How to Do Well in STEP Maths for Cambridge, Warwick and Imperial

hey everyone and welcome back to the channel so if you're new here my name's ray and i'm a second year cambridge student here studying physics and this is my friend michelle who is a first year math student here at st john's college as well and michelle set the step exams which are the maths admissions exams for cambridge and a few other places and he achieved the highest results um like grade wise uh he achieved s in step two and step three um but if you don't know much about the structure he'll explain that shortly um but as for the video uh there will be a few resources which he will be referencing and links to those will be available on his website and a link to his website is in the description down below so do check out his website during the video and he also offers tuition services as well and more information which should uh will be available on his website for that um

so vishal do you want to kick us off by explaining what step is and the format and basically everything to do with the papers themselves for anyone who doesn't know step is the math admissions tests for cambridge and you are given three hours and there are 12 questions on both papers so that's step two and step three and you're marked on your top six questions you might be wondering why it's only step two and step three that's because there is a step one but now you now step one isn't being examined anymore um i'll be discussing step one later in the video though

and uh step is used for several universities it's used for maths at cambridge maths at warwick and computer science site imperial along with some other universities where it's used to reduce the offer the assumption

throughout this video is that um you're applying for maths at cambridge but the information should still be relevant if you are applying to other universities the timeline of the admissions process

for cambridge maths is like all the other courses you apply in october not well by october and then um you get an interview in december and then once you get your interview you'll um hopefully receive an offer in january

and the offer will consist of two parts there's the uh level part and the step condition so the general offer is an sr in maths and further maths and then in your third level followed by grade one in both step two and three but some colleges if you're a state school student will also give you the flexible offer which is three styles and a grade one and a grade two in where the grade two can be in either of the set peppers and that's colleges such as kings for

example so step is graded um with s as the top grade then a grade one then a grade two and grade three and s is generally the top ten percent and then the next grade one is usually about top thirty to forty percent and then grade two is usually about uh fifty to sixty

percent these grades are used for like different offers so for cambridge maths you'll be having to get grade one in both step two and three but for imperial computer science you will be expected to get at least a grade two in uh step two and for warwick maths you um you can be expected to get a grade two in step two or step three uh great s is sometimes also used in offers for cambridge maths this is generally quite rare so it's usually for things like if you're an international student sometimes you could get an s1 offer or if you apply to the same college after being rejected by them the year before or some colleges can also give you an s1 offer if you've been pulled to them after your interview but these are generally quite rare and most people get one-on-one offers

the grade boundaries for uh grade one are constructed so that roughly 160 people achieve their offer out of the generally 550 cambridge office holders and cambridge is trying to fill 250 places for their maths course so once those 160 people who get great like 1-1 or above have been accepted by their college um the next 90 are usually people who get like for example one two or two one and things like that the college will decide whether they'd like to take those students or if they'll they think that another college which isn't full will be able to take them and that's being called put into the summer pool where those different colleges will now look at their entire application so their interview scores and their step grades and decide whether they want to give anyone a place also

step two and step three are designed to be of the same level of difficulty with the difference between them being the content so step two will use both years of a level maths so first and second year while only using the first year so as for the maths content while step three uses both edible maths and further maths so both years of both of them and step one is designed to be less difficult than both step two and step three and it only uses content from edible maths so as i'll be talking about later in the video it's a good place like to start from and when you're preparing right so that

