STEP Prep Thread 2017

Welcome to the 2017 STEP prep thread. This is the place to discuss, post problems, or ask any questions you may have regarding the exam!

Note about timings: based on previous threads, there are always some who will make a start in the 2016 summer holidays. Don't worry if you're not one of them! Most people will start seriously in January 2017, because that's when Cambridge will make their STEP offers. Please do not be put off if you read the thread and can't follow the thread. This thread is open to all, no matter what your level of preparedness - please ask your questions and hopefully someone will be able to help you. The only thing I ask is to read this first post in case it already answers your question. :smile:

If you are reading this ahead of Cambridge interviews, AEA, MAT and STEP I can be great practice for problem-solving, which is basically what the interview is about.

Acknowledgements: most of this information has been collected by people taking STEP in the past so hopefully you'll find the resources here useful. Particular thanks to @Lord of the Flies for making the original version of this and @shamika for the massive renovation (you can attribute this entire thing to him).

0. General information

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.

2017 exam dates

STEP I: June 8
STEP II: June 12
STEP III: June 22

STEP grading and typical offers

STEP is graded as follows

S - Outstanding
1 - Very good
2 - Good
3 - Satisfactory
U - Ungraded

Remember that STEP is aimed at the top 2% of all maths A-level students, so it is meant to be hard. Typical offers are:
- Cambridge: 1, 1 in STEP II and III
- Warwick: 2 in any paper (with A*, A*), ~~or 1 in any paper (with A*, A)~~
- Imperial: typical offers are now based on MAT. Occasionally, there are some STEP based offers (most often a 1 or 2 in STEP II or III)
- UCL: 1 in any paper can make up for an A* (if A* A* A is achieved, there is no need for STEP)
- Bath: Occasional offers include a 2 in a STEP paper.

What is the point of STEP?

I'll defer to Dr. Siklos:

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.

Note: You may have heard that Cambridge is introducing entrance exams at the interview stage for all students. The Mathematics Admissions Committee have confirmed that they will continue to use STEP for the basis of their admissions.

Exam conditions:
- Each paper is 3 hours long.- No calculators are allowed, but you do get a formula booklet- You are given answer booklets with lined paper.

Do all of your working in this booklet. Every year someone asks whether scrap paper is given. You have no need for it - the only way you can get marks is if the examiner sees your work. This includes all arithmetic / algebra that you would want to do on the side. You don't get marks for being neat, you get marks for doing correct maths.

- You are given no reading time, and therefore choosing the right questions is key.

If you're finding STEP hard...

You're in the right place - it is hard and this thread is designed to help you.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 ).

1. Required knowledge

See here for the direct link to the full Specification.

For STEP I and II, the syllabus is:

- Pure (Q1-8): C1-C4 plus proof by induction.
- Mechanics (Q9-11): M1-M2
- Statistics (Q12-13): S1-S2

If you are trying to prepare for STEP I, you really should cover C3 and C4 first to give yourself enough to do - covering this material and being comfortable with it by January 2017 is highly recommended. If you want extension material before you cover C3 and C4, you might want to look at the MAT.

For STEP III, the syllabus also covers Further Maths. Note in particular that for the applied:- Moments of inertia and motion around a fixed axis is on-syllabus (typically in M4/5)- Relative motion is on-syllabus (but not tested often - typically in M4)- Generating functions are on-syllabus (but I believe no longer in any A-level module)

Krollo, Zacken and Number Nine have kindly categorised all questions by topic - see the spreadsheet in this post. STEP II questions here.

New: Dr. Stephen Siklos has very kindly created an online STEP question lookup databse at http://stepdatabase.maths.org/index.html - the instructions on how to use it are provided on the site as well and it's an excellent tool!

2. The STEP Megapack

Download the latest version of the pack here. (Note it is nearly 100MB! See section 3 for details where you can download individual files.)

This includes:

- Past papers from 1987 - 2014
- Official solutions (2004 onwards) and examiners' reports (2007 onwards)
- Both of Dr. Siklos' booklets*
- Specification (i.e. the syllabus)
- The formula booklet

More information about the Siklos booklets:
1. Advanced Problems in Core Mathematics - 67 problems, some from STEP papers. This is the revised version of the original booklet, based on the current A-Level syllabus. More details are given than the original, with a nice intro. It is a good idea to start with this one.
2. Advanced Problems in Mathematics - 43 problems mostly taken from STEP papers, some adapted. As good as the first one but the problems are taken from older papers, so the Core Maths booklet is probably the most relevant.

