What Are the “Errors” on the 2023 VCE Mathematics Exams?

Given the wide interest, I think it is worth compiling all the “errors” on this year’s six maths exams. (See here, here, here, here, here and here for the discussion posts.) So, please list whatever you believe to be an error, and please indicate whether you regard each error as “major” or “minor” (see below). Justification is not required but may be helpful. Then, soon, I’ll try to update the post with a summary.

Of course there will be judgment calls. Does “open hollow surface” amount to an error, or is it just really absurd? And so on. As for what constitutes “major” or “minor”, that will also require judgment calls, of course. They are judgments of both the mathematical seriousness and the likely effect on students in the exams. Here is what I (re)wrote in a recent post:

To be as clear as possible, by “error”, we mean a definite mistake, something more directly wrong than pointlessness or poor wording or stupid modelling. The mistake can be intrinsic to the question, or in the solution as indicated in the examination report; examples of the latter could include an insufficient or incomplete solution, or a solution that goes beyond the curriculum. Minor errors are still errors and will be listed.

With each error, we shall also indicate whether the error is (in our opinion) major or minor, and we’ll indicate whether the examination report acknowledges the error, updating as appropriate. Of course there will be judgment calls, and we’re the boss. But, we’ll happily argue the tosses in the comments.

Of course errors and deceit in the exam reports cannot be known for at least a few months. Such is the way of VCAA.

Get to work.

UPDATE (14/11/23)

OK, here is my list of errors on the 2023 mathematics exams.* First, a little more clarification.

Many items in the list are minor, and I am aware that many teachers would not regard all or many of the items as “errors” or, if errors, as major errors. But mathematicians are fussier: they expect mathematics to be written clearly and correctly and unambiguously. That can be difficult on an exam and there will always be judgment calls and minor slips. But the clear majority of the items listed below would irritate the clear majority of mathematicians.**

Teachers have a tendency to say “it’s good enough”, and for their own tests and SACs they have no choice: they have neither the time nor the expertise to polish to a mathematician’s standard. But, for the VCE exams, “it’s good enough” is not good enough. And there is a choice. VCAA has simply refused to enact the proper and necessary choice.

*) I haven’t checked General Mathematics beyond the reported errors. Also, of course this list cannot yet include the garbled explanations and signs of misgrading that will appear on the exam reports.

**) Beyond the errors, plenty more on the exams would irritate the clear majority of mathematicians.

 

GENERAL MATHEMATICS EXAM 1 (Here)

Nothing yet … (21/11/23. But it was only a matter of time)

MCQ26 (21/11/23) The expression “Q multiplied by P” is absolutely fatal in the context of matrices and, if there is a clear meaning to be had, the meaning is Q x P. The question, however, requires P x Q. (Here.)

 

GENERAL MATHEMATICS EXAM 2 (Here)

Q7(c). The question cannot be properly answered as written. (Here.)

Q7(d). There are two solutions, one of which will reportedly not be accepted as correct. (Here.)

Q9(d). An extra 1 appeared in the matrix. (Here, and everywhere.)

Q11. A poorly written question, with (at least) two correct answers. (Here.)

Q14(d). There is an extra “of” in the preamble. (Here.) (24/11/23) As has been point outed in a comment, since this correction was announced at the beginning of the exam, it’s not kosher to list it here as an error.

 

MATHEMATICAL METHODS EXAM 1 (Here)

Q4. The instruction to “use two trapeziums of equal width” is vague to the point of meaninglessness. Proper reference to the trapezium rule should be made. (The word “trapeziums” is also gauche.)

Q9(b). The point P is undefined. (Here.)

 

MATHEMATICAL METHODS EXAM 2 (Here)

MCQ 9. The term “smooth” is undefined in the study design, VCAA’s apparent meaning for the term is highly non-standard, and VCAA’s indicated method of proving a function “smooth” is invalid. (Here.)

MCQ 13. The pseudocode is marginally incorrect (by VCAA’s own declared style). (Here.)

MCQ 18. (17/01/24) There is no correct answer. One of the endpoints will be a local minimum (and the other a local maximum), and so there will always be \boldsymbol{a^2 + 1} local minima. (Here.)

MCQ 20. The compositions are undefined.

Q3(a). Limits at infinity are not clearly part of the study design. (Here.)

Q4(f). The question should have asked for the maximum standard deviation: asking for “the required standard deviation” is close, but is queered by the definite article. (Here.)

Q4(j). The speed is written as “m per second” rather than “metres per second”. (24/11/23) As has been point outed in a comment, since this correction was announced at the beginning of the exam, it’s not kosher to list it here as an error.

Q5(b). The preamble should have specified that the domains be maximal. (Here.)

