[Farhan.Hanif93]

To get the ball rolling, I've been having a go at STEP II 1991 and Q3 looks like one of those questions which could have a load of different (and if you're good at this stuff, possibly elegant) solutions so I thought perhaps I should share it and perhaps we could see how many decent solutions we can come up with for it? (plus, it's a good algebraic warm-up/practice)

Paraphrasing the question

Given distinct and non-zero and such that , show that and that

The best I could come up with so far is as follows. Don't take a peek until you've had a complete go yourself:

Spoiler:

Show

(1): , (2): , (3):

Collecting the fractions on one side of each equation and moving everything else to the other, then rearranging further we obtain:

(4): , (5): , (6):

Multiplying those three together gives .

For the next part, multiply (1) and (3) together:



Note that (1) gives so

Dividing (4) by (5) and (5) by (6), and using (5) on it's own we find , and as fractions made up of , and factors. Plugging these in to our RHS above and putting everything over a common denominator we get:



Note so:





Hence .

[deejayy]

(Original post by Farhan.Hanif93)
Probably slightly on the easier side than a question found on II should be.

As Thrug said, there's always a couple of questions which seem out of place on the paper.

When you first open the step paper on the day, what is the strategy for picking questions to do? Are we supposed to read through all the questions quickly and then judge the difficulty of the questions?

[Farhan.Hanif93]

(Original post by deejayy)
When you first open the step paper on the day, what is the strategy for picking questions to do? Are we supposed to read through all the questions quickly and then judge the difficulty of the questions?

That is possibly the most important part of the exam (besides actually answering the questions, of course). It's pretty much essential to spend around 5 minutes seeing how far you can dig in to the questions mentally without putting pen-to-paper, finding the one's which are similar to those you've done in practice etc. As soon as you come up with 4 or 5 questions that appear doable, get started. Question choice makes or breaks the exam in a lot of cases, for example I'm willing to bet that most people that didn't take a good enough look at the applied questions in STEP II last year probably did reasonably worse than they could have done (because the pure questions were notoriously difficult last year).

[twig]

(Original post by deejayy)
Ok today I did question 3 of STEP 2 from 2001 in one of my free periods, is that representative of the difficulty of STEP II? I thought it was the same as STEP I

In my opinion there is an overlap (that q being an obvious example). Some questions (e.g. integration, easier mechanics questions, etc.) are just algebra bashing with one or two little insights at most, which I think are similar for I/II/III. The more challenging questions (i.e. the "links" are less obvious to spot) may differ between papers. There are "easy" questions is all three papers.

Also, a tip for guys doing STEP this year, when practising aim to be comfortably within the grade boundaries for S/1/2 offer grade. Working under timed condition is also good. Exam pressure can make you do weird things. For I last year, nerves took me down a grade, as a small mistake in my working prevented me from doing the last part to a certain question.

I'm considering doing II/III. Don't want to do it unless I'm 100% committed to revising for it.

[deejayy]

(Original post by Farhan.Hanif93)
--

What did you get in step last year?

[Farhan.Hanif93]

(Original post by deejayy)
What did you get in step last year?

1,2. Closer to S,1 than 2,2, however.

[Ree69]

(Original post by Farhan.Hanif93)
To get the ball rolling, I've been having a go at STEP II 1991 and Q3 looks like one of those questions which could have a load of different (and if you're good at this stuff, possibly elegant) solutions so I thought perhaps I should share it and perhaps we could see how many decent solutions we can come up with for it? (plus, it's a good algebraic warm-up/practice)

Paraphrasing the question

Given distinct and non-zero and such that , show that and that

I just had a quick look at Q3 of STEP II 1991 - that looks nothing like what you've paraphrased above.

I'm a little scared.

EDIT: Sorry, turns out I was looking at the wrong paper! I may just download them all from the OP.

[Farhan.Hanif93]

(Original post by Ree69)
I just had a quick look at Q3 of STEP II 1991 - that looks nothing like what you've paraphrased above.

I'm a little scared.

EDIT: Sorry, turns out I was looking at the wrong paper! I may just download them all from the OP.

Yeah it should probably warned that the titles for the older papers were not simply I, II and III so it seemed that whomever compiled them into a folder forgot to put the correct papers in the correct sections.

To clarify: Mathematics = I, Further Mathematics paper A = II, Further Mathematics paper B = III.

(Original post by Xero Xenith)
...

You might want to put that somewhere in the OP.

