SolutionsMultiple choice
1 - B
2 - C
3 - D
4 - C
5 - A
6 - A
7 - D
8 - B
9 - B
10 - C
Question 16
Part b)
There's two things I wanna say about this question.
1) It's INCREDIBLY easy to get lost in the diagram. When dealing with too many triangles all in the one go, try to not look at the diagram in its entirety. Instead, either use highlighters, or focus on two or three triangles at a time. Also, see if there's anything hidden that's obvious. I totally forgot about the parallel lines, so it took me ages to realise there were parallelograms I could use.
2) With the second part, that bit of backtracking wasn't immediately obvious either. The intuition behind the problem was that the ratio \( \frac{1}{\sqrt2} \) actually was appearing
everywhere. It's just that we had to use similar triangles to establish that.
But once we've established that, we can try to say "oh, this length is \(\sqrt2\) times that length" over and over, until we get something nice.
Okay, so having done the entire paper, this is what I think. I feel like Q11-Q14 was very fair. Quite lenient marks available in Q11-12, and Q13-Q14 just required a bit more work than the usual. Although,
Q13 d) was definitely an interesting one because I don't think it was that easy to relate i) and ii) together. Maybe some students will have immediately realised the relationship (i.e. the tangent being a chord of the hyperbola), but the line was now 'below' the origin so the analysis is tweaked. That, and also realising the link that consequently \(M\) is also the midpoint of the two intercepts is hard to see.
But then, Q14 didn't look so bad. The reduction formula had weird boundaries, but everything was still reasonably straightforward.
Q15 can be received with mixed reviews honestly. Who knows how many students still remember how the auxiliary circle works with conics for i) even though it was an easy part. And whilst it's no stranger, it's been ages since I've seen the angle between two lines in an MX2 paper for part ii). Also quite cheeky because that formula isn't explicitly on the reference sheet. Q15 b) was just long, but the length of the paper wasn't as bad as last year (2017). Whereas in c), ii) was the more interesting one. Basically, it's alright for people who recognise the need to use cases, and a struggle for others.
And then, well, Q16 was a monster. The induction isn't hard, but even 4U students could struggle with the index law manipulations required. b) was a migraine, and c) was definitely not your usual polynomials question. I genuinely wondered if I had opened a CSSA paper by accident when I got there. That was one of the most brutal Q16's I had ever seen.
Lastly, the M/C. Easy first six questions, weird last four questions. Q7 took me by surprise since I haven't seen \( \arg \frac{z-z_1}{z-z_2} \) problems for ages (if at all since 2001?). Q8 was a 2U type question but without a doubt weirder, but Q9 and Q10 were definitely unusual.
When you balance out that the paper seemed quite polarising with its questions; a handful being mild/easy and a specific bunch being insane, it's so hard to say what will happen. The 2013 paper may be a good benchmark for the difficulty, but that one started getting weird as early as Q14 (although I think they had a slightly better Q16). I'm not sure if it was as bad as 2001-2004, but I definitely felt it was harder than 2014-2017.
So the E4 cutoffs... potentially somewhere in the high 60s?
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Topic: Mathematics Extension 2: Discussion, Questions & Potential Solutions (Read 6855 times)