 

SPECIALIST MATHEMATICS EXAM 1 (Here)

Q4. Asking for an answer in the form -π√a/b with a and b positive integers is not good form, with no unique answer.

Q6(b). There are infinitely many possible answers, and a second and presumably unintended answer is easily findable. (Here.)

Q7. An “open hollow surface” is not a mathematical thing. It is appalling wording and makes the question of “surface area” ambiguous. The specification of the form of the answer as π(a√b/c – d) is highly non-unique and very bad form.

 

SPECIALIST MATHEMATICS EXAM 2 (Here)

MCQ 6. The pseudocode is very poorly written, and will not print out what is indicated. (Here.)

Q1(b). Given VCAA’s use of and multiple misunderstanding of the term “smooth”, it can no longer be taken for granted that “meet smoothly” means simply that the function values and derivatives match at the endpoints. (Here.)

Q2(a)(b). The writers use “root” to mean “solution”. (Here.)

Q2(d) (19/11/23) Part (d)(ii) asks for the polar equation of “the ray” drawn in (d)(i). This equation, however, will necessarily exclude the ray’s starting point, which would legitimately and naturally be included in the answer to (d)(i).

Q2(f)(i) The specification of A and B is not unique (and is poor preparation for (f)(ii)).

Q3(a). Rotating a curve does not give a “solid”.

Q3(b)(i).  The specification of a, b, A and B is not unique.

Q4(e)(ii). The “maximum number of fish that could be supported” is not properly defined, and may not mean what VCAA thinks it means. In general it is, at best, unwise to to use “maximum” to refer to such an equilibrium solution.

Q5(b)(e). It is not clear why such distance questions are examinable, since there is zero reference to them in the study design. If they are examinable, it is not clear why the relevant formulas are not included on the formula sheet. Also “shortest distance” should simply be “distance”. (Here.)

Q5(d). Asking for “an equation [singular] of the line in parametric form” is inaccurate, and may or may not suggest that a vector equation is a desired/permitted answer. (Here.)

Q6(h). Famously, the graph labels were interchanged. (Here, and everywhere.)

 

FOUNDATION MATHEMATICS (Here) (21/11/23)

MCQ 13. The key to the graph is confusing, and wrong. Some indication that “payment” and “interest” are cumulative had to be included. (Here.)

Q1(c). There are two methods of working out the percentage increase, which give different answers. One method is unlikely to have been considered, but this still should not occur. (Here.)

Q2(e). (23/11/23) 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. (Here.)

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. (Here.)

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. (Here.)

Q11. The outer rectangle on the diagram doesn’t mean anything and was probably actively confusing. (Here.)

 

40 Replies to “What Are the “Errors” on the 2023 VCE Mathematics Exams?”

  1. I would argue that the incorrect pseudocode indenting (multiple choice 6, spec 2) is a major error, since it makes the pseudocode quite hard to read, even if students know their stuff. Also, does it even make sense? I would imagine that one “iteration” would mean one runthrough of the whole code, but I’m pretty sure (though I haven’t tested) that VCAA actually means one runthrough of the while loop

      1. 1.it took me ages to find, so here’s an annotated pdf of methods exam 2 https://www.dropbox.com/scl/fi/kokuna8mqsti37xtg8e9q/Methods_2023_Exam-2_Suggested-Solutions_Robert-Liu_vFF.pdf?rlkey=k8qmtkff9dkacbfkcryh3v161&dl=0
        2. I assume you’re talking about multiple choice 13. I’m not advanced enough to actually understand it properly (I’m still in year 11, as my username suggests), but if you’re talking about the lack of `endif`, I think that’s definitely a minor error. It probably goes against pseudocode conventions, but I only noticed that because of a comment on this blog, and I highly doubt it would have confused anyone. I’m slightly biased though, because I’m very familiar with Python code, which doesn’t use `endif` or `endfor`, and instead relies on the code being indented properly

      2. If you’re judging VCAA by the PseudoCode guide (https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/Pages/PseudoCode.aspx) they posted, the Methods question is missing an **endIf**, which isn’t as bad as the Specialist Pseudocode error, but it is just inconsistent with what they’ve published.

        I find the Specialist error worse because they specify “Use indentation to show the hierarchy of processes within an algorithm such as repeating sections and conditional decisions.”, and then they choose not to indent the print statement, which goes against that prior statement. The print statement has no unique reason not to be indented, and normally not indenting a statement like that would mean the statement is executed OUTSIDE the while loop, though they still have the endWhile keyword below it. It’s silly, but I don’t know where to stand on these errors.

