TheMagicMan
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STEP is fast approaching now, so good luck to everyone who's involved!

I will have a go at the papers as soon as I can get my hands on them (it would be great if someone could take the paper out and scan it...).

All credit for the below OP goes to Lord of the Flies

\star For those taking STEP in 2013, here is the place to discuss, post problems, or ask any questions you may have regarding the exam! \star



Download the STEP Megapack here

This includes the following:

Past papers, solutions, exam reports 1987-2012 (download separately for years 1998-2012 here)
Formula booklet (download separately here)
Stephen Siklos' booklets (download separately here and here)
Spreadsheet to print out and keep track of which questions you have done (download separately here)

See here for a cross reference between the first Siklos booklet and the original STEP papers from which the questions are taken.

The University of Warwick has uploaded a few videos of worked out STEP questions here, which you may find helpful.

\star

TSR has a solution bank of its own if you are interested:

1987 · 1988 · 1989 · 1990 · 1991
1992 · 1993 · 1994 · 1995 · 1996
1997 · 1998 · 1999 · 2000 · 2001
2002 · 2003 · 2004 · 2005 · 2006
2007 · 2008 · 2009 · 2010 · 2011
2012 I · 2012 II · 2012 III

(note: 2008 and 2010 are incomplete, and 2009 seems to be non-existant)

Avoid recent papers & solutions at all costs (2009 - 2012)! You will need these as mocks in June 2013!

For the moment, the links are there more for coherence than anything else.

\star

FAQ

When should I start preparing?

Start preparing early (but be careful not to use up all the past papers too fast!).

Where do I start?

S. Siklos' booklets are a good place to start (link above). Once you feel more comfortable with the questions, you may
want to tackle STEP I papers. It is good to begin with papers that are not too old (the exam has somewhat changed since 1987)
but not too recent: I would say start around 2000.
Doing one question a day starting January/February and then moving on to full papers in April/May is a good plan.
Your aim should be approximately 45 minutes per question.

What if I get stuck?

Don't worry if STEP seems difficult at first - it is meant to be hard, and everyone is feeling the same. When you're stuck,
keep searching. This is crucial, because unless you're superhuman, you will get stuck in the exam at some point, and you will not have a hints & answers booklet by your side.
Get used to the idea of spending lots of time on a single question.

Will it get easier?

Yes - but this doesn't mean it will get easy. With practise, you will come to enjoy the problem solving,
and you will start recognising certain techniques/tricks which inevitably make the questions more accessible.
Also, it should be said that many questions seem very difficult from the outside, but turn out to be
easier than expected once you start writing things down.

Is it strategic to focus on pure only?

No. Since preparation time isn't an issue, it is best to give yourself more choice
and work on all areas of STEP questions. You never know where a gift-question might lie.
Also, rumor has it that the applied questions tend to be slightly easier than the pure ones.

Read the post below for more information

(many thanks to shamika)

\star

Required knowledge

Look here or the last pages of Siklos' booklets

STEP I & II:

C1-4 + M1-2 + S1-2 + proof by induction

STEP III:

Above + FP1-3 + M3-5 + S3-4

The syllabus for III is very wide,
so the above is roughly what the questions can touch on.

Useful tricks (TSR thread) & Graph sketching


\star

Marking

STEP grades: S (Outstanding), 1 (Very good), 2 (Good), 3 (Satisfactory), U (Unclassified)

Mark-schemes are not published so it is difficult to say how STEP is marked. What we do know:

Questions are marked out of 20, no bonus points - you should look at no more than
6 questions in the exam (total out of 120). Any correct answer will be awarded maximum marks.
No points are given for mathematical elegance. Most marks are method marks: according to DFranklin
small slip-ups will only cost you 1-2 points. Four good (not necessarily perfect) answers will generally
award you a 1.

The Exam Reports (link above) are informative on marking too - take a look.

