This is the (new) newly established home for Foundation Mathematics exam errors. The guidelines are given on the Methods error post, and there is also a Specialist error post, and a (now renamed) General error post (with unchanged link). As with General Maths, I will not look much at the Foundation exams, only posting errors as they are brought to my attention.
If you suspect that there is an error that is not included in the list, or that an “error” has wrongly been included, please add a comment or contact me, and I’ll check it out.
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2025 Exam (Exam here, marking guide here (W,I), report here (W,I) – discussed here)
MCQ12 The question is ambiguous, and gratuitously so. Encountering heavy traffic “while traveling on both roads” is intended to mean both roads have heavy traffic.
QB9(b) The cost of a quantity of milk being in direct variation to its volume bears no given relation to the percentage of the coffee cost being due to the milk. There is probably only one way to answer the question but the question appears to be plain nuts.
2024 Exam (Exam here, marking guide here (WI, updated 16/02/25) – discussed here, report here (W,I))
MCQ10 There are two possibly correct answers, depending upon rounding.
MCQ20 An improperly defined, and bad, hexagon tiling question. Just a mess, and essentially the same as we hammered as a sample question.
2023 Exam (Exam here, report here (Word, idiots) – discussed here and here, report here (W,I))
MCQ 12 (added 19/07/24) A pretty screwy question, with a list of percentage returns from superannuation accounts (plural), one for each year. In any case, adding the percentages, as indicated in the exam report, makes no sense and cannot indicate whether the returns “showed an overall gain”.
MCQ13 The key to the graph is confusing, and wrong. Some indication that “payment” and “interest” are cumulative had to be included.
MCQ 19 (added 19/07/24) There is no indication in the question prompt that the path corners should be taken to be quarter circles (and the report’s computation of these areas is a pretty tedious way to estimate the area of the path).
Q1(a) (added 19/07/24) The exam report puzzles over “replicated” values, 15 x 15 and so on, whereas it seems clear that this was students answering with Length x Width, where the two dimensions happened to be equal. It seems unlikely that students were penalised for this, but there is no way to be sure. (Possibly, the question was intended to refer to “long single” rather than “king single” mattresses.)
Q1(b) (added 19/07/24) The exam report comments on showing how to “convert 54.33 cm”, when the reference should have been to 54.33 inches.
Q1(c) There are two methods of working out the percentage increase, which give different answers. One method is unlikely to have been considered by students, but this still should not occur.
Q2(a) (added 19/07/24) A very poorly worded and ambiguous question, asking for “the four sport activities” that “are not shown on both lists”. This is intended to refer to sports that appear in one or other of the two given lists, but not both. Some students, however, interpreted the question to permit (or require) the sports to not appear in either list. The exam report then whines about students who thus interpreted the question, not understanding (or at least not admitting) that students were misled by the crappy wording. It is unclear whether students were penalised for such answers.
Q2(e) The question makes zero sense, since it assumes that a person cannot play both a ball sport and a non-ball sport. The question also fails to specify the percentage is of females participating in a sport. (Added 19/07/24) As Jay pointed out in a comment, students were instructed to “use the graph”, even though the graph is faulty. The exam report then whines about students who attempted to follow this instruction as written, “interpreting the graph literally”, rather than as was intended (to use only the existing bar on the graph). For the thousandth time, VCAA stuffs up the wording and then blames students for the stuff up.
Q3(d) (added 19/07/24) As pointed out by Jay in a comment, the question is fatally, hilariously ambiguous. The exam report interprets “the volume of water … needed” to be the water explicitly combined with vinegar and the garden spray to make the custom mixture, ignoring that water had also been used earlier, in the production of the garden spray.
Q4(b) (added 19/07/24) The question asks for the “total sales revenue earned for these two cars” but is ambiguous, since the question can naturally be interpreted as asking for the “total” revenue separately, for each of the two cars. (Not that it matters much, but the proper plural for “revenue” is “revenue”.) The exam report indicates that students who answered the question in this manner were cheated of their mark.
Q4(c) (added 19/07/24) The question is fatally ambiguous, and the solution indicated in the exam report is the worse option. The question asks for the stamp duty on a car, calculated at “a flat rate of $8.40 per $200”. The natural interpretation (and the financial reality) is that the duty is calculated as “or part thereof”: any final fraction of $200 attracts the full $8.40 of duty. This cannot be assumed, however, and the exam report instead provides a pro rata calculation. The final (rounded) answer is the same, but the question is still screwed.
