Editing 2966: Exam Numbers

{{comic
| number    = 2966
| date      = July 31, 2024
| title     = Exam Numbers
| image     = exam_numbers_2x.png
| imagesize = 553x400px
| noexpand  = true
| titletext = Calligraphy exam: Write down the number 37, spelled out, nicely.
}}

==Explanation==
{{incomplete|Created by 10 MORE THAN AVERAGE MATH TEACHERS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

The comic depicts various similarly formatted examination questions that might appear on test papers at various points in a student's potential academic career. While they all share a similar feel, they are asking for different things, some of which might be considered more serious and examinable proofs of study than others.
{| class="wikitable"
|+ Exam numbers
! Exam level !! Question !! Answer
|-
| Kindergarten math || Write down the biggest number you can think of || At a kindergarden-level education, it is assumed that an individual might write down a relatively small number like 300, depending upon whether they have encountered the concept of hundreds. It might also be interpreted as "what's the highest number that you (think you) can count up to". Given the nature of a child's exuberant glee at learning about ''really'' big (but otherwise normal) numbers, they may even try an answer something like "a million billion squillion gazillion". It is not certain what criteria would be used to mark this question correct or otherwise, it may actually by a stealth question in child psychology or a question that everybody 'gets right' so long as they answer it.
|-
| Pre-algebra || Write down the value of x if x=3x-8 || 4
''3x'' refers to the multiplication of 3 and the originally unknown number ''x'', as a convenient shorthand.

By subtracting ''3x'' from both sides, ''-2x = -8''. Divide both sides by -2 to find ''x''=4.  Alternately, subtract ''x'' from both sides to give ''0 = 2x - 8'', and as taking 8 from two ''x''s makes it zero, one ''x'' is half that

(Verify by plugging ''x''=4 into the original equation. '''4''' = (3*'''4''') - 8 -> '''4''' = 12 - 8 -> '''4''' = 4.)
|-
| Calculus || Write down the value of ∫_0^π x sin^2 x dx || The integral of the expression is ''(−2x sin(2x)+cos(2x)−2x)/28 + C''. Plugging in values for ''x'' gives the result as π^2/4, or approximately 2.4674.
|-
| PhD Cosmology || Write down the Hubble constant to within 1% || The exact value of the Hubble constant is not known to this level of accuracy; it is about 2.3 * 10^-18 Hz. This is one question that might have a different acceptable answer in the future, depending upon further developments in the understanding of cosmology.
|-
| Game Theory || Write down 10 more than the average of the class's answers || Game Theory studies "games" in which two or more participants' take actions that will succeed or fail based on other participants' decisions. In this case, all students' answers will be averaged, and the best answer will be 10 more than that average. If a student knew what everyone else was thinking, this would incentivise them to answer 10 more than the consensus (taking into account their own forthcoming answer), which would not necessarily be the largest number written down. For instance, if the answers end up being 30, 40, 50, 60, and 70, the most correct of these answers is 60.

In reality, most game theory exams test your understanding of game theory as an academic subject, not your ability to win games. (A type of class where actual results may result in better grades is a business negotiation class where the results of practice negotiations can determine one's grade on the assignment.)

Something similar to this question is found in the title text of [[2385: Final Exam]].
|-
| Postgraduate Math || Write down the biggest number you can think of || This question echoes the very first example, but would be expected to be answered very differently (unlike a revisiting of most of the others).
Postgraduate math students can probably think of ''very'' large numbers. The 'best' answer could be "infinity" since, depending on your definition of the word "number", infinity may be the largest possible number that you will have encountered. This might heavily depend upon the branch of mathematics you are studying, however, as named (finite) numbers or ones with specific and useful notations might satisfy some questioning contexts, whilst the existence of a whole further set of trans-finite numbers (i.e. increasingly large types of "infinity") would be important considerations in others. For those associated with more computational mathematics, any infinity be {{w|NaN|Not a Number}}, and their answer might instead be the ceiling of some binary representation (typically ''2<sup>8n</sup>-1'' for some value of ''n''), the largest value reliably storable in byte form (e.g. a {{w|Integer (computer science)|double quadword}})

As with the kindergarten question, they may be no previously anticipated 'correct' answer. It could be another "correct just so long as you answer it" (or perhaps 'sensibly' so) or the mark goes only to those giving the greatest number across all submissions.
|-
| Calligraphy (title text) || Write down the number 37, spelled out (as "thirty-seven" or "thirty seven"), nicely || Calligraphy, in a nutshell, is the art of fancy writing. The title text expands the joke outside the realm of math and points out that since calligraphy does not require any math skills, the only way a calligraphy exam would even mention numbers is if one had to write them out in such a way as to showcase their calligraphic skill. {{w|37}} is a number that some people believe [http://thirty-seven.org mysteriously appears more often than it should]; this was a subject of a [https://www.youtube.com/watch?v=d6iQrh2TK98 recent Veritasium video].
|}

This final exam question, un-numbered and therefore possibly the ''only'' question upon the whole of each final paper, in some ways (for some instances) echoes the question "What is your name?" that Randall will be aware was the sole question given to Discworld's {{w|List of Discworld characters#Victor Tugelbend|Victor Tugelbend}} in an attempt to ensure he comprehensively passed (or utterly failed) his final student-wizard's exam, after many prior times of deliberately not-quite-passing.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[6 different math test questions.]

:[The first panel:]
:Kindergarten math final exam 
:Q. Write down the biggest number you can think of
:A. [empty box]

:[The second panel:]
:Pre-algebra final exam
:Q. Write down the value of x if x=3x-8
:A. [empty box]

:[The third panel:]
:Calculus final exam
:Q. Write down the value of [integral sign, from 0 to pi] x sin^2 x dx
:A. [empty box]

:[The fourth panel:]
:PhD cosmology final exam
:Q. Write down the Hubble constant to within 1%
:A. [empty box]

:[The fifth panel:]
:Game theory final exam
:Q. Write down 10 more than the average of the class's answers
:A. [empty box]

:[The sixth panel:]
:Postgraduate math final exam
:Q. Write down the biggest number you can think of
:A. [empty box]

{{comic discussion}}

[[Category:Math]]
[[Category:Cosmology]]