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.
Q2. An intrinsically nice question on integration by substitution, which shoots itself in the foot.
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.
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.
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.
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.