Q5(b) (added 19/07/24) The question asks students to round to the nearest year, but the exam report rounds up. While the final answer is the same, the method indicated in the report is wrong for the question as asked.
Q6 An awfully written question, throughout confusing usage with market share. There is probably only one plausible way to answer the questions, but this is teaching Not Maths.
Q6(a) The 2022 percentages in the graph do not total to 100%. This in itself is ok, but it leads to two potential answers to (a); one answer is unlikely to be given, but this still should not occur. The graph should have been appropriately labelled.
Q6(b) (added 19/07/24) The “percentage decrease” (of something) is not the same as the decrease in the percentage (where the percentage is itself the thing decreasing), the latter being what was clearly intended.
Q6(d) (added 19/07/24) The same issue as in 6(b).
Q7(a) (added 19/07/24) The questions asks for the answer to be given in cent per litre, and then the exam report whines about students “including the units of dollars”. Which would be fair enough, except that the exam report’s answer provides no units at all.
Q9(e) (added 19/07/24) The question asks for the cheaper option and the amount of money saved. The exam report then whines about students failing to indicate “the time period linked to the saving”, even though this was not asked for in the question (and which anyway was indicated as a fixed period of time in the question prompt).
Q11 The outer rectangle on the diagram doesn’t mean anything and was probably actively confusing.
Q11(b) (added 19/07/24) Part (a) asks for the volume of concrete for the slab of a house, rounded “to the nearest cubic metre”. That is absurd in the context, and results in rounding down from 6.006 to 6, which are also confusingly numbers that should be avoided on an exam, but whatever. Part (b), however, first notes that concrete “is sold in cubic metres” and then asks students to “calculate the cost of the concrete for the slab”. The report then whines about students using the rounded answer of 6 rather than 6.006 for the volume, leading to an “inaccurate response” (although the required rounded answer was the same). Which is sort of fine, except that one would in fact need to purchase 7 cubic metres of concrete. One might argue that “the cost of the concrete for the slab” refers to the 6.006 m3 concrete used rather than the 7 m3 concrete purchased, and one would have to be a bona fide idiot to try to defend the question in such a manner.
I believe the 2023 exam can be found here: https://www.vcaa.vic.edu.au/sites/default/files/Documents/exams/mathematics/2023/2023foundation-math-w.pdf
Thanks very much, Jay. Post updated and also with the exam report link.
I don’t think the objections to 2e are necessarily correct:
> The question also fails to specify the percentage is of females participating in a sport.
It states at the start “All females aged 15+ participating in a sport were grouped into the categories of playing a ball sport or a non-ball sport.”
> it assumes that a person cannot play both a ball sport and a non-ball sport
In this context I think the word “or” is being used exclusively, so it would imply that a person cannot play both
I must admit, I was kinda surprised to see “100-26” on a VCAA exam
PS: on second thought, I actually do have an objection to that question:
The report stated “Many quoted answers less than 30%, linking it to the provided vertical graph scale”. The question stated “The bar showing the percentage of females aged 15+ playing a non-ball sport is missing”. If a bar is “missing”, it must fit on the graph, hence I’d award 1 point to those students and 0 to VCAA
The funniest part is VCAA whining “Some students quoted 0%, interpreting the graph literally” which I’d paraphrase as “oh no, some students were in a hurry and didn’t read the last sentence properly. Even though the graph clearly implied 0%, the question stated that it was missing a bar (which by the way also didn’t fit on the graph)”
I think students read the question perfectly. The problem is, the question is stuffed by the instruction to “use the graph”, irrespective of what was in the preamble.
Again the motto for VCAA minions: if you cannot write, then do not write.
Thanks, Jay. They’re good points, although I’m not sure I agree. Yes, one can glean the intended meaning, both for the percentage and for the exclusivity, but I don’t think “one can glean” suffices. One has to make these things clear and, in the statements of the questions, VCAA did not. The exclusivity in particular is such an unnatural assumption, it must really be hammered, from the beginning: a belated “grouped into categories” doesn’t come close to cutting it.
Having said that, you had pretty much convinced me to un-red the error, to be minor. Except, your “second thought” objection, which I’ll add, is hilarious and plenty enough to keep the thing red.