      3. I’m a year 11 student (as stated in my username), so I’m not advanced enough to actually understand the methods pseudo code, but I assume you’re talking about the lack of an `endif` statement. I guess it really depends on what your definition of “major” and “minor” are. The methods pseudo code would fail if it was actual code running on a computer. The spec pseudo code would run perfectly, because computers don’t care about indenting*, and it only exists for readability.
        At the same time, whilst I’ve never done a VCE exam, I imagine I would skip the spec question if I was on a time limit, and I probably wouldn’t even notice the issue with the methods question. At the very least, the spec question would take me longer to understand, and I don’t think exam time should be spent trying to interpret VCAA’s errors.
        Tbh there’s only one correct answer for both of them, and there’s no ambiguity for either (“iteration” might** not be an accurate word, but it’s not really ambiguous, since you can still understand what it means). So I guess you could call them both minor errors in that regard.
        At the same time, I keep thinking that the spec error should be a major error, simply because it’s so obvious and it really should have been picked up.
        Or maybe the spec error was intentionally done to make it harder…I guess we’ll have to wait for the exam report 👀 😂

        *computers don’t care about indenting if your syntax includes `end` statements, which VCAA’s syntax does
        **and this is definitely up for debate, if anyone wants to weigh in?

        1. In some languages, yes indenting is just for readability, but in others indentation is an integral part of the syntax. Notably the Python language relies on indentation not brackets or “end” statements.

          In pseudocode, the most important thing is readability. That is what rules/conventions (as in the VCAA guide) are for. I would argue, since the rules were not followed and can have a serious detriment to readability (especially in the SM case) and hence student performance on the question, these are bordering on major errors.

          1. Isn’t it simply a question of what VCAA has declared acceptable pseudocode for students to write and, then, whether what VCAA has written in the exam is acceptable by their own declaration?

            1. I still can’t find where, but I’m certain VCAA have stated (somewhere) that students are not expected to write pseudocode. Although no broad standard for pseudocode syntax exists, VCAA has published ‘The constructs of pseudocode’

              https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/Pages/PseudoCode.aspx

              which one would assume is the VCAA’s attempt to define a ‘style guide’ for pseudocode in its mathematics subjects.

              My understanding is that the term ‘pseudocode’ is so broad that it can include a description of how an algorithm works written only in plain English text. So, for example, a plain English description of how Newton’s Method works could be considered ‘pseudocode’. Without VCAA’s ‘style guide’ for pseudocode, I think it is difficult to argue that the VCAA questions are erroneous. But VCAA did publish a ‘style guide’ – So I think whether or not the questions on the Maths Methods and Specialist Maths exams follow this ‘style guide’ determines whether or not the questions are erroneous.

  2. Restating the obvious, but in summary; SM Exam 2, ERQ6h is mislabeled, with the labels corresponding to the hypotheses being swapped. I believe this is a major error, and while there have been announcements before the start of an exam on typographical errors, I believe this was not the case for this question. I know several students who resorted to manually crossing out the 0 and 1, to not be confused about what region to shade.

    There is nothing conceptually wrong with the question, just that the typo breaks the question, and would cost time for anyone trying to understand why the labels may have been swapped. To not be confused by the question requires the student answering the question to just assume that the diagram was labelled erroneously, which is a terrible precedent to set.

    1. Thanks, Sai. Obviously this error counts as major. Anything that seriously screws around with students during the exam is automatically major.

  3. Worth mentioning there was a 7th maths exam this year, the Foundation 3&4 one, first of its kind. I haven’t seen it yet, so can’t comment whether it has any errors or not.

      1. True, but given its the first one, it will set a bad precedent if it is error ridden.

        Tungsten, that probably explains it. Clearly getting my dates crossed at this time of year.

  4. Come on you guys: do your homework.

    I’m too busy to be hunting. Even if it’s just transcribing what people wrote on the discussion posts, please list the known and claimed screw-ups, if you think they amount to errors.

  5. OK, no one is listening. I’m exhausted and I want you guys to do some transcription work.

    No one makes any further comment on this post without also transcribing across an error or semi-error.

  6. General Mathematics Exam 2:

    p 25 Preamble to part (d): Line 3 there is an extra “of”.
    Minor (*) typographical error.
    VCAA sent instructions for making this correction to all schools during the exam. The instructions were considered unclear/wrong by some invigilators.

    p 16 Question 9 part (d): Extra 1 in column H of matrix.
    Major (**) typographical error.

    p 13 Question 7 part (c): Potential error in construction/wording of question (there is no answer that leaves the final amount owing to be exactly zero dollars).
    Minor error.

    Mathematical Methods Exam 1:

    p 12 Question 9: The point P is under-specified.
    Minor error.

    Mathematical Methods Exam 2:

    p 19 Question 4 part (f): Should have asked for “maximum” required standard deviation. (This error is repeated from the 2009 Exam 2 Question 3 upon which Question 4 is so obviously copied from).
    Very minor error.

    p 20 Question 4 part (j): “m per second” instead of “metres per second”.
    VCAA sent instructions for making this correction to all schools during the exam.
    Minor or major error (depending on fluency in English).

    p 21 Question 5 part (b): The word “maximal” is missing.
    Minor error (probably).

