Zacken
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Welcome to the 2020 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 2019 summer holidays. Don't worry if you're not one of them! Most people will start seriously in January 2020, 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.

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 heavily updating it.

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.

2020 exam dates

STEP I: TBC
STEP II: TBC
STEP III: TBC

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: A*A*A* without STEP, A*A*A with grade 1 in any STEP paper

- Imperial: require STEP if you missed the MAT deadline, or if you had a borderline MAT result

- King's College London: require STEP or AEA if you are doing AS Further Maths - rather than the full A-level

- UCL: A*A*A without STEP, A*AA with STEP grade 1 or distinction in AEA

- Bath: recommend, and will give alternate offers if STEP is offered

-Lancaster: AAA without Further Maths or STEP, drops to ABB if a grade 3 in STEP and Further Maths

- Bristol: reduced offer with STEP

What is the point of STEP?

I'll defer to Dr. Siklos:


(Original post by Dr. Siklos;undefined)
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

- You are not given a formula booklet from 2019 onwards. You may use a formula booklet when practicing past papers, but Siklos himself has said that the formula booklet has never been essential.

- You are given a 40 page answer booklet with lined paper. The current rules state that you may not get additional answer booklets, so be wary of your usage. This is currently volatile and may change. The first three pages of the answer booklet are admin, where you have to enter your candidate information and questions answered so the marking process can be anonymized. Do not write your name anywhere in the answer booklet where it is not explicitly asked for.

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 2016, 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

- STEP I is based on A Level Mathematics. The paper has 11 questions across two sections: the first contains 8 pure questions, and the second contains 2 mechanics questions and 1 probability question.

- STEP II is based on A Level Mathematics and AS Level Further Mathematics. The paper has 12 questions across three sections: the first contains 8 pure questions, the second contains 2 mechanics questions, and the third contains 2 probability/statistics questions.

- STEP III is based on A Level Mathematics and A Level Further Mathematics. The paper has 12 questions across three sections: the first contains 8 pure questions, the second contains 2 mechanics questions, and the third contains 2 probability/statistics questions.

The specification changes do not mean that STEP is entirely different and you don't have any preparation resources. In the words of the ATS: "The style of the questions will remain unaltered, and most of the STEP questions from previous papers can be used for preparation."

If you are trying to prepare for STEP I, you really should cover the pure section of A-Level Mathematics - covering this material and being comfortable with it by January 2019 is highly recommended. If you want extension material before you cover C3 and C4, you might want to look at the MAT.

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

Dr. Stephen Siklos has very kindly created an online STEP question lookup database 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

You can download the STEP Megapack from here: https://github.com/mzjp2/step-resources - the link contains instructions to download a zipped copy of the repository, but you should also monitor the repository for updates and additions. Feel free to suggest improvements or things you'd like to see. Also feel free to submit a pull request.

The megapack includes:
- Past papers from 1987 - 2017
- Official solutions (2004 onwards) and examiners' reports (2007 onwards)
- Both of Dr. Siklos' old booklets*
- Dr. Siklos' new book
- The grade boundaries for 2000-2018
- The old formula booklet
- A STEP questions spreadsheet.

The repository contains more information about each resource.

More information about the (old) 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 (it is also included in the megapack): http://www.openbookpublishers.com/pr...for-university

*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 2017 papers will be released and is the official site for STEP.

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

- A spreadsheet cross-referencing the Siklos booklets to STEP questions - University of Warwick videos of worked STEP solutions (follow the links from this page).

- STEP Support programme and in particular their discussion forum is a Cambridge run website to support students taking STEP - it's a replacement to the STEP Easter school that used to be run.

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

- STEP Questions Database by Dr. Siklos

- 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.


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:



Graphs

Spoiler:
Show





6. FAQ

When should I start?

Whenever you want. January 2020 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!)

Don't worry or feel intimated by the handful of people starting preparation in the summer of 2019, they are very much in the minority. As above, starting in January 2020 gives sufficient time to prepare.

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!

Should I panic about the STEP specification changing?

No! There changes will not be particularly grand. It's simply a reshuffle of the content (which has never been the focus of STEP) to better fit the content you now learn as part of your linear A-Levels, which is a good thing. All the previous preparation resources and advice applies equally, the style of the questions should still be the same. There is some slightly new content that hasn't featured in STEP for a while (in particular, matrices) - maths.org/stpe has a few assignments and questions to help you get used to the STEP style of those questions, for example, here is the one for matrices: https://maths.org/step/step-ii-matrices-new

7. After the exam

This advice will be updated if the 2020 process is different to 2019

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!
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I hate maths!
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Good luck guys!!!!! Work hard.
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d0nkey_dude
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i’m already stressed for step, i’m not the best at maths but i work hard jus to achieve an A, so step is gonna be a massive challenge!
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LowIQ
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I'm stuck on the 1st worked example in Advanced Problems in Mathematics. I don't understand how to complete the square to get the first equation so could someone explain it please?
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I hate maths!
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(Original post by LowIQ)
I'm stuck on the 1st worked example in Advanced Problems in Mathematics. I don't understand how to complete the square to get the first equation so could someone explain it please?
Hmm, I've not seen that way of completing the square before either, it's quite strange. I wouldn't get hung up about it though, as Siklos says it doesn't matter how you complete the square. His 2nd version is the normal way people complete the square and the one he ends up using anyway.

