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Dalek1099
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URGENT UPDATE:This is the Official Thread there is a fake thread about that you can tell is fake because it has a later start date so be wary about making sure you post in this Official Thread.

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 two years ago, with a few small adjustments, so thank you to him for that.

This is not too early to start as there are other a 1000 questions to attempt and I would suggest we start from 1987 so that we can be really good at STEP once we reach the more useful recent STEP questions (2000-), that reflect the current syllabus- we need to leave those questions till the end when we will be stronger at STEP.Although it may be useful to skip to 2000 a few months before if we are running out of time, so that all of the more relevant papers are completed.

The earlier you start the better and I find that students often come on here for procrastination but with this thread now available you will hopefully become distracted by Maths and it will feel as if you are procrastinating.

\star For those taking STEP in 2015, 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)
or Alternatively(this is probably easier) click on this link.
Formula booklet (download separately here)
NRICH STEP Prep:
http://nrich.maths.org/step this website can get you use to the problem solving type skills you often need for unusual STEP questions, these questions often involve(prime numbers,even odd,difference of two squares,combinations of summing up a number).
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 2013-14 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).However solutions are included in the links above that link you to the recent past papers.

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 because there are lots of papers from 1987 onwards in STEP I-III to complete and even if you are only doing STEP II-III, STEP I will be good practice for those.

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.

Your aim should be approximately 30 minutes per question because the exam lasts 3 hours and your top 6 questions are marked(I plan on looking at the solution to a question if I can't get anyway with it in 30 minutes but if you can get somewhere I would advise trying as much as you can to battle it out,by asking for help on here because it is extremely satisfying to reach that conclusion to a hard problem and you don't want to get into looking at the answer too much and copying it because you won't have developed the skills necessary to ace the paper.

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,if this is the case for you then look through all the STEP papers and you should find some questions that you can get your teeth into and then gradually you can attempt the harder ones.I would advise you to leave STEP II-III for quite a while because they are much harder and STEP III is based on the Further Maths Syllabus and focus on STEP I. 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
http://www.thestudentroom.co.uk/show...2#post43519412

(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.I would heavily advise self teaching modules and possibly doing Additional Further Maths to open more STEP questions to you and remember it would be very wise to learn C3-C4,M1-M2 and S1- S2 quickly so you can attempt all of STEP I, which is a very good place to start at even if you are only doing STEP II-III.I would highly recommend making sure you know both of FP2 and FP3 and not all colleges teach both for STEP III.Decision Maths is very useless(particularly for STEP) so avoiding do it if you can.

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-it is very hard usually to attempt the last parts of a question/get a perfect answer so I would advise possibly leaving a question partially complete if you get stuck and attempting up to 6 questions because then 6 satisfactory answers will probably do.

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

Image

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


2014

http://www.thestudentroom.co.uk/atta...7&d=1407975680

\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...

The STEP exam dates haven't been determined yet but will be released in September and the exams are usually in late June and the exam dates are designed so that they don't clash with Mathematics A Level exams and if possible Physics, since this a very common subject took by mathematics students.
In the week before the exam...

Read this post.

(thank you shamika)

\star

Good luck!

Fortunately, lessons don't start until 1st September(for me at least) so for the moment there is plenty of time to get things done, before we get really busy and have to go to college and prepare for STEP.

If you have any contributions/comments please let me know!
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Kvothe the Arcane
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Eager
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Dalek1099
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(Original post by keromedic)
Eager
I'm not too sure I am that eager because there are 1092 questions to complete plus the interview ones and if you want all those other links.As stated in the OP I actually started preparing for these exams 2.5 years before I will sit them(in Mid Y11) but now I am seriously going to prepare for them.I completed STEP questions with a few mistakes back in Y11 so I should be able to do well if I put my mind to it but I know how hard STEP is hard, in particular STEP II-II so I'm predicting 122.

If you miss the offer of A*A*A and 11 then you have a 25% chance of getting in and I met someone on the Summer School who got in with 1,2 and He knew another who got in with 1,3 so 2,2 might be enough but I am going to put everything into getting into my dream university and going to the Summer School has made me desperate to return(link to a description of my Summer School experience) , it was so good and I almost never cry(last time almost 2 years ago when my nana died).

I have wanted to get into Cambridge since Year 11 and I really want to get in.
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Dalek1099
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Do you think this would get all the marks for Question 1 1987 STEP 1?My working out is quite scruffy and although I managed with the question I found it hard to explain the key concepts that led to my conclusions.Anyone know to improve this?Its something I found hard in the Cambridge Summer School.I forgot to draw the negative part of the graph, showing that it becomes close to a straight line as e^-ax decreases as x decreases.
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Ilovemaths96
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(Original post by Dalek1099)
Do you think this would get all the marks for Question 1 1987 STEP 1?My working out is quite scruffy and although I managed with the question I found it hard to explain the key concepts that led to my conclusions.Anyone know to improve this?Its something I found hard in the Cambridge Summer School.I forgot to draw the negative part of the graph, showing that it becomes close to a straight line as e^-ax decreases as x decreases.
fairly difficult to read i'm afraid

