# 2013 STEP thread mark II

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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

If you have any contributions/comments please let me know!

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

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

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.

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)

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

Start preparing

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.

Don't worry if STEP seems difficult at first - it is

keep searching. This is crucial, because unless you're superhuman, you

Get used to the idea of spending lots of time on a single question.

Yes - but this doesn't mean it will get

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.

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

(many thanks to shamika)

Look here or the last pages of Siklos' booklets

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

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

The syllabus for III is very wide,

so the above is

Useful tricks (TSR thread) & Graph sketching

STEP grades:

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

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

The exam lasts 3 hours sharp. With the exam sheet, you will be given the

It is the same each year. Calculators have been banned since 1997.

You will have to write in black ink, and correction fluid is

Drafting paper

write

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)

Read this post.

(thank you shamika)

**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.

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.

**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)

**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

**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:

STEP I: 93 -

STEP II: 91 -

STEP III: 84 -

Show

**2012**

STEP I: 93 -

**77**- 54 -35

STEP II: 91 -

**72**- 60 - 31

STEP III: 84 -

**65**- 53 - 32

**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 towrite

*most*of your working down on the exam sheet - even if this means writing out multiplications.**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)

**In the week before the exam...**Read this post.

(thank you shamika)

**Good luck!**If you have any contributions/comments please let me know!

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(Original post by

....

**Lord of the Flies**)....

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#5

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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#6

(Original post by

wow, this year's lot are clearly the keenest ever. I don't think a 2nd thread has ever been needed!

**ben-smith**)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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#7

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

http://www.youtube.com/watch?v=Nwv61Uu1fdA

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#9

(Original post by

Why was a second thread needed - is there a limit on posts or something?

**davros**)Why was a second thread needed - is there a limit on posts or something?

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#10

(Original post by

x

**DJMayes**)x

Regarding your question about Nellie the elephant

Spoiler:

Show

Spoiler:

Show

With SHM, i'm sure that the equation for motion 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 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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#11

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?

Posted from TSR Mobile

Posted from TSR Mobile

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#12

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!

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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#13

(Original post by

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"?

**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"?

"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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#14

(Original post by

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".

**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".

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#15

(Original post by

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?

Posted from TSR Mobile

**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?

Posted from TSR Mobile

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#16

(Original post by

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".

**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".

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#17

(Original post by

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?

**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?

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(Original post by

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

**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

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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#19

**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?

Posted from TSR Mobile

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#20

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 ? (This is what I did :/)

Or is that a no-no in STEP I?

Just having a look through it now.

In Q2, am I allowed to use ? (This is what I did :/)

Or is that a no-no in STEP I?

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