Btw, I think he's just trying to emphasise that when you're looking at STEP problems for the first time, your work might be a bit messy and not the ideal method, because there are definitely quicker ways to solve this particular problem that you'll spot once you have a bit more practice. I think he goes more into this in the post-mortem.
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Sir Cumference
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(Original post by I hate maths!)
Hmm, I've not seen that way of completing the square before either, it's quite strange. I wouldn't get hung up about it though, as Siklos says it doesn't matter how you complete the square. His 2nd version is the normal way people complete the square and the one he ends up using anyway.

Btw, I think he's just trying to emphasise that when you're looking at STEP problems for the first time, your work might be a bit messy and not the ideal method, because there are definitely quicker ways to solve this particular problem that you'll spot once you have a bit more practice. I think he goes more into this in the post-mortem.
Do you mind linking to the problem/solution?
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I hate maths!
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(Original post by Notnek)
Do you mind linking to the problem/solution?
https://www.openbookpublishers.com/r...ge/22/mode/2up

Page 11 is the problem, pages 12-13 is the discussion. I think LowIQ wants the motivation for A+Bx^2+Cx^4 = A(1+(B/2A)x^2))^2+(C-B^2/4A)x^4. It's an unusual way to complete the square, I think.
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thekidwhogames
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Yess boyss, the journey begins
Spoiler:
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Spoiler:
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we're gonna get step'd on

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I hate maths!
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(Original post by thekidwhogames)
Yess boyss, the journey begins
Spoiler:
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Spoiler:
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we're gonna get step'd on

Oooooh it's your turn now. You're gonna be fine m8.
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thekidwhogames
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(Original post by I hate maths!)
Oooooh it's your turn now. You're gonna be fine m8.
Time actually goes too quick Thanks and enjoy Cambs
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3pointonefour
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Step is the only example where I feel like 1 year of preparation isn't enough 😂
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Here's to hoping there's no error in step 3 (or any of the papers for that matter)
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LowIQ
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(Original post by I hate maths!)
https://www.openbookpublishers.com/r...ge/22/mode/2up

Page 11 is the problem, pages 12-13 is the discussion. I think LowIQ wants the motivation for A+Bx^2+Cx^4 = A(1+(B/2A)x^2))^2+(C-B^2/4A)x^4. It's an unusual way to complete the square, I think.
Yh I was able to get the second one but I feel like knowing the first method may be useful too.
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JeevesWooster
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Good luck to everyone doing beginning their STEP prep! Be happy that you're not gonna get a typo in your STEP III

On a slightly unrelated note, can Cambridge see your mark in additional modules that didn't contribute to your final grade (discrete/add pure in further maths)?

Or do they only see the raw mark?

If anyone knows I'd appreciate a clarification
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I hate maths!
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(Original post by JeevesWooster)
Good luck to everyone doing beginning their STEP prep! Be happy that you're not gonna get a typo in your STEP III
Oh man the typo was ****ing traumatic. I sincerely hope none of you have to experience something like that.
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Work hard everyone!!!
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TheTroll73
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Yay I will probably be here because I'll have to retake STEP 3 thanks to all that mess (and I did get a 1 in STEP 1 and 2 so my STEP 3 score is way too low in comparision imo).

Anyway, my situation is that when I took A level math the first time I only got an A so never applied to Cambridge. Was anyway rejected by all unis (none thought I would get A*A*A apparently) except Birmingham but since I ended up with A*A*A there was no way I would go there (my offer was AAB although they normally ask for AAA so I guess my PS and personal statement were quite good).
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(Original post by TheTroll73)
Yay I will probably be here because I'll have to retake STEP 3 thanks to all that mess (and I did get a 1 in STEP 1 and 2 so my STEP 3 score is way too low in comparision imo).

Anyway, my situation is that when I took A level math the first time I only got an A so never applied to Cambridge. Was anyway rejected by all unis (none thought I would get A*A*A apparently) except Birmingham but since I ended up with A*A*A there was no way I would go there (my offer was AAB although they normally ask for AAA so I guess my PS and personal statement were quite good).
What were your predicted grades?
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TheTroll73
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(Original post by I hate maths!)
What were your predicted grades?
My referee predicted A*A*A I believe.

Anyway, I do have plans for this year and some uni math books at hand which I'm going to learn from. That plus STEP prep should be more than enough to not forget any math (or lose some skill).

I self-studied A levels and would really emphasize that I would recommend NO ONE EVER to do that, no matter how good they are in the subjects they chose.
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LiveOnTSR
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"UCL: A*A*A without STEP, A*AA with STEP grade 1 or distinction in AEA"

Are you use it's grade 1 in STEP? I hope it's not.

Name:  step ucl.PNG
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https://www.ucl.ac.uk/prospective-st...atics-bsc/2020
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(Original post by TheTroll73)
My referee predicted A*A*A I believe.

Anyway, I do have plans for this year and some uni math books at hand which I'm going to learn from. That plus STEP prep should be more than enough to not forget any math (or lose some skill).

I self-studied A levels and would really emphasize that I would recommend NO ONE EVER to do that, no matter how good they are in the subjects they chose.
You got predicted A*A*A and got four rejections? Damn... That's unfortunate and really surprising. It's normal for medicine maybe, but for maths it sounds like a rare situation. Hopefully you'll fare better in this cycle. And I agree with your point on self-studying, most of the fun with A Levels was making friends at sixth form college tbh.
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