STEP Prep Thread 2015

Doing the same things as in the earlier parts, what can you deduce about p(-1) and the factorisation of p'(x)?

For II 2006 Q3 in the first part. I'm not really sure how to approach the question. I could turn the number into one fraction then expand all the terms to show it's an integer but surely there must be a more efficient method?


Posted from TSR Mobile

(5+root24)^-4 = (... - ...)^4

I need some help with STEP III 1993 Q9 (iv).

My generalisation is

$\displaystyle (n-1)\sum^{n}_{i=1} a^2_i \geq 2 \sum a_i a_j$

I'm not quite sure how to prove it. My first thought was induction, but I think the inductive step will be quite complicated here.

Also, I wasn't sure on the notation for the sum on the RHS. The part after this uses the following to define the summation so I think it works here as well "where the latter sum is taken over all pairs $(i,j)$ with $1 \leq i < j \leq n$".

Step 3 2012 (i) is giving me a head ache, when it says 'touch' does that include intersections? Or literally just when they touch (no intersection)?

Would anyone know if this is the last year for AEA? The information seems quite mixed.

Yes it is.

Yes it is.

Well ****. Is it worth doing it this year then?

Hello clever STEP people

I am stuck with a problem and need to show something which I do not think is too bad
(me being too tired and having a bad day...)

In order to process the problem I need to show the result in the attachment.
It has to be true because then the problem works.
I tried the obvious substitution/translation to the left but I am stuck
anyone please?

Did you try the sub $u = 2L - x$?

I tried u = x - L

I think u = 2L-x works.