1a) “Many responses showed the values replicated, e.g. 15 × 15 or 6 × 6” I don’t know if that’s the correct notation, but otherwise both answers are literally solving for length and width. Sure, the question only asked for length, so I guess those answers are wrong, but why the hell did VCAA assume that they’re the “values replicated” as opposed to people misunderstanding the question. Unless, of course, if the foundation maths examiners don’t know any maths at all and just read an answer sheet they’ve been given
Sigh. Thanks, Jay. I’ll look. (In general, I will not look at anything in the exams or reports of Foundation or General unless it’s flagged.)
Hi Jay. I’ve started looking through your comments (and the entire exam). I think you are likely correct, that the examiners mistook students providing both the lengths and the widths as “repeating” the lengths, which, if true, is pretty damn obtuse. Having said that, an answer like 15 x 15 is fundamentally wrong for capturing the changes in both length and width. Also, it is not clear that students were penalised for writing e.g. 15 x 15, and I suspect not, if only because the examiners misunderstood the students’ intent. (It would of course be nice to know how such glitches were graded, which, post-Bennett, should occur much more regularly.)
1B) From the report: “Students wrote responses that did not show how to convert 54.33 cm to the correct imperial measurement“
The report clearly meant 54.33 inches, but I guess it’s a bit confusing since one could reasonably assume that 138cm converts to 54.33cm, couldn’t they🤦
And sigh again (and thanks again). Keep going. I’ll look tomorrow.
Yep, just a straight out report glitch. Not big, but not great.
Question 2A:
Question: “State the four sport activities that are not shown in both lists.” (with “not” in bold)
Report: “Some responses included a sport that was not found in either list”
My take: The word “both” is ambiguous. Honestly wtf is this question anyway. And even if “both” isn’t ambiguous, the question never specified that the sports have to be in one of the lists. Good grief
> In general, I will not look at anything in the exams or reports of Foundation or General unless it’s flagged.
That’s fine, at this rate I’ll be flagging every question😈
Sigh, thanks, and repeat as necessary.
Hi Jay. It is extremely bad wording, and I have some sympathy for students who answered with a non-listed sport, but I don’t think the question is ambiguous, at least not in this context.
3D) The answer is completely wrong. The garden spray contains water. Absolutely ridiculous! I guess they accidentally wrote a good quality question, but then proceeded to solve the bad quality question they had meant to ask
In VCAA’s words “This question was not answered well”
Oh, that is majorly screwed, at the very best fatally ambiguous. I wonder if any students gave the better answer. (I can’t see how the “common incorrect responses” were arrived at.)
4C) I’m curious to hear your opinion on this. In my opinion “$8.40 per $200” is ambiguous if the value you’re calculating it for isn’t a multiple of 200. For $300, for example, does “$8.40 per $200” calculate to $8.40 or $12.60? VCAA assume the latter, and I can understand why, but I’m not sure if it’s actually an accurate assumption
I can’t edit this comment anymore but I withdraw this complaint, because I imagine that tax is covered in the curriculum, and students will be aware which one is the correct answer as a result. I guess financial questions aren’t pure maths and can require background context
No worries, Jay. I’ll check all your comments, to see what I think. I’ll fix your comment formatting tomorrow, when I work through it all.
For future, the site assumes dollar signs are to indicate LaTeX input. So, it thought you were typing algebra, up until the next dollar sign signalled the off button.
If you actually want a dollar sign, you type \[dollar sign].
No, you should withdraw your withdrawal. The question is flawed.
5B) “Calculate the minimum number of years before the car is no longer considered an asset. Round your answer to the nearest year.” Whilst both have the same answer, it needs to be noted that VCAA simultaneously asked for 2 different methods of rounding
Yes, I think you are correct. They seem to be rounding up in the exam report, when the instruction was to round nearest.
6b) surely percentage decrease doesn’t mean what VCAA think it means. If I decrease a value from 2% to 1%, what’s the percentage decrease? I would say 50%, VCAA would say 1%
EDIT: same applies for 6d
Yep, you’re absolutely correct. Probably most or all students autopiloted through it, but what VCAA wrote is wrong.
7a) comically, they whined about students not including the correct unit, then didn’t include any unit in their answer
Hi Jay. Maybe make a list of the questions that are *not* stuffed? It’ll seemingly be shorter.
Yeah, pretty sloppy, and pretty anal.
7b) “Many students did not interpret the question correctly. Many gave a written interpretation of the graphical data rather than addressing the requirements of the question.” I guess they forgot to delete the first sentence of the question, which asked for exactly that
I think you’re off base on this one. Yes, the students were meant use the graph, but that didn’t mean the answer required a discussion of the graph.
