multiple-year volumes of a periodical, making it extremely difficult to pin down a particular year as the publication date of the snippet shown.)

Earliest definite Google Books matches for 'worst-case scenario'

The earliest confirmable Google Books match that I could find for "worst-case scenario" is from Michael Kramer, "The City Politic," in New York Magazine (November 25, 1974):

A good many Republicans resent [Nelson] Rockefeller for having gotten out while the getting was good. Such is their ingratitude that they ignore the fact that Rockefeller created the ship that is now sinking. [Perry] Duryea, like them, had no place to go. And now, Nelson Rockefeller's "worst case" scenario has come true—the man who survives to haunt him is the one man above all he had hoped would now be politically dead.

The next-earliest matches are from 1975. From John Albers, Walter Bawiec & Lawrence Rooney, "Demand for Nonfuel Minerals and Materials by the United States Energy Industry, 1975–1990" (1975), a U.S. Geological Survey professional paper:

To meet the new demands for fossil-fueled energy for 1985, about 406 coal-fired plants of 900 MWe capacity and 166 combined cycle powerplants will be required. These projections are based on a worst-case scenario of large, standalone, conventional fossil-fuel plants with add-on 59 MWe turbine generator sets.

And from "Fiscal Year 1976 and July-September 1976 Transition Period Authorization for Military Procurement, Research and Development, and Active Duty, Selected Reserve, and Civilian Personnel Strengths: Hearing Before the Committee on Armed Services, United States Senate, Ninety-fourth Congress, First Session" (1975) [combined snippets]:

Me ALDRIDGE. I think we are getting into the assumptions for the next part of the presentation soon to be scheduled. But usually for the worst case scenario the problem is to define what is the worst case. I think it is better to say that we take our best estimate of Soviet capabilities and we run excursions around these capabilities to insure that we are not on the on the edge of the cliff. That is, to insure that if some factor is changes slightly our force capabilities do not deteriorate very rapidly. So we try to take the best case and run excursion about that best case, such as bomber reaction time and/or depressed trajectory.

Conclusions

The most striking thing about the earliest instances of "worst-case scenario" in Google Books searches is that they are all closely connected to U.S. government research—appearing either in pure research papers by scientists working for government agencies (like the U.S. Geological Survey) or in testimony taken at hearings before governmental committees.

Even the earliest clear use of scenario as a hypothetical situation to be used as the basis for real-world activity—the U.S. Army's 1957 Military Training field manual—is a U.S. government undertaking. Whether the earliest instance of "worst-case scenario" arose in the subcategory of military planning (as I think is most likely), energy resource planning, or some other branch of government, the connection to government is direct and obvious.

My working conclusion is that the term became a buzzword/catchphrase in one particular area of the federal government apparatus in the United States (probably the Department of Defense), and spread from there to other departments and their concerns, to politicians and theirs, and thence into the private sector—to the business world and to everyone else.

I think that you are merging two different uses of "couldn't have" that need to be divided back apart.

1. The idiomatic "Couldn't have" that reflects someone's feeling that something in the past is impossible.
2. The genuine "Couldn't have" or "could not have" that reflects a true impossibility.

The answer to your question, "When can I use 'could not have passed the test'" is that you can always use this construction when the context or the circumstances warrant it. You don't have to worry much about accidentally straying into the territory of the idiomatic usage of "couldn't have" when you don't mean to, and you also don't have to worry about being misunderstood by people as to which of the two usages you're employing at any given time.

Here are some examples labeled with [1] or [2] that will hopefully show the difference between the two kinds.

• I couldn't have passed a physics exam. I'm only in 3rd grade. [1]
• I couldn't have passed the physics exam. I was sick, and then my girlfriend left me, and I never studied, so there was no way I could have done it. [2]
• I couldn't have passed the test. I didn't even show up to take it. [1]
• I could not have passed the test without the help of my tutor. [2]
• I couldn't have passed the driving test. I've never driven a car in my life. [1]
• I could not have passed the driving test. No matter what, that particular driving instructor always gives a failing grade to women drivers. [2]

In a situation where you didn't have the clarifying follow-up sentence (and were simply hearing someone say, "I couldn't have passed the test"), I would typically gravitate toward interpretation [1] for all situations, unless you had strong reasons from the context to believe otherwise.

Also, I would differ from your interpretation on Case 2. I would say that in Case 2, it would be correct to say, "I couldn't have passed the test" and NOT "I can't pass the test." I would only use "I can't pass the test" in a case where the student was speaking before even taking the test.