    Specialist Mathematics Exam 2:

    p 2 Question 2: Poorly worded question (it’s perhaps a fine line where poor wording ends and erroneous wording begins).
    Major error.

    p 3 Question 6: Incorrectly formatted pseudocode.
    Minor error.

    p 23 Question 6 part (h): Mis-labelling of normal curves in the diagram (H0 and H1 are the wrong way around).
    Major error.

    * Minor error = low impact effect on students getting intended answer.
    ** Major error = high impact effect on students getting the intended answer.
    Subjective opinion, sometimes based on anecdotal evidence.

    1. Forgot about Specialist Mathematics Exam 1:

      p 5 Question 4: No unique form for required answer.
      Very minor error.

      p 6 Question 6 part (b): No unique answer.
      Minor error (unless two answers – the ‘obvious’ and the ‘less obvious’ were always intended).

      p 7 Question 7: Very poorly worded (two interpretations of “open hollow surface” leading to two different answers).
      Minor error (probably).

      p 7: Question 7: No unique form for required answer.
      Very minor error.

      Specialist Mathematics Exam 2:

      p 15 Question 3: Poorly worded (rotations of curves do not form solids).
      Minor error.

      1. SM Exam 2, ERQ6c:

        It would’ve been better if there was an extra sentence starter “instead of using the original sample size 20”
        Because 6c follows immediately after 6b (which introduced ‘sixty such random sample’). In a way it was a bit confusing as to whether n=20 should be used or n=1200 should be used.

        In hindsight, I would argue that it would be less ambiguous if the original ERQ6a and b were set as ERQ6a.i and ERQ6a.ii, as two sub parts of part a, while making the orginal 6c as a distinct part 6b…

        Minor slip. Maybe it should be categorised as an formatting/structuring issue.

        1. Thanks, Sentinel. There’s often a question of whether the wording is merely clumsy, or whether it’s strayed into error. I’ll look carefully when I get to it.

          1. SM 2 ERQ5d
            “Write down an equation of the line L in parametric form”

            Have trouble with “an” equation. Would’ve been better if it was phrases as:

            “write down a set of three parametric equations to represent the line L”.

            Also curious how the kids would be marked if his/her answer was a vector equation rather than three parametric equations.

            1. Yes, this is a definite problem. It would be madness if VCAA didn’t permit a vector equation, since it has a parameter. But the formula sheet refers to the three x-y-z equations as “parametric equation [singular] of a line”. At best, it’s clumsy phrasing, in the exam and the formula sheet.

        2. yeah, I agree. Not an “error” but the wording could have been better. Just the inclusion of a “now” would have helped.

      1. The difference is most likely either major or minor. What’s important is the list. Best wishes using these lists in your hunt.

        By the way, you’re welcome. Very happy to pitch in with anything that can help and ‘lighten the load’.

        1. No. it is important that significant mathematical errors are considered major, irrespective of whether they affect many students. But I’ll correct for thsi when I update the post.

  7. Methods Paper 2 MCQ 19. I still (and have yet to be convinced otherwise – am prepared to let it go though) of the opinion that the command term Find to start this question is wrong.

      1. I’m not sure. I expected the pseudocode to be garbage because… well, it is.

        It may be minor, but I would not expect it to happen on an IB paper, for example and I think the comparison is a fair test for whether something is an error or not.

  8. I’m still catching up on things, and trying to get out one more 2022 exam post. But with a brief look, it seems to me there is at least one, standard, error on each of MM2 and SM2 that no one has mentioned. I may be wrong: they may not be errors, or I may have overlooked them being mentioned. But I don’t think so.

  9. OK, I’ve updated the post with my list of “errors” (and people are off the hook for hunting further ).

    People are free, of course, to argue against my inclusion (or exclusion) of any items (and indicate glitches). I’m probably using “major” here in a slightly more general sense than previously, but not much. I regard the error as major if it will cause at least some students to be (slightly or greatly) puzzled, and/or makes the question actively ambiguous, and/or is significantly mathematically flawed, and/or is significantly in conflict with the study design.

  10. I’m late to the party, but I’m surprised to see that the MCQ18 from the Methods exam 2 is not on your list. Since the function is defined on the closed interval the two endpoints will also be local extrema (one of which will be a local minimum). Looking at the case a=2 gives a counterexample to all the listed options.

    1. Thanks very much, LH. Yep, you’re absolutely correct. I’ll update the various posts soon.

      It’s amazing that no one had yet mentioned it. But if you see the way local extrema are semi-defined in the textbooks, it’s perhaps a bit less of a surprise.

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