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    This year's STEP exams having finished, it is about time for all of us taking the exams next June to take the baton. Below is the familiar OP put together by LOTF last year, with a few small adjustments, so thank you to him for that.

    \star For those taking STEP in 2014, 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.

    The June 2013 papers can be found using the following link:

    http://www.admissionstestingservice....ring-for-step/


    \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
    2013
    (note: 2008 and 2010 are incomplete, and 2009 seems to be non-existant)

    Avoid recent papers & solutions at all costs (2010 - 2013)! You will need these as mocks in June 2014!

    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 2000-2013 (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

    2013

    STEP I: 100 - 82 - 64 - 40
    STEP II: 100 - 79 - 67 - 32
    STEP III: 85 - 63 - 48 - 27


    \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

    This year's exams take place as follows...

    STEP I - Friday 20th June 2014
    STEP II - Thursday 26th June 2014
    STEP III - Friday 27th June 2014

    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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    Subbing EDIT: It's a good thing that I was the second post - here's the FAQ referred to in the first post:

    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 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?

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

    Spoiler:
    Show
    Credit ultimately goes to Xero Xenith who developed the post for the 2012 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.

    New: What should I know before starting STEP I and II?

    C3 and C4 are pretty key - if you go to a school where A2 maths isn't taught in the first year, your goal over the summer holidays should be to get comfortable with this material.

    Note that the STEP I and II syllabus also includes things like proof by induction (see below). Concentrate on C3 and C4 first and then at some point you can pick up the rest.

    New: What should I know before starting STEP III?

    Learn both FP2 and FP3 to get maximum coverage of the pure section.

    Geometry, vectors and complex numbers tend to be the least popular questions in any STEP paper. 2013 STEP III was a skewed paper in that lots came up in these areas. You might want to spend at least a bit of time practising these areas in case you find them to be OK with a bit of work.

    Spoiler:
    Show
    No one is good at everything and so it should be fine if you decide to concentrate on other topics in your STEP prep. People wanting more advice on this should quote me and ask in the thread.

    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.

    EDIT: It's becoming apparent that people are ignoring this advice. Do so at your own peril. I wouldn't learn loads of stats (for example) for STEP alone, but remember that all good university courses are around half applied in the first year. You won't get away with not doing any applied in your first year, so might as well get in some practice now.

    The good news is that if you're doing STEP III, you get an early introduction to a lot of university ideas. Given that this stuff tends to be easier than the pure, might as well get double advantage by doing well on STEP and learning some interesting ideas in the process.


    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 the 2012 thread(s)?

    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.

    Is there anything I can learn from the 2013 thread(s)?

    Probably, but we'll have to wait until results day to find out
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    As always if you want help of any kind quote or PM me


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    The trauma of STEP 2013 is still very much fresh in my head but once calm, I'll be keen to provide whatever useless advice hasn't been said, from the nature of the answer booklet to suggested breakfast techniques for the day of the exam! Anyway, I've been helped greatly so I'll be happy to help
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    Something I feel should be said here and now so that everyone is aware: If you are planning on taking STEP in 2013, but do not go to a school which teaches AS and A2 Maths in one year, then you should learn C3 and C4 early so that you have the prerequisite knowledge to start STEP prep early. You don't want to lose valuable preparation time because you haven't learned the content until very late.
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    (Original post by DJMayes)
    Something I feel should be said here and now so that everyone is aware: If you are planning on taking STEP in 2013, but do not go to a school which teaches AS and A2 Maths in one year, then you should learn C3 and C4 early so that you have the prerequisite knowledge to start STEP prep early. You don't want to lose valuable preparation time because you haven't learned the content until very late.
    Thanks for the advice - when you would suggest getting them both done by?


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    (Original post by DJMayes)
    Something I feel should be said here and now so that everyone is aware: If you are planning on taking STEP in 2013, but do not go to a school which teaches AS and A2 Maths in one year, then you should learn C3 and C4 early so that you have the prerequisite knowledge to start STEP prep early. You don't want to lose valuable preparation time because you haven't learned the content until very late.
    Iv been through about 4 Step I papers answering about 35 questions now and have been through about 1/8 of the Siklos Booklet- do you have any advice on when i should make the transition to Step 2 and 3?

    Modules completed :
    C1 2 3 (I know 4 but not sat ridiculously)
    M1 2 3
    FP 1 2 (halfway through FP3)
    (Did S1 last summer refreshing memory)

    Should I give Step III time? I fear of forgetting a lot of Further by the time I start since ill be long done with those modules
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    May the force be with you guys! Good luck!
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    This is getting exciting- i was around to watch the big dogs participating in 2013 thread- now i get to join in at last- the new cycle begins
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    Does anyone know what is up with the mechanics diagrams for Step I 2002 ? They labels show up d,G etc but the actual diagrams are not there- does anyone know where i can find them please?
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    (Original post by nahomyemane778)
    Does anyone know what is up with the mechanics diagrams for Step I 2002 ? They labels show up d,G etc but the actual diagrams are not there- does anyone know where i can find them please?
    On the STEP website:
    http://www.admissionstestingservice....ring-for-step/
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    oh i see- thanks
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    Will be spending a large proportion of my gap year preparing for STEP. Hi
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    I down, II and III to go
    Spoiler:
    Show
    Subbing
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    (Original post by joostan)
    I down, II and III to go
    Spoiler:
    Show
    Subbing
    oh you did I in year 12? you must be good.
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    (Original post by nahomyemane778)
    oh you did I in year 12? you must be good.
    Haha - not really, just keen
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    (Original post by DJMayes)
    Something I feel should be said here and now so that everyone is aware: If you are planning on taking STEP in 2013, but do not go to a school which teaches AS and A2 Maths in one year, then you should learn C3 and C4 early so that you have the prerequisite knowledge to start STEP prep early. You don't want to lose valuable preparation time because you haven't learned the content until very late.
    Agreed with this. Similarly for STEP III, people should take both FP2 and FP3 to get maximum coverage of the pure section.

    I've updated the second post with my FAQ. Annoyingly the thread got locked so had to reformat myself, grrrr Can we not post as much in this one?
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    PS Reviewer
    Ooh, new thread
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    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?
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    (Original post by nahomyemane778)
    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?
    Your logic sounds familiar, although I haven't sat down and looked at the question. The thread isn't so much drying up though; it's just the middle of the summer and not even past the 2013 results! You will find that it remains pretty much dead until the start of the new school year, and will be inhabitated by a small group of people up until about Christmas. Around January/February is when you can expect it to start getting particularly active.
 
 
 
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