And you’re done (unless you’re doing Foundation). I hope the exams went well for all of you, and all of your students.
And, finally, my thoughts on Part B. In brief, it’s shallow drivel. One 3-mark question, and nothing above. The entire exam is a disgrace, just poorly written semi-maths. With errors.
Q1. Yet another idiotic walking track. The “minimum turning point” should be “turning point”, which still means pretty much nothing for a walking track. In part (b), the curves meeting “smoothly” would be sort of ok, since this has a casually accepted meaning of the derivatives matching, except the uncorrected 2021 exam report might screw kids up. The entire problem is aimless and as boring as dirt.
Q2. An OK but too easy complex question. In (a) and (b), the writers use “root” to refer to a solution of a polynomial equation: the kind of thing of thing examiners love to whine about in the reports. Part (c) has the points “represent” complex numbers, and in (d) a point is “represented” by a complex number: both version are needlessly clumsy, but at least make a choice and stick to it. The wording of (d)(ii) is atrocious. Part (e) is just depressing, but (f) is better. In (f)(i), specifying A and B are positive reals is oddly neither here nor there, does not uniquely determine either, but more importantly B, and could have been much better targeted for (f)(ii). The “[g]iven that w = cis(2π/7)” in (f)(ii) doesn’t really mean anything.
Q3. Jesus. Rotating a curve does not give a solid. VCAA can keep saying it, and it will keep being wrong. Part (b) should just be “the surface area”, not “the curved surface area”, but of course the idiots screwed up the preamble. Why is (b) split into two parts, which also means (b)(i) has a zillion different answers? Yes, one answer is more natural, but it’s bad mathematical style. The “[h]ence or otherwise” in (b)(ii) is weird and unhelpful: what could possibly be the “otherwise”? Parts (c) and (d) might have been interesting algebra, but are just boring numerical crap.
Q4. A boring and clumsy logistic question. The population Q is “modelled” by the solution in the preamble to (c), and then the differential equation is given in (e). Part (e)(i) could be nice algebra, but is presumably just 1-mark CAS crap. The wording of (e)(ii) is atrocious. Part (g) is poorly worded and, although better than the related WitCH, is still borderline wrong: what does “the maximum number of fish that could be supported” mean? One can have more fish in the pond than the equilibrium number, but this seems to be no part of VCAA’s presentation of logistics.
Q5. A pedestrian lines and planes question. Parts (b) and (e) should refer to “distance”, not “shortest distance”. More importantly, as discussed here, why are these distance equations examinable? Given they are examinable, why are the relevant formulas not included on the formula sheet? This really seems remarkably incompetent. As Sentinel has pointed out, (d) asks for “an equation [singular] of the line in parametric form”: it should be three equations, and it is not clear a single vector equation will be marked correct (and it damn well should be). Lastly, and it’s no big deal, but the choice of ψ to refer to a plane is eccentric.
Q6. It’s stats crap. I don’t do stats crap. But, famously, VCAA screwed up (h).
Thank you to everyone for your comments. Here are my thoughts on the multiple choice questions. In brief, they suck.
MCQ 3. Excruciatingly bad wording, a genuine literary offence.
The endpoints of the interval are included, even though the function is undefined there. (12/11/23. The function is fine at the endpoints, but not at all points in the interval. That means the wording is a little poor, but we’ll leave it be.)
MCQ 4. A poor question, fundamentally simple but with gratuitous, distracting noise.
MCQ 5. In principle a reasonable question but, as discussed below, the specification that is weirdly pointless: students who falsely conclude that will still likely wind up with the correct answer. Plus, for the thousandth time, the proper word is “equals”, not “equivalent”.
MCQ 6. It’s pesudocode crap. I don’t do pseudocode crap. But commenters have pointed out that the question is badly flawed: the code does not follow VCAA’s own style guide, and following the code will not print out what is claimed will be printed out.
MCQ 7. Gradient field or slope field is more accurate than direction field.
MCQ 9. An OK question, but it is slightly odd, and clumsy, to ask for “the slope of the tangent to the path of the particle”. This is not particularly meaningful for a path in space, and “slope” is an oddly casual word.
MCQ 10. A very good question with extraordinarily clumsy wording.
MCQ 11. In principle a good question, but very clumsily written and too busy. There is no need to say “the curved surface”: it is simply “the surface”. Similarly “part of the curve” should just be “the curve”, since the domain is immediately specified. Then, it is simpler and preferable to say the “the area equals …”, rather than the “the area can be found by evaluating …”. Finally, the last two multiple choice options are different in character, making the question improperly confusing, and the specification “where u = sin(y)” is mathematically meaningless (even if the reason to include it is clear and was well-intentioned).
MCQ 13. What trivial SUVAT is doing on an SM exam, God only knows.
MCQ 14. An odd and interesting question, but probably not a good question. The point is that c must be perpendicular to both i and j, and then the question is easy. But it is not clear how SM students are supposed to get there. (Plus, the dots for the dot product should be centred.)
MCQ 15. A good question.
MCQ 16. More trivial SUVAT. Also, “vertical distance” is not really a thing, but ok. Why specify that i points east and j points north? Who the hell cares?