9D) “This question was not answered well. Students should review the concept of GST and its associated calculations. Common errors included students rounding their answer to the nearest $10 ($40), adding 10% to the ticket value ($44), subtracting 10 cents ($39.90) and deducting 11% ($36.37).”
I’m pretty sure this was written by ChatGPT. There’s no way an actual person is this stupid:
1. The question said that the ticket price was $40 including GST and asked for the ticket price without GST. If a student answers with $40 I can guarantee it’s not because of “rounding their answer to the nearest $10”.
2. The answer was 36.3636…. If a student answered with $36.37, it’s a rounding error, not the student “deducting 11%”. 81% of $40 isn’t even $36.37😂
Yeah, empathy doesn’t seem to be their strong suit. Nor is attention to detail.
Obviously their explanation of the answers of $40 is plain nuts. The “deducting 11%”, I wonder if they had intended to list “rounding error” instead or as well, and then Frankensteined the two complaints.
9e) “Many student responses…did not proceed to explicitly state…the time period linked to the saving”
I don’t know what’s in the foundation maths curriculum, but surely the time period doesn’t need to be stated here. It’s equivalent to:
Question: “an apple costs $10, an orange costs $14. Which is the cheaper option and how much money would be saved?”
Report: “many student responses failed to explicitly state that the calculation was per fruit”
NOTE: if the question said that the adult visited the zoo 6 times every year, then I would understand
Definitely students were not required to state the time period. The complaint is nuts.
10c) I don’t know much about interest, but it’s intuitively very obvious that VCAA have gotten this wrong and ignored the monthly repayments. I’m not sure if this is compound interest, but the fact that they said students who applied that formula got it wrong makes me kinda suspect it is compound interest😂
EDIT: who needs the answer sheet when the answer for 10c is included in 10di’s question🤦
10di is so lazy. It’s equivalent to:
a: solve 2+2
b: show that 1000+(2+2) is equivalent to 1004
Also, 10c is one mark so I’m pretty sure students who “cheated” would still have gotten the mark. Furthermore, according to the answer sheet students could reference their answer for 10c in 10di’s “show that” question, so the inclusion of 10di literally allows students to “show” less knowledge
Yeah, it’s unclear whether students would have gotten away with simply peeking at (d), but it’s not a “show that” question, so maybe so.
I don’t think VCAA has necessarily gotten it wrong: I think it simply a nutty plan, where “outstanding amount” means the initial outstanding amount, even after one year of monthly payments. In any case, “outstanding amount” is definitely ambiguous.
2B) “Some students missed the prompt of the three sports mentioned in the information before the question and included them all”
I’m gonna take this as a silent admission that the question was worded horribly. Whilst students who read the question in English (as opposed to Intended Meaninglish) would have gotten the same final answer (I think), they would have wasted valuable time and hence been disadvantaged
Hi, Jay. It is poor framing and poor wording, but I wouldn’t regard it as an error.
11B) “Some who did attempt the question did not carry the accuracy of the previous question into this calculation, thus producing an inaccurate response.”
1. If question 11A instructs students to round the answer, and 11B is a follow-on from 11A, it doesn’t seem fair to penalise students for using the rounded answer from 11A instead of the full answer
2. Regardless, VCAA are just making stuff up, because I checked 3 times and 6.006*280 and 6*280 give the same answers when rounded to 2 significant figures (or even 3 significant figures)
Yes, this is pretty nuts, but I have a different angle on it, which I think makes the question much worse.
First of all, note that the report doesn’t indicate that students who used the rounded answer got the wrong answer in (b): rather, they “produc[ed] an inaccurate response”. Once again, pretty damn anal.
But i think it is much worse. Sure, you can argue that one should use the more accurate answers all through, and I think students should be aware of this. But, the correct figure to use in (b) is neither 6 nor 6.0006: the correct figure is 7.
Wow, you’re correct!
I’m actually quite concerned about this question, because, based on your observation, the correct answer is “$2000” (thanks VCAA for the stupid rounding requirement!). $2000 would look to an examiner like a random guess, meaning there’s a high likelyhood that students were marked incorrectly. 12% of students got 11e correct, so I think it’s a very likely that some of those students would have gotten 11b “incorrect”
Yes, it would be surprising if some students didn’t use the 7, and it would be surprising of the assessors didn’t notice. Which raises the question …
Reading the question again, it asks for “the cost of the concrete for the slab”, which one might argue technically requires using the 6.006. It would be insane if VCAA relied upon that argument.