when ddo you register to sit the exams btw?
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Dalek1099
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(Original post by Ilovemaths96)
fairly difficult to read i'm afraid

when ddo you register to sit the exams btw?
March 2015.Most of it is legible I think but some of it is just a mess my working is all over the place I hope I can correct this for the STEP exams.Are you taking STEP?I have now completed the 1st of 1092 STEP questions, the solutions linked in he OP seem very similar to me but a lot more tidy and better explained-I have attempted/completed around 10 questions though but I am going to do them all again.None of the solutions show the graph for some reason.
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Ilovemaths96
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(Original post by Dalek1099)
March 2015.Most of it is legible I think but some of it is just a mess my working is all over the place I hope I can correct this for the STEP exams.Are you taking STEP?I have now completed the 1st of 1092 STEP questions, the solutions linked in he OP seem very similar to me but a lot more tidy and better explained-I have attempted/completed around 10 questions though but I am going to do them all again.None of the solutions show the graph for some reason.
hopefully yeah and maybe aea
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Dalek1099
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(Original post by Ilovemaths96)
hopefully yeah and maybe aea
Is that not a bit too much to prepare for or are you not doing all of STEP I-III.Most people seem to do one of STEP/AEA.I am self teaching Additional Further Maths(full A Level) on top of STEP so my workload will be enormous so I need to get started as soon as possible.I can only get fully cracking STEP in about March,when I hope to have completed the self study of all my Additional Further Maths modules, at the moment I will get myself use to STEP I.
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Kvothe the Arcane
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(Original post by Dalek1099)
...
You need to make ur handwriting more neat.
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Ilovemaths96
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http://www.mathshelper.co.uk/oxb.htm

just another websit, not sure if already mentioned before, hope it helps
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alpen
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I sat STEP I and II this year so I'll offer help when I can

/subbed
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Dalek1099
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(Original post by alpen)
I sat STEP I and II this year so I'll offer help when I can

/subbed
I'm stuck on 1987 Question 2 shouldn't Y=([pi*(R+r)^2]-[pi*(R-r)^2]-[n*pi*r^2])/2
because this is the area of the bigger circle(radius R+r) takeaway the area of the smaller circle(radius R-r) then takeaway the area of the n circles of radius r and then they want the area adjacent to the smaller circle so just half of that but their expression for y looks nothing like that and I can't get that expression:confused:

For the first part(which may be related) I think that the area of the bigger circle(radius R+r) must be bigger than the area of the smaller circles(radius R-r) + the area of n circles(radius r) such that there is still area left and I ended up with 4(R/r)>n.

I am not a huge fan of Geometry so while you answer this I will skip to the more appealing next question but I haven't had much practice of y=vx substitution because I have just really self taught it a bit so I might need help on that.
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alpen
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(Original post by Dalek1099)
I'm stuck on 1987 Question 2 shouldn't Y=([pi*(R+r)^2]-[pi*(R-r)^2]-[n*pi*r^2])/2
because this is the area of the bigger circle(radius R+r) takeaway the area of the smaller circle(radius R-r) then takeaway the area of the n circles of radius r and then they want the area adjacent to the smaller circle so just half of that but their expression for y looks nothing like that and I can't get that expression:confused:

For the first part(which may be related) I think that the area of the bigger circle(radius R+r) must be bigger than the area of the smaller circles(radius R-r) + the area of n circles(radius r) such that there is still area left and I ended up with 4(R/r)>n.

I am not a huge fan of Geometry so while you answer this I will skip to the more appealing next question but I haven't had much practice of y=vx substitution because I have just really self taught it a bit so I might need help on that.
Honestly this was never my strong point, not geometry in general, but questions like these. I would check out this post here:
http://www.thestudentroom.co.uk/show...05#post9754105 and try cover up bits you don't want to know yet, as it explains it much better than I could.
I did say I sat the exams, doesn't mean I did every single question

however I am particularly fond of d.e's so tell me if you get stuck
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Dalek1099
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(Original post by alpen)
Honestly this was never my strong point, not geometry in general, but questions like these. I would check out this post here:
http://www.thestudentroom.co.uk/show...05#post9754105 and try cover up bits you don't want to know yet, as it explains it much better than I could.
I did say I sat the exams, doesn't mean I did every single question

however I am particularly fond of d.e's so tell me if you get stuck
The solution isn't even complete and doesn't include a diagram?I can form a right angle triangle with hypotenuse R as described but the angle should be 2pi/n and I can't follow most of it-I think I am just giving up with that question.I hate Geometry like that there was a much much simpler question on a C2 paper and I couldn't do it first time but that didn't come up on the exam.

Anyway I'm stuck on the differential equation too I ended up with dy/dx=(1+y^2)/((xy)(1+x^2y^2)) and I can't make that into a separate variables equation.
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alpen
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(Original post by Dalek1099)
The solution isn't even complete and doesn't include a diagram?I can form a right angle triangle with hypotenuse R as described but the angle should be 2pi/n and I can't follow most of it-I think I am just giving up with that question.I hate Geometry like that there was a much much simpler question on a C2 paper and I couldn't do it first time but that didn't come up on the exam.