Siklos has amalgamated the above booklets into a book: you can download this for free from the link at: http://www.openbookpublishers.com/product/342/advanced-problems-in-mathematics--preparing-for-university

~~If you can afford it, please consider buying the paperback, because it's nice to give a little something back to the person who's torturing you with STEP papers~~ [Disclaimer: Siklos has commented that he does this on a non-profit basis, so he doesn't actually get anything from you buying the book, but of course, feel free to purchase it if you think it'll be helpful!]

*Siklos has had an awful lot to do with STEP, including writing exams, being the principal examiner, organising the Cambridge Easter prep sessions and advising on the admissions process for Cambridge. These booklets come highly recommended and are a great place to start preparing for STEP.

3. Other Resources

- The Admission Testing Service "preparing for STEP" page - this will be the official place the 2016 papers will be released and is the official site for STEP.

- Individual STEP papers can also be downloaded from The Maths Orchard or Mathshelper.

- A spreadsheet cross-referencing the Siklos booklets to STEP questions

- University of Warwick videos of worked STEP solutions (follow the links from this page).

- Dr. Siklos' videos of worked STEP solutions (follow the links from this page)

- STEP Support programme and in particular their discussion forum.

- The STEP Correspondence course (this is outdated), which is designed for early STEP preparation. Assignments are on this page. They also have a forum which might be helpful.- Meikleriggs website is an oldie but has worked to solutions to STEP papers (you might need to sign-up to the site).

- NRICH STEP preparation modules. (I'm not convinced that these are particularly helpful. However they were developed by Cambridge so I would be remiss not to include them on this list.)

- TSR hints and tricks

- STEP hacks and tricks (made by the 2016 year!)

- STEP Questions Database by Dr. Siklos

- Notes on logic and proof provided by ATS.

- Notes on Mechanics by Krollo

4. Solutions

If you're stuck on a problem, you're basically like every single person who has prepared for STEP. Do not look at solutions unless you've thought about a problem seriously (i.e. at least for more than one day), and have asked on this thread for help.If you do need the solutions:- The Megapack has all of the official solutions since 1996. Some of these are basically hints, which are better for you in the long run (because once you see a solution, the question is basically ruined for you).- TSR has worked solutions to most papers (no idea why we don't have 2009 here - something for you to work on? Update: we did go ahead and made the 2009 one!)

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 2013 2014 2015 2016

4. Marking and Grade Boundaries

All questions are marked out of 20. Best 6 answers contribute to your final score.

After a Freedom of Information request, Admissions Testing Service provided the 2014 solutions (with mark schemes). I am releasing these in the public interest to help students prepare for STEP.

Individual links straight to the files are below:

STEP I 2014 mark scheme
STEP II 2014 mark scheme
STEP III 2014 mark scheme

Also, thanks to the correspondence course, we have:

STEP I 2013 mark scheme
STEP II 2013 mark scheme
STEP III 2013 mark scheme

The 2015 markschemes are available on the ATS's website, along with STEP 2011 I. There's also some miscellaneous markschemes here.

Note that the general guidance given regarding marking remains unchanged - see this link for details.Grade boundaries are shown in the picture below

6. FAQ

When should I start?

Whenever you want. January 2017 should be sufficient time for a good Cambridge offer holder to get a 1,1 if they work hard. Using that as a benchmark might be helpful (be honest with yourself about how good you are!)

I need inspiration before the exam...

This post seems very popular. I think it's useful well before the exam though. In particular, the stuff about knowing what

A \Rightarrow B

means, what "if and only if" means, and the fact that

\sqrt {x^2} = |x|

comes up again and again in STEP.

Can I get by with just the pure?

Maybe. But the applied is often straightforward and if you ignore it, you'll be in for a shock at uni because your first year may be up to 50% applied. Things that tend to be relatively simple:

- Mechanics: collisions, projectiles
- Statistics: definitions of a pdf/cdf, expectations, counting arguments for probability.