> Concrete is sold in cubic metres
It’s actually incredibly clear that you can’t buy 0.006 cubic meters of concrete. The only reason it’s ambiguous is because of part a forcing you to round down
Of course. But one can argue that the concrete actually used in the slab was 6.006.
That’s all the mistakes I could find in the short answer section.
In summary:
Flawed questions (with VCAA’s allocated marks):
2B-1 mark (MODERATE, because the mistake led to some students being disadvantaged by spending more time than required, and likely led to some students skipping the question)
2E-1 mark (EXTREMELY MAJOR, because the report listed 3 common mistakes, and there’s a strong argument for all 3 being correct. In my opinion this question should be invalidated)
5B-2 marks (MINOR)
7B-1 mark (MODERATE, because it wasted some student’s time, and resulted in some students skipping the important part of the question)
10C/10DI-1 relevant mark (MAJOR, the answer for 10C absolutely should not have been included in 10DI’s question)
11A/11B-2 mark (MINOR)
Wrong answer in report:
2A-1 mark (MAJOR, because a correct answer was listed as wrong in the report)
3D-1 mark (EXTREMELY MAJOR, because a wrong answer was listed as the correct answer in the report. If any Foundation Maths teachers wish to chime in, I’d be curious whether there’s something in the curriculum that provides an argument for VCAA’s answer?)
9E-1 mark (UNCONFIRMED, possibly explainable by the Foundation Maths curriculum)
10C-1 mark (UNCONFIRMED since I’m not familiar with interest calculation. Regardless, I have a strong suspicion that the “correct” answer is wrong and the “wrong” answer is correct)
Mistakes in report (which indicates general sloppyness):
1A-2 marks
1B-1 mark
7A-1 mark (but the mistake is hillarious)
9D-1 mark (but absolutely outrageous, and an indicator of either complete incompetence, not knowing what question is being marked, or use of AI)
11B-1 mark (would be a MINOR flawed question if I hadn’t fact-checked the VCAA report. That said, this does require an explanation of how that sentence was written, and whether students were marked wrong for “incorrect” working, which I doubt happens for 1 mark questions but may have happened accidentally)
15 mistakes in a 60 mark test. Absolutely outrageous!!!
Thanks very much, Jay. I’m not quite sure why you went so hard, but it’s interesting. I’ll Look soon.
Hi Jay. Still working through, question by question. I agree, 2(e) is a mess, and I agree with your implicit claim, that students who answered by attempting to draw in the correct bar were seemingly cheated.
OK, I finally got through the thing. I don’t think there are as many “errors” as you suggest, but there are definitely some, and there is a baker’s ton of nonsense.
I’ll update the post tomorrow, and ponder further. Thanks very much, Jay, and please don’t do it again.
OK, I’ve updated the post, adding all of what I regard as errors in either the exam or the report. An impressive list.
> MCQ 12 (added 19/07/24) There is no indication in the question prompt that the path corners should be taken to be quarter circles (and the report’s computation of these areas is a pretty tedious way to estimate the area of the path).
I assume you meant MCQ 19. I actually disagree though. I think the claim that “the owners plan to build a 0.5 m wide path” means the radius will always be 0.5m, and I’m pretty sure that it would have to be quarter circles for there to be a constant radius
Nah. “wide” makes no sense at the corners, and in any case it is absurd for students to ponder what “wide’ means at a corner. It’s not big deal, since it’s reasonably obvious the intention is for the the corner bits to be quarter circles. But they still have to say.
And yes, thanks, obviously I meant MCQ19. Corrected.
3e) “Many students were able to perform the calculations to find 11.89 capsicums but did not proceed to round this to 12 capsicums”
I know the question specified “minimum number of whole capsicums each day”, but technically I’d argue that they could re-use capsicums from the previous day, resulting in an average of 11.89 whole capsicums being provided each day. Maybe I’m being a bit too pedantic though
I think whole number is reasonable here, although I think there’s something to your argument.
Click to access foundation-math-sample-w.pdf
Sample question 5: B is listed as correct, although II is only proportional if it’s rounded, whilst IV is proportional. As such, I’d argue E is actually correct
(this is partially a joke, I’m not actually gonna go through the whole sample test)
Life is too short for sample Foundation exams.