STEP Prep Thread 2014

Man this threads already drying up in a few days. Joostan where are you?

Ok - so Step II 2002 q3 i am unfamiliar with the rigour of proof that the examiner is looking for- so the last part- i said 2^x +1 is always odd so all fermat numbers are odd-
F0.F1.F2...Fk-1=Fk - 2

none of F0,1,2... have a factor of 2 they are all either prime or made up of primes so adding 2 you get F0.F1.F2...Fk-1 + 2=Fk
By adding two Fk has now no common factors with F0, 1, 2...
Fk must be made up of new prime numbers or itself be prime
Since there are an infinite amount of fermat primes- (just change value of k) with each one bringing in a new prime there are an infinite number of primes.

Can anyone see a way to improve this- anything i should mention or havent explained well to the examiner? Assuming I have got the previous parts perfectly how many marks would i get for this solution?

I don't think you have shown 'there are an infinite number of Fermat primes', so I don't think your reasoning holds. I'm guessing you know what you mean, but haven't said it.

Sorry i did not mean to say fermat primes. i meant fermat numbers. Fermat numbers are obviously infinite and since non of them have a common factor- prime numbers must be infinite

Subscribing, though I will try not to get too involved (especially after the summer).

If anyone needs any help on questions and thinks that I am somehow good at explaining things and/or providing an inappropriate number of hyperlinks, then feel free to 'quote' me (regardless of the topic).

My advice to those embarking on the treacherous journey:

Forget what you have been told. It is extremely important that you cover all or nearly-all topics. Despite the so-called STEP philosophy being to provide a range of questions to suit preferences, we must face that we do not live in this idealistic reality. You may get an entire paper filled with all of your favourite topics, in which case you will likely get an S if you have focused your preparation on them, though you may also get a paper filled with the precise topics that you despise, in which case you will likely struggle to get a I. It i for this very reason that I urge you all not to focus narrowly on your favourite areas. i know from experience that you can get as many Ss and near-full marks you like on mocks and simply assume that, if one thing has happened the last 26 years, it is likely to happen similarly on the 27th. Unfortunately this is not even slightly the case as those who sat STEP III learnt this year. So not take many of the past papers you have attempted as a good indication of what the paper is going to be like. If you are doing well on mocks you are likely to do well in the actually exam if you are literally prepared for anything. Be prepared to do 3 or 4 applied questions if need be, be prepared for an entire paper full of geometry or complex numbers or number theory or any other topic so un-emphasised at A-level that only those who have actively prepared for it will stand a chance.

In summary, it is better to know you can get a I on any paper they throw at you than to know you can get an S provided your favourite topics come up. At the end of the day, you are heading in to courses with non-optional fire year courses. You are going to be learning probability and dynamics as well as the core emphasised areas from A-level that you are likely to already enjoy (such as Calculus) and your preparation for STEP needs to reflect this as, more and more, Cambridge and Warwick seem to start testing students on what are undoubtedly student's key weakness' when they arrive at university.

I stupidly thought that I will begin preparing for vectors, complex numbers, probability and mechanics in the summer and that mastery of almost-all Calculus/Algebra questions would be enough to get me an impressive grade in STEP. I am now coming to terms with those very areas and have realised that it is best to learn them sooner rather than later. This seems rather obvious but I was told to focus predominantly on your strengths as there are going to be enough of these questions on the paper for you to really show what you can do (as was the case in all but 2 or 3 past papers that I attempted). My naivety and unwillingness to expect the unexpected may have cost me a place at Cambridge, but don't let it happen to you! Plan now everything you are going to learn. It is expected that you should finish C3 and C4 at least before january (though many of you will probably have done so already) so that you can begin attempting questions. When you begin questions, don't drift towards the questions that you never have any problems with (though such questions should still take up a considerable amount of your time), aim to improve upon your weakness'. Your goal should be to be able to be able to have a decent shot (meaning 4 or so full-ish solutions or more) at any randomly-selected 6 questions from a paper. Forget always choosing the 5 or 6 questions that you are comfortable with, what if only 2 or 3 such questions appear on the actual paper?

Excuse the 'fear-tactics' but this very advice 3 or 4 months ago would have benefited me. Good luck to you all!

Thank you I will take to heart what you have said but for III do you mean M4,5 S3,4 because this is just too much. is doing fp1-fp3 and the rest of them not enough? Surely of the 8 of the questions a few must fall into you're comfort zone and then there will be a few from applied from m1-3 or s1-2? I know there is a broad syllabus for III but if i do not priotise on my pure especially i fear i will be a jack-of-all trades , master of none .What kind of stuff came up in III 2013 anyway?

Thank you I will take to heart what you have said but for III do you mean M4,5 S3,4 because this is just too much. is doing fp1-fp3 and the rest of them not enough? Surely of the 8 of the questions a few must fall into you're comfort zone and then there will be a few from applied from m1-3 or s1-2? I know there is a broad syllabus for III but if i do not priotise on my pure especially i fear i will be a jack-of-all trades , master of none .What kind of stuff came up in III 2013 anyway?

