Go for it.
As for Methods 1, there is not too much to say about this exam except for the final Q9, which is a mess. Commenters, who are better able to judge, have suggested the exam was too long; the exam did feel pretty fiddly in parts. Here are our question by question comments.
Q1 A simple kinematics question.
Q2 A trivial definite integral. As SRK and others have noted, 3 marks – equating to 4.5 minutes – to evaluate is absurd.
Q3 An OK statistical hypothesis question, to the extent that’s not a contradiction in terms. As commenter John Friend noted, the modelling scenario is ridiculous.
Q4 A straight-forward volume of revolution question, which is screwed up. A minor but telling example of the examiners not knowing, or teaching, how maths works. And more than a few students will probably be cheated a mark.
Part (a) has students calculate the volume Vs of a solid resulting from rotating a region around the x-axis. Part (b) then squishes this solid by a factor k in the x direction, meaning the volume gets scaled by 1/k. That’s fine, although squishing in the y direction, resulting in the circle radii being scaled, would have been more interesting and a better test. The problem is that Part (b) asks for the new volume in terms of Vs, which is ridiculous. The point of writing Quantity B in terms of Quantity A is exactly when you don’t know Quantity A, or when Quantity A will vary. But students just calculated the fixed Quantity A, like two seconds ago. Part (b) is just a dumb question, and it seems likely that a number of students, who are smarter than the examiners, will lose their one mark.
Q5 A straight-forward but pretty grungy implicit differentiation question. Compare to Q2, worth the same marks.
Q6 A really, really stupid question. Well, yeah, these linear independence questions are always stupid, and the whole sub-topic is stupid. But including a vector , and asking for which we get independence is a good mile stupider. Plus, as commenter Worm has noted, these exam questions have almost always been couched in terms of dependence in the past. So, yes, VCAA might have put “independent” in bold; but why pass up an opportunity to screw students of a mark and then sermonise on how students should read the question?
Q7 An ok if rather odd initial value problem. As noted by commenter SRK, there is no reason to exclude negative t in Part (b), although it was probably intended that students assume t ≥ 0. Both interpretations should be permitted, and it would be surprising (and reprehensible) if VCAA did otherwise.
Q8 An ok complex polynomial question. Part (b) asks students to solve , which is easily done by splitting into real and imaginary parts, but will probably be missed by many students.
Q9 Just a mess. The question involves two particles, A and B, travelling respectively according to the equations and , for . Which is fine, except we’re not told the value of . Why aren’t we told? Because the writers can’t write.
Part (b) asks students to show that the particles collide, and then where they collide. Of course, the first thing to do is to find out when the particles collide, which turns out to be when . Unless, of course, , in which case the particles don’t collide. Which is stupid. And wrong. So, why not have some specific choice of ? Because, of course, the particles won’t continue along their paths after they collide, and setting would give the game away. Apparently no Specialist exam writer could figure a way out of this dilemma, could figure out a clear and correct way to write what they intended. So they left it stupid and wrong. Which is stupid and wrong.
The rest of the question is better, but not by much. Part (a) has students show that the path of particle A is (part of) an ellipse, and then show that the path “in the first quadrant” – i.e. all of it – can be written as . Why would anyone care? Well, they wouldn’t, but it means we can now pretend to be interested in the function . Which brings us to Part (c).
Part (c)(i) presents the students with the pretty gross antiderivative of , and in effect asks students to verify by differentiation that it is indeed an antiderivative. Pretty painful for 3 marks; compare to Q2. And, what do we do with this antiderivative? Part (c)(ii) asks the students to calculate a chunk of area under between a couple who-cares limits.* The area under the path of a particle that would have already collided. How impressive. How it-really-makes-you-want-to-study-maths-for-the-deep-insightish.
*) (11/02/21) As John Friend has noted below, there are infinitely many forms of the answer to (c)(ii). We are aware that one cares about this, but we’ll keep hammering it.