This one was brought to our attention by frequent commenter, SRK. It is similar to the previous WitCH (and note this post), in that it is more properly a PoSWW but there may be some discussion (and there is some cloudiness in the grading). It is Q17(a) from 2025 General Mathematics Exam 2. The network above is introduced with some preamble about a gym hosting a competition, with activities at various stations; the edges of the network are the walkways between the stations. The students are then asked,
Here is the assessment guide and the report on the question (W,I)):
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A to E, then no way back.
Are we taking issue with the fact that the question artificially requires students to answer with reference to the degrees of the vertices when it can be explained trivially using the A-E edge?
Sure. Degrees of all? some? vertices, whereas 1’s degree suffices.
Jesus. It would have been so so easy to construct a problem with an odd vertex but no dead-end.
We’ll never get it, but I’d love a breakdown of that 60% of kids who got zero. In terms of total number of stiffed marks, suspect this would be up there with the very worst “errors”.
Gotta love a tell me what I’m thinking question!
That’s a very generous use of the word “thinking”, JJ.
I take it that just mentioning that you can’t go from point A to point E and back without a repeated edge is enough for full marks? Silly question… why did they add point E?
Yes, my understanding is that an answer like “There is a vertex of degree 1” would have been marked incorrect.
Why did they add vertex E? Dunno. Because they’re idiots, maybe?
Possibly an example of the setter having the required answer before they have a question.
OK, question (for debate/discussion).
The statement “not all vertices are of even degree” to me seems to be identical/logically equivalent to “at least one vertex has odd degree”.
But, the evidence, and discussion so far, suggests that the second of these statements would have been marked as wrong.
That seems a bit unfair.
Thanks, RF. Taking the idiot question as a given, the guide+report and, it seems, the grading, is nuts from go to whoa.
There are four statements one might consider (with variations), all of which justify the conclusion.
A) Not all vertices are even.
B) There is an odd vertex.
C) There are two odd vertices.
D) There is a vertex of degree 1.
The guide+report specifically point to (A) and (C).
Was (B), which, as you point out, is equivalent (D), accepted by the assessors? Possibly, given the possibility that common sense overruled the implication of the guide, but it is no gimme. I don’t know.
Was (D), which is clearly the best answer, accepted? I am not 100% sure, but my understanding is that it was not.
That is just plain unfair.
And in direct contradiction of VCAA’s own statements about grading (looking to award marks).
Well, I have not confirmed any of this (although I’m willing to bet plenty of money). But if it is true, it is well beyond “unfair” and “direct contradiction”. It would be insane.
One does not need to be “looking to award marks” for a 100% valid and crystal clear answer.
A fair point, but I think my claim remains valid.
Not awarding a mark for (B) might be the most insane grading decision I’ve seen.
I do not know that this occurred, but I will be endeavouring to find out.
Even ignoring the omission of the better answer, I’m struggling to see how these answers constitute an “explanation”. Stating a fact like “Two vertices are of odd degree” doesn’t *explain* anything. This is coyly winking at an explanation, for the benefit of someone who already knows the answer.
Of course you’re right. But in the context of General Mathematics, for a gimme 1-mark question (that 60% got “wrong”), I think it’s ok.