Well, tbh, if you are not learning those modules it is unfortunate but not the end of the world. To put yourself in a good position though, I would suggest that you be comfortable with at least a 'chunk' of the applied syllabus for STEP III. Also, learning them for the sake of A-levels is entirely different to learning them for the sake of STEP III. Unless you put a lot of effort in to your mechanics (and are very good) you will likely not be able to complete most STEP III mechanics questions unless you have gone further than M4/M5 and have actually being practising a lot of the relevant STEP questions.

Hmm, that is what I was told and is certainly what you would think would be the best preparation. Unfortunately you are playing dice in some sense. I think the bottom line is that if you are struggling with STEP, then it is probably best to play dice (by hoping your paper will be full of your favourite topics) as this will likely be your best chance of success. If you are not struggling with STEP then, rather than excelling at your favourite topics, it is better to leave your favourite topics until the summer and focus on improving your weaknesses.

Sorry if this sounds like mixed advice.. it probably is... and so is likely not all that helpful. Perhaps the examiner's report they publish next month will give some clues as to whether or not that paper was as intended.

- A vectors question for the first time in over 10 years
- 3 complex numbers questions
- the Differential Equations question (Which for reference is one of the preferred topics) was harder than usual
- the easiest Mechanics question (in my opinion) involved M5 content for Edexcel
- One of the statistics questions involved knowledge on co-variances that not all exam boards cover even in their final statistics modules.

Ok both of you i am getting really scared now-
If i have to do M4 and M5 that will be one hurdle over- but its not even halfway there though is it? On top of learning content I will actually have to be good at the STEP III questions which is going to be a massive feat. In a way i feel the way the further maths content in STEP III is tested is brutal- when you start you are thrown straight in the deep- there is no I like there is for II to ease you in.

I am not attempting to scare you and a lot of people manage fine without going into that. You simply asked what was different about this years paper and I told you. If you were very strong at complex numbers then you'd likely have loved it but for me (and a lot of others) it was difficult to have been asked a harsher paper.

- A vectors question for the first time in over 10 years
- 3 complex numbers questions
- the Differential Equations question (Which for reference is one of the preferred topics) was harder than usual
- the easiest Mechanics question (in my opinion) involved M5 content for Edexcel
- One of the statistics questions involved knowledge on co-variances that not all exam boards cover even in their final statistics modules.

x

Summed up perfectly^ ..though I am tempted not to include the differential equations question in the category of the things they shouldn't put on there. I feel as though it was extremely accessible as the insight required was very raw as you had to deduce it from the 'clues' you had been given before. I am all for extremely hard STEP questions so long as the content is spread evenly throughout the main topics (in such a way that the past papers offer a great preparation). Do you agree?

It seems as though you are preparing early enough to be in an excellent position. Try not to let it take over your life! Remember you have al your uni applications to do first!

I thought the DE's question was an interesting question, but a lot of people seemed quite unhappy about it especially as the DE question was the one people were looking forward to. The idea was accessible, the final part did hinge on a very specific insight regarding the nature of the function you were choosing as the E, something which was never looked at previously in the question. I thought it was a good question though.

I have no stake in this exam (and certainly wouldn't have enjoyed doing it for real!), but I thought the DEs question was a brilliantly designed question - you had 2 parts with increasing complexity leading you towards the concept of setting up a particular 'E' function which could be used to prove certain properties of the solution of the DE; then part (iii) basically expected you to set up the same situation for a DE that looked horrible, but was constructed in such a way that the obvious 'trick' worked.

There were a couple of steps in part (iii) where things could have gone wrong (e.g. needing wsinhw to be > 0 without knowing what w was, and proving that an expression in sinh x and cosh x was greater than 0), and if they had it would have been totally demoralising, but if you just followed your nose, everything worked out perfectly

I agree with all of what you've said, except for the trick being necessarily obvious. I thankfully did spot it in the exam and completed the entire question but distinctly remember thinking that it was a bit devious.

Well 'trick' is perhaps too strong a word - the point is that in order to use the same method as in parts (i) and (ii) you want to construct a function E that looks like (dw/dx)^2 + f(w) for some function f. The first term will give you a factor 2 when differentiated, so in order for f'(w) to give the extra bit you need to substitute from the original DE you just need a factor 2 times the integral of the final term in the original DE.

Perhaps I'm underestimating the effect of exam conditions, but I do think this question is more a case of "modify and repeat", rather than anything devious.

I haven't tried all the pure questions, but to my mind the final inequality in Q6 was more of a jump from the earlier (easy) parts - I floundered around myself without getting it out and had to look at the TSR solution! I'll be interested to see the Examiner's report to see how many people made it to the end of this question!

BTW, did you try Q8? Although it has an element of complex numbers, it's basically a straightforward summation question, and probably less challenging than some of the others?