STEP Prep Thread 2016 (Mark. II)

How'd you do the second bit about a < 0 is a is a real root? I said that for x > 0, f_(n-1) was obviously > 0, so derivative was > 0, so f_n(x) was increasing and f(0) = 1, so f_n(x) > 1, so the only real root could happen for x < 0.

all terms were positive was another possibility

Everyone here seems so experienced with STEP so I was hoping for a grade estimate Thank you and if anyone would like me to write up a solution for these I'd be more than willing

Q3: Did this one fully (including repeated roots for n is even case)

Q4: showed (ycos-sin)^2 > 4(y-1)^2 (albeit by an ugly method involving showing that (x+1/x)>= 2) and expanded some trig stuff in y^2 + 1 > 4(y-1)^2 but didn't really do anything

Q5: Fully done, although sometimes my writing may have seemed not too rigorous ("adding the different ways to make x^n from each of the sums, we need x^j from the first and x^(n-j) from the other", but I think it was all there

Q6: Fully done

Q7: Did it all until the integral of 1/(cos(x)(cos(x)+sin(x)) which I worked with until something like 1/(cos(2x) + sin(2x) + 1), used the identity again and got nowhere xD (now that i see one just divides by cos(x) i feel so stupid haha)

Q8: Evaluated the integral at the start and drew a really rough sketch but had 1/m rather than 1/m^2 box heights and stated that clearly the area under the curve approximated the area under the boxes (possibly getting no points for the diagram)

Also I'm not sure how confident I should be of getting 20s in those I did fully :/ (looking to get 1,1 for trinity)

It seems to me like it's probably a first, but I want to be really sure (for some reasons I may have to make an important decision based on this before I get results (has to do with choosing to go to Berkeley instead and losing lots of money))

How'd you do the second bit about a < 0 is a is a real root? I said that for x > 0, f_(n-1) was obviously > 0, so derivative was > 0, so f_n(x) was increasing and f(0) = 1, so f_n(x) > 1, so the only real root could happen for x < 0.

Any solutions yet?

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In regards to q8, How did people do part iii? i got an answer although felt like i was waffling. Overall it was a carcrash, started well with q3 getting a full. by the end managed to get 7, 2 parts of 5 what i described in q8 and two abysmal attempts at q2 and 12. Feel like i got 70 so probably a few marks below a 1

Might as well see how people think I did:

1: Mostly full - showed there were intersections like the question asked but didn't find the exact coordinates - still think I drew an accurate sketch though.
2: Pretty confident of a full on this.
3: Happy with everything here bar the sketch justification - I think mine was very shady and rushed.
4: Wrote line one line and then decided to do a different question.
6: Everything bar the last part - differentiated v(x) and left at that.
7: All the integrals done bar the last one which I also wrote a single line for before moving on. Maybe a minor slip on one of the previous integrals but nothing massive.

you got into berkeley? congrats

Everyone here seems so experienced with STEP so I was hoping for a grade estimate Thank you and if anyone would like me to write up a solution for these I'd be more than willing

20 + 4 + 20 + 20 + 17 + 4 = 85, certainly a 1.

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Sigh, everybody seems to be getting a 1 except me.

Not the only one we can beg cambridge to let us in together haha

We need to do really well in STEP III to still have a reasonable chance.

Yeah, Although i think we can easily get an S on a good day so all's not lost yet

I'm still in sort of a daze though, I can't seem to get myself to do any work and I just feel so down. Arghhh, this really sapped my confidence.

Really don't let a bad STEP II get you down - I, and plenty of others, thought the offer had been missed after II (which in my case was nearly the case, I was jammy and was dead on the boundary! :P ) and honestly you've probably done better than you think. Just make III as good as possible: even if you do miss the II grade but have a good III (and I grade since you sat it) you should be given the place. Which college have you applied to?