Anyway I'm stuck on the differential equation too I ended up with dy/dx=(1+y^2)/((xy)(1+x^2y^2)) and I can't make that into a separate variables equation.
Divide top and bottom by y giving: \dfrac{dy}{dx}=\dfrac{\frac{1+y^{2}}{y}}{x(1+x^{2})}

I've checked btw, your expression for dy/dx is wrong

here's what I did:
Spoiler:
Show

\dfrac{dy}{dx}=x\dfrac{dv}{dx}+v
Which leads to

x^{3}\dfrac{dv}{dx}=x^{2}\dfrac{dy}{dx}-vx^{2} then sub that in

then RHS=\dfrac{1+x^{2}v^{2}}{(1+x^{2})v}=\dfrac{1+x^{2}(\frac{y^{2}}{x^{2}})}{\frac{y}{x}(1+x^{2})}=\dfrac{x(1+y^{2})}{y(1+x^{2})}
Then you should find this leads to the expression above which you can then separate the variables
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DomStaff
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(Original post by Dalek1099)
Is that not a bit too much to prepare for or are you not doing all of STEP I-III.Most people seem to do one of STEP/AEA.I am self teaching Additional Further Maths(full A Level) on top of STEP so my workload will be enormous so I need to get started as soon as possible.I can only get fully cracking STEP in about March,when I hope to have completed the self study of all my Additional Further Maths modules, at the moment I will get myself use to STEP I.

Quite scruffy, you say. Very scruffy, you meant.

I'll try this question soon and post my solution! Perhaps slightly neater
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Dalek1099
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(Original post by alpen)
Divide top and bottom by y giving: \dfrac{dy}{dx}=\dfrac{\frac{1+y^{2}}{y}}{x(1+x^{2})}

I've checked btw, your expression for dy/dx is wrong

here's what I did:
Spoiler:
Show

\dfrac{dy}{dx}=x\dfrac{dv}{dx}+v
Which leads to

x^{3}\dfrac{dv}{dx}=x^{2}\dfrac{dy}{dx}-vx^{2} then sub that in

then RHS=\dfrac{1+x^{2}v^{2}}{(1+x^{2})v}=\dfrac{1+x^{2}(\frac{y^{2}}{x^{2}})}{\frac{y}{x}(1+x^{2})}=\dfrac{x(1+y^{2})}{y(1+x^{2})}
Then you should find this leads to the expression above which you can then separate the variables
My expression for dy/dx is y^2 too much on the second term of the bottom I multiplied by y on the bottom along with x when dividing and factorised incorrectly 2 very silly mistakes.Now I have integral y/(1+y^2) dy=integral 1/x(1+x^2) dx.I can integrate the left side as 0.5ln(1+y^2) but the right hand side is a problem impartial fractions should do it but I don't know which ones I have tried a/x +b/(1+x^2) but that's not getting very far.

EDIT:x=tanu works very nicely.
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Dalek1099
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(Original post by alpen)
Divide top and bottom by y giving: \dfrac{dy}{dx}=\dfrac{\frac{1+y^{2}}{y}}{x(1+x^{2})}

I've checked btw, your expression for dy/dx is wrong

here's what I did:
Spoiler:
Show

\dfrac{dy}{dx}=x\dfrac{dv}{dx}+v
Which leads to

x^{3}\dfrac{dv}{dx}=x^{2}\dfrac{dy}{dx}-vx^{2} then sub that in

then RHS=\dfrac{1+x^{2}v^{2}}{(1+x^{2})v}=\dfrac{1+x^{2}(\frac{y^{2}}{x^{2}})}{\frac{y}{x}(1+x^{2})}=\dfrac{x(1+y^{2})}{y(1+x^{2})}
Then you should find this leads to the expression above which you can then separate the variables
I completed the question and integrated nicely using x=tanu and manipulating sin(arctanx) in to x/sqrt(1+x^2) using a right hand triangle and some algebra in o,a,h but after doing this a ln disappeared suddenly and messed it up after looking at the final solution but correcting that made everything go right.How harsh would Cambridge be? and in the solution it says partial fractions should be routine and doesn't show how to do it?how would you do it using partial fractions and not x=tanu?

I have completely skipped Question 2 and for guys needing some confidence do question 4 because it works out lovely and I have completed that nicely in a page.
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jtSketchy
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Hey everyone - it's good to see that you all have started preparing this early for STEP, but don't forget to enjoy your summer as well! (Maths is enjoyable of course, but try not to stress out if you can't do some STEP questions!)

I took all three papers this summer, so feel free to ask me any questions or queries you have about STEP, and I'll try to help


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(Original post by jtSketchy)
Hey everyone - it's good to see that you all have started preparing this early for STEP, but don't forget to enjoy your summer as well! (Maths is enjoyable of course, but try not to stress out if you can't do some STEP questions!)

I took all three papers this summer, so feel free to ask me any questions or queries you have about STEP, and I'll try to help


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