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The 2013 STEP Prep Thread!

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    New thread here




    \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

    Please read this post before asking questions.
    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



    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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    An introduction to STEP

    This post is for all of you who are interested in preparing for the 2013 STEP exams. Early January is traditionally the time when serious STEP preparation starts, and so I thought it would be good to calm a few nerves and clear up a few misconceptions about STEP from the start.

    Apologies for the length of this post. It is meant to serve as a starting point to answer any questions you might have before you start serious STEP preparation.

    Pretty much all of this post is already covered in multiple sources. What is new would be my take on a few things. Please feel free to ignore my opinion on a certain topic, but I would think twice about ignoring my experience.

    What is the STEP?

    STEP is a series of three exams taken late June each year, usually in Year 13, almost always because it forms part of a university offer. Which papers are sat depends on the university.

    STEP I is the easiest, and STEP II and III are meant to be of similar difficulty.

    Until recently, STEP was a Cambridge entrance exam in everything but name. These days, the majority of STEP candidates are not Cambridge offer holders.

    What is the purpose of STEP?

    I'll defer to Dr. Siklos, who for a long time had an awful lot to do with STEP:

    (Original post by Dr. Siklos)
    From the point of view of admissions to a university mathematics course, STEP has three purposes.

    First, it acts as a hurdle: success in STEP is thought to be a good indicator of potential to do well on a difficult course.

    Second, it acts as preparation for the course, because the style of mathematics found in STEP questions is similar to that of undergraduate mathematics.

    Thirdly, it tests motivation. It is important to prepare for STEP (by working through old papers, for example), which can require considerable dedication. Those who are not willing to make the effort are unlikely to thrive on a
    difficult mathematics course.
    From my perspective, these are all excellent reasons for aspiring mathematicians to give STEP a go. Note that there is something very important that STEP does not do. It is not meant as a bridging course between A-Levels (or equivalent) and university. In particular, STEP requires very little additional maths beyond what you are taught at A-Level. What is different is the style and ingenuity required to answer a STEP question compared to an A-Level question.

    I've heard STEP is really hard...

    It is hard. Some stupendously intelligent people do not do well at STEP, either through lack of preparation or just a bad day. STEP is aimed at the top 2% of those who take A-Level mathematics. About 2100 STEP papers were sat in 2008, which equates to about 1000 people (because most people sat 2 papers). You have to be very good at maths to think about giving STEP a go.

    That's not to say you can't prepare. If you're reading this, it means you want to do well. There are plenty of resources to help, including this thread. Most importantly, with practice and dedication, you have every chance of excelling.

    You do not have to be a genius to do well in STEP (but it does help of course ).

    You mentioned some resources?

    Lord of the Flies has done an excellent job of collating everything in the first post of this thread.

    Note that this includes things like past papers, solutions, syllabi and grade boundaries.

    This thread is here to help you prepare, so please feel free to ask any questions

    Any other resources?

    There are a few STEP prep courses popping up. MEI has one, which you have to pay for I think. Cambridge holds an Easter school for those who hold offers from non-selective state schools.

    How much work do I need to do?

    This will depend on each person. At the very top, there is actually still a very wide spectrum of mathematical ability. Even for the brightest, thorough preparation is required.

    If I were pinned down to an answer, at this stage I would start slowly, probably look at a couple of questions a week. That will ramp up to full papers in due course, but really at the moment you want to be able to look at a STEP paper and not swear because it is so hard. That's a fine start

    Why are other universities starting to ask for STEP?

    A-Level Maths is no longer an qualification designed for the best to go on to university to study mathematics. Because of the fundamental importance of mathematics, it is now treated more of a 'service' subject, so that those who need it to study anything quantitative have those skills.

    This is not necessarily a bad thing - and really, our opinions on whether it is a good thing or not quite frankly don't matter. What is important to appreciate is that university maths and A-Levels are completely different from each other.

    If a good university taught the A-Level syllabus, the final exam would pretty much be a STEP paper. It is definitely a great way of seeing whether you have potential to study the subject at a top university.

    What about other exams?