Grade boundaries for years 2000-2012 (previous years are not available):

Spoiler:
Show

Image

2012

STEP I: 93 - 77 - 54 -35
STEP II: 91 - 72 - 60 - 31
STEP III: 84 - 65 - 53 - 32


\star

Exam conditions

The exam lasts 3 hours sharp. With the exam sheet, you will be given the formula booklet (link above).
It is the same each year. Calculators have been banned since 1997.
You will have to write in black ink, and correction fluid is not permitted.
Drafting paper is allowed (ask your school to provide some if you want any), but generally it is advised to
write most of your working down on the exam sheet - even if this means writing out multiplications.

\star

Standard (STEP) offers

University of Cambridge: 1,1 in STEP II, III
University of Warwick: 1 (if A*A* not ach.) or 2 in any paper
Imperial College London: 2 in STEP II or III (occasionally)
University College London: 1 (if A*A* not ach.)
University of Bath: 2 in any paper (occasionally)

\star

In the week before the exam...

Read this post.

(thank you shamika)

\star

Good luck!

If you have any contributions/comments please let me know!
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Lord of the Flies
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:cheers:
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TheMagicMan
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(Original post by Lord of the Flies)
:cheers:
:evilbanana:
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TheMagicMan
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(Original post by Lord of the Flies)
....
One possible addition to this is the following: Make life easy for the examiner. Use full sentences as much as possible and write legibly. Use alternate lines. Don't be afraid to take up masses of paper. That way, if you do get something wrong, the examiner will be much more inclined to give you marks. Also, it drastically reduces the chances of an error if your solutions are well set out.
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Dirac Spinor
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wow, this year's lot are clearly the keenest ever. I don't think a 2nd thread has ever been needed!
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davros
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(Original post by ben-smith)
wow, this year's lot are clearly the keenest ever. I don't think a 2nd thread has ever been needed!
Why was a second thread needed - is there a limit on posts or something?
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Zakee
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Best of luck everyone! Little time left, but I hope that everyone triumphs in the exam and comes out content. I'm sure you'll all do amazingly well. If there's anything I can add, just make sure you've a good night before the exam. That's pivotal, as it can make all the difference. I'm sure you've all put in effort, and with your natural ability as well, (in the wise words of Rob Schneider):


http://www.youtube.com/watch?v=Nwv61Uu1fdA
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hypercube
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(Original post by Aurel-Aqua)
STEP II, Question 10
Please check it

q=e. We also know that v_{n\text{-final}} = (1-e)V
Where is it from?
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bananarama2
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(Original post by davros)
Why was a second thread needed - is there a limit on posts or something?
Yep. 10000.
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Sketch
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(Original post by DJMayes)
x

Regarding your question about Nellie the elephant
Spoiler:
Show


Spoiler:
Show
With SHM, i'm sure that the equation for motion v^2 = \omega^2 (a^2 - x^2) is only true for the oscillations of a spring/string when it is "pinged" from rest, or rather, gently depressed, and then released, from some point away from the centre of oscillation? I don't think that you can use the above equation and then give a particle attached to it a velocity. The v in this sense is only for velocities which will "naturally" occur within the oscillations. I think the best way is to consider the combined mass moving at 4m/s and then find out any equations for SHM, rather than the other way round.. I think considering energy losses/gains is the better method IMO
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tommyridges
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I was just doing STEP I 2003 Q6 and was wondering why they've put the second part of the question in when a simple substitution makes it the same as the first part. Does anyone know why that second part got put in the paper or what the point of it was? I know it's likely no one really knows but was wondering what anyone's opinion on it is?


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Genesis2703
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Yay, great we managed to get onto a second thread!

I have a query about sufficient and necessary conditions. I know to prove something is sufficient you just need to show that said condition means that it works, and to show it is NOT necessary you describe a different case that still works. But how do you go about proving something is necessary, I mean the method as it seems very hard to prove that no other possible case will ever work. I'm sure there was a question I was thinking of in reference to this, but my memory has slipped. Is this the same as "if and only if"?

Oh and one thing i've noticed is hindering me a lot in the statistics section is my lack of knowledge of conditional probability (notation, formulas etc.) as apparently that isn't formally done in OCR until S4, it is very annoying that I can do half of a stats question, then get undone because they make it conditional. I'm struggling to find good notes online which explain it and help me to tackle some questions as well...