[Ree69]

(Original post by Farhan.Hanif93)
Yeah it should probably warned that the titles for the older papers were not simply I, II and III so it seemed that whomever compiled them into a folder forgot to put the correct papers in the correct sections.

To clarify: Mathematics = I, Further Mathematics paper A = II, Further Mathematics paper B = III.

Yeah I think I have a wad of Further Mathematics paper As missing from my STEP collection . Where did you download your old STEP papers from?

[Farhan.Hanif93]

(Original post by Ree69)
Yeah I think I have a wad of Further Mathematics paper As missing from my STEP collection . Where did you download your old STEP papers from?

If I'm being absolutely honest, I can't remember! It was quite a long time ago.

I recall that it was quite hard to find the 1988/1989 papers (might not be the case anymore) so if anyone has any difficulties finding those then I could upload them if necessary.

[Xero Xenith]

(Original post by Farhan.Hanif93)
Yeah it should probably warned that the titles for the older papers were not simply I, II and III so it seemed that whomever compiled them into a folder forgot to put the correct papers in the correct sections.

To clarify: Mathematics = I, Further Mathematics paper A = II, Further Mathematics paper B = III.


You might want to put that somewhere in the OP.

I was not aware of this - my apologies! I didn't mean to mislead anyone

What do you mean by the correct 'sections'? And when was the cutoff year between the old style and new style?

[Farhan.Hanif93]

(Original post by Xero Xenith)
I was not aware of this - my apologies! I didn't mean to mislead anyone

What do you mean by the correct 'sections'? And when was the cutoff year between the old style and new style?

I think we may have a slight misunderstanding here.

By "whomever compiled them into a folder", I was referring to the person that compiled the folder that I have, which was downloaded nearly two years ago. I haven't downloaded your folder yet so I couldn't judge it's contents.

By correct sections, I meant that all the STEP III papers (even the old ones with the weird titles) should be in the STEP III subfolder, same for I and II etc. You possibly may have done that already.

EDIT: As for the old style - new style thing, assuming you're talking about the syllabus change I think it was 2001 or 2003 but don't quote me on that.

[Xero Xenith]

(Original post by Farhan.Hanif93)
I think we may have a slight misunderstanding here.

By "whomever compiled them into a folder", I was referring to the person that compiled the folder that I have, which was downloaded nearly two years ago. I haven't downloaded your folder yet so I couldn't judge it's contents.

By correct sections, I meant that all the STEP III papers (even the old ones with the weird titles) should be in the STEP III subfolder, same for I and II etc. You possibly may have done that already.

Ahh I see!

But many thanks - you made me notice I have some mislabelled ones, with some duplicates. I'm missing Further Maths Paper A from 1990-1993 - does anyone have these?

And yes, this means the packs I've been posting have these mistakes - it's just mislabelling of STEP II and III from 1990 to 1993. Very sorry to anyone who's already downloaded my mistakes

(Original post by Ree69)
I just had a quick look at Q3 of STEP II 1991 - that looks nothing like what you've paraphrased above.

I'm a little scared.

EDIT: Sorry, turns out I was looking at the wrong paper! I may just download them all from the OP.

It's a trap! My 1991 papers are screwed up, sorry will upload a full, complete pack of ninjas when this is fixed

[Farhan.Hanif93]

(Original post by Xero Xenith)
I'm missing Further Maths Paper A from 1990-1993 - does anyone have these?

Here.

[Kangaroo_rampage]

hi,
I am currently doing a levels in maths, further maths, physics, chemistry, biology. I am hoping on applying to Cambridge next year for engineering. I am currently in next round of the mathematical Olympiad and also doing my maths a level in one year. I was wondering if doing step 1 and step 2 would increase my chance of getting in to Cambridge.

[Xero Xenith]

(Original post by Farhan.Hanif93)
Here.

Thank you so much

I've sorted these - if anyone who downloaded my package from before is reading this, it has 1990-1993 mislabelled. Delete them and download this file to replace them (might take a few minutes to appear):
http://www.mediafire.com/?kvy45k85w0sf9b6

[Aristotle's' Disciple]

Quick, question, are we not using the STEP mega thread?

[Zhy]

Personally I'm better at the applied. I did a mock and just did all the mechanics and stats questions, which was enough for a 1. Less good at the pure, but I have time to get better.

[Xero Xenith]

(Original post by Aristotle's' Disciple)
Quick, question, are we not using the STEP mega thread?

It was suggested that we make our own - I think previous years did as well.

[Aristotle's' Disciple]

(Original post by Xero Xenith)
It was suggested that we make our own - I think previous years did as well.

Oh right, awesome.