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.
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.)
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 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.)