What is the correct term for a must-answer-correctly question in a test?
In some tests a question is critical, ie. answering that question incorrectly makes you fail the whole test, even if that's your only wrong answer. I tried serching for 'sudden death question' but it does not seem to be the right term. So is there a name for such all-losing questions?
This is called a gating question. Think of the question as a gate to the rest of the test. If you don't get past the gate, the rest of the test doesn't matter. If you do, you still need to get past the rest of the test.
In the 20th century, one of the earliest and best-documented instances of a gating item occurs on the FAA pilot’s flight test. During the flight test, the prospective pilot is asked to demonstrate proficiency in a number of flight procedures, including pre-flight inspection, takeoff, navigation, flight maneuvers, and stalls. At the conclusion of the test, the pilot must do one last thing – land the plane. If the pilot cannot land the plane in three tries, the FAA examiner takes over the controls, lands the plane, and fails the pilot – no matter what level of proficiency the pilot has exhibited in the prior exercises. Landing the plane is a gating item. - Wallace Judd, Gating items, pare online, V14, No9, May 2009
You can call those questions as "make or break"
Cause either total success or total ruin
[The Free Dictionary]
Although, I am not sure what type of examiner would administer such questions. Losing all the points for previous right answers just because you got one question wrong sounds terrible, at least for academic exams.
While I do not know if it is regularly used in this context, you could say that the question is the sine qua non for passing.
An essential condition; a thing that is absolutely necessary: grammar and usage are the sine qua non of language teaching and learning
Oxford Dictionaries Online
The term is derived from Latin, and literally means without which, not [or nothing]. 1:
You also could say that it it the critical question
Having a decisive or crucial importance in the success, failure, or existence of something: temperature is a critical factor in successful fruit storage getting banks lending again was critical to any recovery
Oxford Dictionaries Online
Note that this term is often used for one of a number of important items, so the definite article is needed. In speech the article might be emphasized, as in This is the critical question (and in AmE, the would be pronounced thee).
http://www.oxforddictionaries.com/us/definition/american_english/sine-qua-non