Busy week, huh?
Thank you all for your comments. Mostly the exam was OK (at least as much as it could be given the idiotic mark distribution), but was hampered by bad wording. Again a few comments, mostly amplifying what has been noted below, but a couple other thoughts as well.
Q1. The minor problem is bad wording: “Show that the rule for the function …” should be replaced by “Show that the function …”.
The major problem is that, in the VCAA world, this appears to be a very bad question. The simplest (and perfectly valid) approach to the question is to start with x + 2 – 4/(x – 1) and establish the equality by writing the expression over a common denominator. But will VCAA accept that? And, even if VCAA will, I’m betting plenty of kids didn’t do the problem this obvious way, exactly because they fear that VCAA won’t accept it.
Q3. The wording for (b) is just nuts. If infinite limits are in the curriculum (are they?), then talk properly in the language of limits and/or use limit symbolism.
Q4. Asking for an answer in the form -π√a/b with a and b positive integers is sloppy. Yes, it’s standard in VCE, but it’s sloppy.
Q6. There’s lots of words in this question. Like a real lot of words. I fell asleep reading this question and then woke up, looked at the question and went back to sleep. I can’t even count the words. But it’s a lot. There’s a lot of sentences, and a lot of words in each sentence. I think there’s an average of ten words a sentence, with a standard deviation of who knows and who cares.
Plus, as commenters have noted, but have not sufficiently emphasised, part (b) is screwed: there are infinitely many answers for a and b, with two being very natural and non-CAS findable. Even if there were only one findable answer, it doesn’t matter: you don’t ask for “the value” when multiple values answer the description.
Plus, the proper word is “equals”, not “equivalent”. If a teacher, or education authority, is using the word “equivalent” then they almost certainly using the word incorrectly.
Q7. The phrase “open hollow surface of revolution” will become legend. And, π(a√b/c – d) is multidimensionally sloppy.
Q8. Clumsy wording throughout.
Q9. Show that AB = … and AD = … . Why is this hard?