UPDATE (31/12/20) The exam is now online.
We’ve finally gone through the exam, we’ve read the discussion below, and here are our thoughts.
In brief, the exam is OK but no better, and there are issues. There is some decent testing of skills, but the emphasis (as in the Methods 1 exam) appears to be on fiddly computation rather than deeper concepts. That isn’t great for a 1-hour sprint exam, and commenters have suggested the exam was overly long, but of course a 1-hour sprint exam is intrinsically insane. At a deeper level, some of the questions are contrived and aimless, which is standard, but it feels a little worse this year. And, there are screw-ups.
Here are our question-by-question thoughts:
Q1. The kind of pointless and boring mechanics question whose sole purpose is to make mechanics look bad. Part (a) asks students to compute the normal force, but to no end; the normal force is not required for the rest of the question.
(10/09/21) Apparently there is an issue, every year, of whether g = 9.8, or g = g. Given VCE contains no proper mechanics (which would require g = g), we couldn’t care less. But it’s the kind of trivial matter that teachers and students must worry about, and which means they’re too busy to teach or to learn mathematics. In any case in 2020, and in 2018, g = g. In 2015 and 2016, however, g = 9.8. Go figure.
UPDATE (02/02/2022) As tom has indicated below, Part (b) is fundamentally flawed, since it is expecting students to treat the acceleration as a scalar rather than as a vector. In particular, a non-sensical remark in the examination report suggests that students who gave the negative answer were invalidly marked down. tom has also noted that 1(a) is, in some sense required for 1(b), although, more accurately, this points towards the stupid wording of 1(a).
Q2. An intrinsically nice question on integration by substitution, which shoots itself in the foot.
(10/09/21) The examiners are clearly unaware that their foot has been shot off.
Q3. A routine and nice complex roots question.
Q4. A good inequality inequality question involving absolute values. The question is not difficult but, as commenters have suggested, it seems likely that students will do the question poorly.
Q5. A pretty nice vector resolute (projection) question, sort of a coherent version of last year’s debacle. Part (a) is contrived and flawed by having to choose the integer solution from the two roots of the quadratic; it’s not a hanging offence, but it’s the kind of oddity that would make a thoughtful writer think again.
Q6. A mess. See the comments below, and here.
(10/09/21) Part(a) is a 1-pointer requiring students to “show that” the derivative of equals . The examination report provides the solution
and then remarks
Students needed to demonstrate the use of the chain rule to find the (given) answer.
What does that mean? Has the report’s solution demonstrated use of the chain rule? How?
The larger issue is with Part (b), instructing students that they should “Hence” show that f has an inflection point at x = 2. The “hence” would seem to indicate some kind of first derivative argument is expected, but the report indicates a standard second derivative argument. For people who fusspot everyone to death over words, that’s pretty stupid wording. Especially so, given that the only step indicated in Part (a) is to expand the square, which is entirely irrelevant to the application in Part (b).
Q7. An OK if (for a Specialist exam) unusual integration question involving continuity and differentiability of a “hybrid function”. The wording is clumsy, since all that is required is to demand that the function be differentiable; continuity of the function is then automatic, and the demanded continuity of the derivative is irrelevant. Sure, spelling out the continuity may simply be being nice, but including the continuity of the derivative suggests the examiners don’t really get it, or are planning a sleight of hand. We’ll see. Given the most authoritative (Methods) textbook makes a complete hash of this topic, it will be interesting to see if the examination report can get it right. We wouldn’t be betting the house on it.
(10/09/21) Yep, they squibbed it. No indication of what is required for a function to be differentiable at a join.
Q8. An ok but ridiculously contrived volume of revolution question. Asking for the volume to be given in the form where is needless, ill-defined and dumb.
(10/09/21) There goes the other foot.
Q9. An OK but ridiculously contrived arclength question. The introduction of the symbol for the arclength is gratuitous and confusing. And (reviews notes), asking for the arclength to be given in the form where is needless, ill-defined and dumb.
(10/09/21) And there goes the third foot.