What should I leave as mocks?

Make sure that during your prep you cover the most recent papers as this is the best indication of the current difficulty of STEP. I do not recommend that you have to leave all of the most recent papers as mocks.

You should see this post for a very detailed FAQ - no need to read it all!

7. After the exam

This advice will be updated if the 2017 process if different to 2016.

- Do not register for results until 5 days before the exam. This is due to a quirk in the results page, which has caused issues in the past.

- Some browsers, particularly Chrome, don't work well with the results page. The best browsers seem to be IE and Firefox

.If you are a Cambridge offer holder and have missed your offer:

- Check UCAS Track: your original college may have accepted you anyway. Congrats!

- If not, you may be in the summer pool. Call up your college and provide your A-level UMS - assuming this is good it may help your case. You should keep your emails / phone with you as you may be get told that another college has accepted you. Note that the pool has access to your actual STEP scripts, not just your marks, so they will be looking in detail for who to accept.

- Your best place for advice will be the TSR Summer pool thread, where experienced people will hopefully be on hand to deal with your situation.

No matter what happens, you have become a better mathematician for attempting STEP and if you're good enough to try it, you should have no problems being a success in whatever you do, wherever you end up!

Above all, best of luck!

(edited 6 years ago)

Scroll to see replies

PRSOM

I doubt I'll need to do STEP but I'm following just to challenge myself during my gap year.

Reply 3

EricPiphany

Lovely.
I've been redoing some STEP questions over the last few days.

Reply 4

DonAchille

Definitely getting inviolved!

Reply 5

girlwonder17

Hey thanks for making this.

Firstly what is the natural progression of difficulty of pre university maths.

Should I be going along the lines of: AS>MAT>A2>AEA>STEP/Olympiad. Looking to do I II III in summer 17

Also from I 2009:

A proper factor of an integer N is a positive integer, not 1 or N, that divides N.(i) Show that 32 × 53 has exactly 10 proper factors. Determine how many other integers ofthe form 3m × 5n(where m and n are integers) have exactly 10 proper factors.(ii) Let N be the smallest positive integer that has exactly 426 proper factors. Determine N,giving your answer in terms of its prime factors.

Having done i fine. It is the second part I am having difficulty doing. How am I supposed to give an answer to a number I dont know in terms of prime factors.

Thanks :smile:

Reply 6

Krollo

I'll be knocking around here to help... I have a STEP mechanics guide in the works that will hopefully be of some use to you all. :sexface:

Posted from TSR Mobile

Reply 7

EnglishMuon

pls help me with the steps. any1 know how to sketch quadratics??

Reply 8

ValerieKR

Original post by EnglishMuon

pls help me with the steps. any1 know how to sketch quadratics??

Type 'How to sketch quadratics into google'.

Seriously though that's far more a PC1/2 problem than a STEP problem - try posting in a PC1/2 thread or a general help thread.

Edit: I think I might have just been trolled :/
Edit 2: Seriously though, stay roughly on topic

(edited 7 years ago)

Reply 9

EnglishMuon

Original post by ValerieKR

lol yea dw, was a joke. Did step this year :wink:

Reply 10

11234

Original post by EricPiphany

Lovely.
I've been redoing some STEP questions over the last few days.

You should try step III 2007 q2, its a beauty

Reply 11

11234

Original post by Krollo

I'll be knocking around here to help... I have a STEP mechanics guide in the works that will hopefully be of some use to you all. :sexface:

Posted from TSR Mobile

What was your choice of questions did you go all pure or some mech

Reply 12

IrrationalRoot

Original post by EnglishMuon

pls help me with the steps. any1 know how to sketch quadratics??

m8 I'll be sketching quadratics all day at warwick.

Reply 13

11234

Original post by EnglishMuon

pls help me with the steps. any1 know how to sketch quadratics??

what college you get into

Reply 14

EnglishMuon

Original post by 11234

what college you get into

King's

Reply 15

Paraphilos

Gosh this thread title brings me back. I remember when I took STEP in 2012 and planned to 'ace' the mechanics only to find halfway through the exam I was making hardly any progress at all. Gave up and went pure :wink:

Luckily it worked.

Reply 16

11234