STEP Prep Thread 2016

No Q8?

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We all have bad days. This is probably your first one, isn't it? We've all gone through that. You'll positively smash the next paper you do.

Curious to know if I'd lose marks for skipping showing S is less than 3 and two thirds and going straight to proving it was less than 3.5?

Q1 was recycled, I think. I remember doing it in Siklos' booklets. I did not attempt Q4, but regretting it now since you are second person who tells me it is a good question. I was going to try Q9, I ranked it 7/10 but had 20 minutes at the end and mech questions are not my strongest. I ****ing despised Question 7, but that was because I made the mistake of differentiating 3 times. I am not surprised why you would get algebraic errors to be honest, that **** was really algebraic intensive; the examiner's reports even commented on that IIRC.

Why didn't you enjoy Q3? I thought you from all people would love this question, unless complex numbers is your only weak spot. I found it pretty difficult, but it is about cyclotomic polynomials (https://en.wikipedia.org/wiki/Cyclotomic_polynomial) so I feel bad right now for not making a good attempt on it.

Did you mean to write this the other way around? If so, I think you would lose marks because they were rather specific about the "hence"/"deduce" nature of the question and this was remarked upon in the examiner reports/solutions (if I'm understanding them correctly).

We had a long lecture on cycatomic polynomials in the IMO camp.


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I interpreted the deduce as being for showing S is greater than 3? It then proceeds to say "show also that S < 3 and two thirds". Would you take this as a hence then?

My thinking was that if I showed it was less than 3.5 it would immediately follow that it is less than 3 and two thirds. Reading it the examiner's report it seems to be clear what was intended for showing the lower bounds but not quite so much the upper bounds.

actually how was that btw? Was it interesting?

In the step solutions for question 7 of 1,2011, how do they get from the second to last line to the last line of part (i)? It's when they are showing the value of kT for large alpha.

Are you talking about how $\frac{1}{\alpha} - \frac{1}{2\alpha^2} \approx \frac{1}{\alpha}$? If so, the $\frac{1}{\alpha}$ is small so $\left(\frac{1}{\alpha}\right)^2$ is teeny tiny tiny and can be ignored and treated as negligible, i.e: it's almost 0.

Got it, thanks, but I thought 1/alpha must also tend to 0 also.

It's not thaaaat small. A large part of this sorta question is just getting to the required answer by means of "hand waving approximations", so you're like, I want $\alpha^{-1}$, bleh this must mean I need to throw away $\alpha^{-2}$. I know how you feel, though. I'm stupendously bad at this sort of stuff.

Thank you!!

No worries. :-)

Do you know if we can have an electronic stopwatch in the STEP exam? I find it difficult to keep time with my mechanical watch.


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Can someone explain what Laplace transforms actually do? I know they're useful for solving differential equations but that's about it (Zacken 4 paragraph explanation NEEDED)


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