The 2012 STEP Results Discussion Thread

The best advice I can give is to keep doing questions. If you can manage a question per day, then that will be certainly very good.
Considering the numbers, from I, II and III papers 2011-2004 you have roughly 150-160 pure questions only. So, it can keep you busy for about 5-6 months.
Also, in my opinion, doing a whole paper in a day and then no questions for two weeks is a bad strategy.

Mwhaha, that was a really bad way to put it i guess! But it's not very neat, i was hoping i could carry n from the earlier part of the question, im sure of a link but cannot see it

STEP i 2002. ]

Heres the solution http://www.thestudentroom.co.uk/showpost.php?p=18451574&postcount=31
I cant do the very last bit where you need to find the roots of a quartic. The solution uses guess work to find the roots, and then factorises, but surely theres a more 'mathematical' way that relates to the question? Maybe im just being pedantic..

I agree mostly. Just felt I had to mention it as the OP hadn't got the k=4 case comfortably despite (I assume) trying it so generalising might not have been the best option in that situation.

Is it okay to adopt pi notation? I isn't on the a-level spec....

Having actually worked the question through in full, I think we may have a contender for the step question with the shortest solution

You can use any accepted notation...or you could just define it in the exam: '$\prod^n_{i=1} a_i$ is the product of the first n terms of the sequence $a_i$' or something like that

Possibly! Seems like any difficulty in the question is based around spotting the pattern. If you can do that with minimal working, the question is short.

The shortest STEP question I've ever done is STEP I 1987 Q4.

Fair enough. Thanks...

Although if they won't accept it you could always use for $a_i>0$

$\displaystyle\prod a_i \equiv \exp({\sum ln a_i})$

I think spotting the first root by inspection helps a lot. Then you can form three equations relating the roots with the coefficients of the remaining cubic. For the equation with the minuses in it, try factorising the number on the RHS. What do you notice?

How many lines was that?

Does 0 count as a positive integer?

Nope, zero is only included when it says non negative.

Wow, I always thought it counted, or at least thought it was a 'grey area' and you could include it.

the definition of +ve means it can't be.

Wow, I always thought it counted, or at least thought it was a 'grey area' and you could include it.

The natural numbers can include 0 (although I would not use this definition) but the positive integers cannot. There are also of course the whole numbers which is another grey area