    There are quite a lot of competitions and alternative exams that people take on top of A-Levels in the UK. In order of increasing difficulty:

    - MAT: this is Oxford's way of vetting people before interviews. It is based on a restricted syllabus but are very different from A-Levels. Probably the gentlest introduction to harder questions than A-Levels you're going to get, so if you want a gentler climb up to STEP it might be worth flicking through.

    - AEA . Used by Warwick and sometimes by Imperial, this is aimed at around the top 10% rather than the top 2% of A-Level mathematicians. It's therefore more routine than STEP, but there is the odd question that is genuinely tricky. I make it sound easier than it is; getting a distinction is still quite an achievement, and would fulfil the 'hard' part of a standard Warwick offer.

    One great thing that Warwick has done is to write extended solutions to the questions. A brilliant piece of work and should be very useful to Warwick candidates

    - Oxford's old entrance exam: Thought Cambridge had it bad? Oxford had a similar paper until they abolished it; someone on TSR put this together. They're interesting questions, about STEP difficulty, so if you want to try something new...

    - BMO: This is where its starting to get serious I won't say a huge amount about this, except suffice to say that general consensus is that even BMO1 is quite a bit harder than STEP (unless you've been subjected to that level of problem solving at an early age).

    Would you recommend I look at any of those exams?

    Not particularly. Doing hard maths is never a bad thing, but STEP has a certain 'style' and therefore it would be best to get to grips with that if your aim is to do well on STEP.

    Should I bother with mechanics and statistics?

    Absolutely. Please don't ignore them. I am staggered at how much easier they tend to be compared to the pure questions, yet very few take them for the gifts they are.

    In particular, if you want to look at some of the stats questions, you only need to know the following to do a lot of them:

    - the definition of probability
    - the definition of a probability density/mass function
    - the definition of the mean and variance of a random variable

    That's it. With just that, a huge number of stats questions open up for you.

    Is there anything special to learn for pure?

    For the pure section, you should definitely learn:

    - how to count (see e.g. STEP I 2005 Q1)
    - how to work with prime numbers (see e.g. STEP I 2009 Q1)
    - factorising quadratics and cubics (nearly always it is a good idea to factorise wherever possible)
    - the difference between a necessary and a sufficient condition (this is pretty fundamental)
    - to be careful about proving if and only if statements (you have to make arguments in both directions)
    - that there can be spurious solutions to a set of equations (basically, check all the conditions the solution needs to satisfy are actually satisfied. If you understand the difference between a necessary and a sufficient condition, you will understand why this is necessary)
    - to be careful when proving inequalities (in particular, proving a strict > versus a \geq inequality
    - how to solve a problem by separating it into a number of distinct cases (see e.g. STEP I 2009 Q3)
    - how to write a careful proof, including by contradiction (see e.g. STEP I 2008 Q1)

    All of these things are absolutely fundamental to all of mathematics, and you will have to learn this at any university in your first few weeks there. None of this stuff should be fundamentally new to you, it's just A-Levels no longer require you to know this stuff properly.

    What sort of maths should I know that's not on the A-Level syllabus?

    There is very little point of learning advanced university maths purely for STEP, so don't bother. Dabble at stuff by all means, but don't think it'll make you better at STEP.

    The only exception I can think of is modular arithmetic. Some STEP questions become easier if you do it via modular arithmetic. However, all questions I've seen are fairly easy to do the intended approach too.

    STEP I and II require proof by induction, and you should also know that you can write exp(x) as an infinite series (look in your A-Level formula book ). Those of you who do stats modules should also make sure you fully understand conditional probability, which I understand is no longer covered fully in S1 on every board.

    This is all a bit overwhelming. Where the heck do I start?

    The Siklos booklets (links in the first post) are a good place. If you don't get on with the style, then I think STEP I 1994 is a nice paper.

    I'm really struggling

    Do not look at the solutions except as a last resort. Many universities, including Cambridge, and professional exams do not issue official solutions. Might as well get used to that right now.

    There is some excellent advice in the Siklos booklets. Read that. If you've mulled over a problem for a day or so and you're still not getting anywhere, ask on this thread and someone will give you a hint. This sounds annoying but believe me when I say the satisfaction of finally solving a problem makes it all worthwhile.

