Cambridge Math STEP 2

I thought it was pretty similar to previous years. Maybe a couple questions were more straightforward this year but most years usually have a couple easier questions.

I really liked question 3 and question 6. question 1 was a nice starter. q2 was ok until the very last part in my opinion and i could only make it half way through q4 and q7. overall id say not too bad

Ah, 3 and 6 were decent. For me, 6 was manageable all the way until the very last two parts. 3 was fine; if I recall correctly I only struggled with the final integration part. 7 I kind of made it to the last part, but didn't manage to solve it. I barely did the first two parts of 2 and 4 though...

i was stuck at part v) on q7 for ages i had no idea how to carry on xd. q4 looked doable at first (probably because it only took up a paragraph instead of a page) but i was wrong. for q2 i hope i was able to count correctly because it got quite tedious.

Yeh hahaha for the last part I was struggling to solve some simultaneous equations because the numbers were huge, so I just gave my answers as fractions lol. I share the same sentiments about q4 - I just wasn't in the mood to expand the surds. q2 I kind of had some mental block, so I did not go beyond the first part.

yeah some annoying questions but some nicer ones as well. i shouldve probably done some mechanics prep tho because i reckon they wouldve been a better choice than q4 for me :/

Mm, personally I don't like stats but I might consider tackling the stats question for the next paper. Did you attempt Question 5 on the sequences, by the way?

no, i didnt do that one. was it good because it looked long xd

Fair enough, respect that. All the best for STEP 3!

Just wondering does anyone have a solution sketch for Q2? From what I can remember,

(i) required solving tan(θ) = tan(8θ) --> find 8θ = k(pi) + θ, k is integer and theta is between -(pi)/2 and (pi)/2, remove overcount in cyclic combinations
(ii) required solving tan(θ) = tan(27θ) --> find 27θ = k(pi) + θ, k is integer and theta is between -(pi)/2 and (pi)/2, also remove overcount of cases
(iii)(a) required solving cos(θ) = cos(8θ) --> find 8θ = 2k(pi) + θ and 8θ = 2k(pi) - θ, k is integer, and theta is between 0 and (pi), remove overcount.
(iii)(b) needed to be proved by contradiction.

Not sure if i missed something, or if this was entirely wrong to begin with :P
Did anyone get anything different?

sounds good to me except i didnt do the last part other than find the degree 8 polynomial

Ahh I see. From what I can remember I think the last part involved showing that: if |x|>1, then eventually you'd get y>x, and by symmetry this could be extended to x>z>y>x which is impossible --> contradiction complete.

Got super confused on how to remove the overcounting though, and eventually I just gave up on it and ignored it altogether. To clarify the "overcounting" i was refering to, say in (i), just as an example I somehow got

8θ = k(pi) + θ --> θ = (pi)/7 is a solution. This means that x = tan((pi)/7) y = tan(2(pi)/7), z = tan(-3(pi)/7) is a valid solution.

Contining, along, we get θ = 2(pi)/7 also being a solution, which means that x = tan(2(pi)/7), y = tan(-3(pi)/7), z = tan((pi)/7) is a valid solution, but it seemed to me that this was exactly the same as the θ = (pi)/7 case, meaning that there is an "overcount".

This seemed to also be true in (ii) and (iii), but I began spending way too much time on this problem so I just wrote the most obvious number of cases and didn't account for any sort of "overcounting".

does anyone how many parts question 5 was divided into?

for anyone who actually did question 5, in the second to last part (iirc), there was an inequality that was required to be shown. would contradiction be a valid method here? also, does anyone know if STEP marks nicely if you know what to do, but don't have time to do it? pretty sure the last part of q5 was a proof by induction, but i only finished the base case and assumption step before having to put my pen down. maybe i'll get a mark or two for that? Lmao

For those who took the STEP 2 paper today, how did you think it went and how would you compare its difficulty to those of previous years? Curious about everyone's opinions.