Good luck to everyone though of course!
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Lord of the Flies
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(Original post by Genesis2703)
I have a query about sufficient and necessary conditions. I know to prove something is sufficient you just need to show that said condition means that it works, and to show it is NOT necessary you describe a different case that still works. But how do you go about proving something is necessary, I mean the method as it seems very hard to prove that no other possible case will ever work. I'm sure there was a question I was thinking of in reference to this, but my memory has slipped. Is this the same as "if and only if"?
The idea is the same, the argument is just going in the opposite direction. "A if B" is equivalent to "if B then A", or in other words, that A is necessary for B to be true.

"C only if D" is just another way of saying "if C then D".

"if and only if" means that the condition is both necessary and sufficient i.e. that "A if B" (if B then A) and "A only if B" (if A then B). The statements are then said to be equivalent.
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bananarama2
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(Original post by Lord of the Flies)
The idea is the same, the argument is just going in the opposite direction. "A only if B" (B is a necessary condition for A) is equivalent to "if B then A". So, if I wanted to prove that "y is strictly increasing only if y'>0" I just need to prove that "if y'>0 then f is strictly increasing".

"if and only if" means that the condition is both necessary and sufficient i.e. "if A then B" and "A only if B".
All this logic stuff reminds me of the TSA I took for Cambs :moon:
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hassassin04
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(Original post by tommyridges)
I was just doing STEP I 2003 Q6 and was wondering why they've put the second part of the question in when a simple substitution makes it the same as the first part. Does anyone know why that second part got put in the paper or what the point of it was? I know it's likely no one really knows but was wondering what anyone's opinion on it is?


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Just to examine whether you can find the right substitution I guess. I also wondered that though. How many marks would it be , any idea?
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Genesis2703
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(Original post by Lord of the Flies)
The idea is the same, the argument is just going in the opposite direction. "A only if B" is equivalent to "if B then A". So, if I wanted to prove that "y is strictly increasing only if y'>0" I just need to prove that "if y'>0 then f is strictly increasing".

"if and only if" means that the condition is both necessary and sufficient i.e. "if A then B" and "A only if B".
Hmmm ok I think i get it, I see what you mean about if and only if. But surely is a condition is necessary it is in itself sufficient? Because if you need it then of course it will work with it :s
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tommyridges
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(Original post by hassassin04)
Just to examine whether you can find the right substitution I guess. I also wondered that though. How many marks would it be , any idea?
I was thinking that too, it surely can't be worth many marks.... I just thought it seemed a bit pointless, including that second part


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TheMagicMan
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(Original post by Genesis2703)
Hmmm ok I think i get it, I see what you mean about if and only if. But surely is a condition is necessary it is in itself sufficient? Because if you need it then of course it will work with it :s
No!

For example, for real x, x>2 is a necessary condition for x>3, but it is not sufficient (say x=2.5)
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Llewellyn
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(Original post by tommyridges)
I was just doing STEP I 2003 Q6 and was wondering why they've put the second part of the question in when a simple substitution makes it the same as the first part. Does anyone know why that second part got put in the paper or what the point of it was? I know it's likely no one really knows but was wondering what anyone's opinion on it is?


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I imagine they would want you to complete the square so you can see the link to the first part... but yeah it is pretty trivial, and a very obvious substitution given the limits. I imagine it may be worth 4 or 5 marks along with the comment that once you substitute the same cases arise as in part i)
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Appeal to reason
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Did I 2008 as a mock today, went fairly well, especially considering I'd already done 2 of the pure questions in the STEP problem solving thread (so I wasn't allowed to do 5 or 8 - had I been able to, it would have gone even better still)
Just having a look through it now.

In Q2, am I allowed to use \int\frac{1}{\sqrt{a^2+x^2}}\dx = sinh^{-1}(\frac{x}{a})? (This is what I did :/)

Or is that a no-no in STEP I?
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