    Looking at a solution genuinely deprives you of most of the benefit of doing the problem. You're meant to struggle, honest. Everyone struggles, even those who end up with an S grade. (In 2012, no-one got full marks in STEP I or II).

    Is there anything I can learn from last year's thread?

    Two things, actually. The first is that taking all three papers might not be a bad idea. Some people who missed a Cambridge offer by a grade but then got an S on STEP I got fished by the pool.

    The second is that the STEP I examiner has changed in 2012, and the paper is more of an algebraic slog than it was recently. (Judging by the examiners' report, the STEP I and STEP III examiner is the same person, but you really don't need to care about details like that.)

    Examiner's reports are great at getting nuggets of info, well worth a look once you're done with a question to see how others performed under exam conditions.
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    If you need to keep bumping the thread, it's probably an indication that no-one's wanting to talk about it.

    With moderator hat on:

    Don't bump a thread until several hours have passed. Bumping twice after 20 minutes is ridiculous.
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    Hey there. I've started looking into the papers.

    This was posted from The Student Room's Android App on my GT-I9100
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    Started looking into them - at least the questions are interesting! Need to finish C4 before I can start having some proper practice though

    What's everybody looking at applying for then?
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    (Original post by Seanyboy57)
    Started looking into them - at least the questions are interesting! Need to finish C4 before I can start having some proper practice though

    What's everybody looking at applying for then?
    That would be a good idea.

    I hope to apply for Maths with Physics - you?
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    Guys - the bodies of 2012 takers aren't even cold yet! Sick...
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    Hey! I've started to have a look at them. Nice and challenging! How is everyone going to prepare for them? Anyone going to any seminars/lessons for them at all in the year?
    • 98 followers
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    Is there a need for this thread, the 2012 exams haven't even done the exams let alone results :facepalm2:
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    You might look at http://www.mei.org.uk/index.php?page=stepandaea
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    (Original post by Maths_Lover)
    That would be a good idea.

    I hope to apply for Maths with Physics - you?
    Looking at doing Computer Science with Maths, so I'm probably going to be in the minority in this thread! At the end of the day, I'll be doing STEP no matter what any offers specify, just as a bit of a challenge really
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    Nahh. You can never be too eager.
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    (Original post by Seanyboy57)
    Looking at doing Computer Science with Maths, so I'm probably going to be in the minority in this thread! At the end of the day, I'll be doing STEP no matter what any offers specify, just as a bit of a challenge really
    There'll probably be others.

    I'll also be doing STEP no matter which unis I end up getting into and whether or not it's included as an offer. I really like this style of Maths and also as a challenge and excellent preparation for uni.
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    Looks good - thanks for the link!
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    (Original post by Seanyboy57)
    Looking at doing Computer Science with Maths, so I'm probably going to be in the minority in this thread! At the end of the day, I'll be doing STEP no matter what any offers specify, just as a bit of a challenge really
    I'm with you for CompSci with maths , although I haven't looked at STEP at all yet, only just started C4 this week.
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    Im thinking of
    Maths or MORSE... Still undecided.
    Looked at a step paper and only tried 1 question so far .
    So how was the summer exams people?


    This was posted from The Student Room's iPhone/iPad App
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    (Original post by M2k13)
    Im thinking of
    Maths or MORSE... Still undecided.
    Looked at a step paper and only tried 1 question so far .
    So how was the summer exams people?


    This was posted from The Student Room's iPhone/iPad App
    I think they went well - much better than in January. We'll see in August, though. How about for you?
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    (Original post by Maths_Lover)
    I think they went well - much better than in January. We'll see in August, though. How about for you?
    It was good overall..
    Better than January on some exams >.>.
    But yes we shall see in August :P


    This was posted from The Student Room's iPhone/iPad App
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    (Original post by M2k13)
    It was good overall..
    Better than January on some exams >.>.
    But yes we shall see in August :P


    This was posted from The Student Room's iPhone/iPad App
    Good stuff.

    So - have you started looking at any STEP papers yet?
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    (Original post by Maths_Lover)
    Good stuff.

    So - have you started looking at any STEP papers yet?
    I'm spending my last FP3 lesson this term on STEP.
Updated: June 12, 2013
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