basically explains everything to do with step and what it is in case you didn't know um but now as for like preparing for step how did you go about preparing for it so what i started with was the step foundation modules and these are like mini assignments which have been developed by cambridge there's 25 of them and each of them consists of a step question usually from step one and they cover a wide range of topics uh in like an attempt to make sure you're well prepared by the time you start doing other stuff after this like peppers and generally they have some like on some topic they have a step question but then before that they also have some easier questions to help prepare like to refresh your knowledge of it or to teach you tricks which are useful in the step question and then the same question itself followed by what they call a warm down which is just like a fun little puzzle or something to kind of like calm you down after this problem and did you always do the warm down uh generally i didn't do them but i feel like i should have because they're generally like very different in flavor to what you get in step and probably more like the interview with questions kind of like out of left field i guess so the way i approached the foundation modules was i generally looked at the step question first and then tried it if i could do it then that means i knew that topic well enough and just moved on because that means that the preparation and things like that won't be that useful um but if i couldn't do it then i would look at the preparation and all the hints and then trying the same question again if you get really stuck there's also solutions which have been written by cambridge and then like i'd say generally it's if you get stuck on a problem especially with step because they're designed to be really challenging and take quite a while you should take a break from it and a lot of the time that break will give you a new perspective when you come back and you'll be able to do the problem but sometimes if you're really sick you could look at the solution and read like the first line after you've got stuck and that'll give you a hint to carry on but generally you should try to solve as much of the problem as you can by yourself after the step foundation modules you'll notice on the website that there's also a step two and step three modules but these aren't really as guided as the step one modules so they come in like packs of several questions on a certain topic such as um calculus or mechanics or vectors and mechies and stuff like that i generally found that these modules weren't too useful i preferred to just go straight away with doing step one papers or step two or step three peppers but you should keep in mind that these modules also have um what they call topic notes and that's a really like they're like really condensed notes on that topic which make a really good revision also it's like a good refresher of what's actually on the steps specification because it's it doesn't exactly match the a level specification for maths or further maths like cambridge decided to pick and choose some of their own topics to add in like when i started doing papers i personally found that doing papers as timed marks made it so that it actually forced me to do work because when i tried to do standalone questions usually i just ended up procrastinating or going on my phone or something like that but how you like when it comes to papers or individual questions that's kind of up to you like i think another good thing about peps is that it keeps track of how you've been doing throughout and um where you've been improved and things like that like something i noticed uh about halfway through my preparation was that generally my scores were a fair amount higher if i tried to do mechanics or statistics instead of just going for pure only and that leads on to probably the most important thing i'll say in the video um the biggest piece of advice which all the first years i know gave like after we all sat step we made it like we wrote down a list of our advice for future candidates and um the main one which everyone said was to prepare doing statistics because it looks quite annoying and quite ugly because it doesn't look very familiar but once you look past the words with like the probability terminology and the notation and things like that generally it splits into two topics which are much more like pure and i think most people are more comfortable with pure maths than statistics or mechanics so statistics splits into discrete and continuous probability and the discrete probability is generally a lot about counting or combinatorics which is like counting discrete objects and using that to find probabilities and there's also the other type is continuous where you generally are integrating density functions or and using that to find probabilities of a distribution so um these topics are usually quite familiar for people especially the people who've been doing a lot of pr because um like integration for example is one of the biggest topics on pure instep so i think they're really good once you get used to them like it'll take some time to get used to it but it's definitely worth the effort now the other applied section is mechanics and mechanics i think well personally i found it quite a bit more challenging than pure and statistics but i feel like it still is worth doing if you've got a lot of time because having a wide range of questions to do in step is really important because if you only have a small amount and then an ugly question comes up on the topics you like you might be kind of screwed because you could end up struggling a long time on a question when there was a different topic which you could have learned and that's how we kind of nice question so i prepared for all three and mechanics seems mechanics is like an extension of what's done in further maths so with more difficult situations sometimes more um like things which are we've built upon the situations you've seen before in further math such as projectiles and collisions and simple harmonic motion and circular motion but sometimes it's completely new situations like there was one step question about shooting a bullet into a block and considering the forces inside the block and how it slides um so generally i found that the questions which were easiest in step mechanics were the ones which required the least modeling because modeling the physics is generally the hard part i think because once you've got the equations solving them usually isn't too rough it's generally just differential equations or a lot of algebra so it's definitely worth for even if you're not too keen on mechanics it's definitely worth learning projectiles and collisions because those questions usually um are quite simple to set up and then just require a lot of fluency with algebra and then after that i would say the next easiest topics are circular motion and simple harmonic motion because they generally follow the same sort of strategy with resolving radial and tangential forces and considering simple harmonic motion about an equilibrium point and then i found things like circular no centers of mass and moments the most difficult in step because they rely on really um precise modeling of the situation so i think if you prepare for them in roughly that order then mechanics will feel more approachable so when you were do you said you were doing papers in the time conditions uh whereas over people were doing standalone questions so when you were doing the papers you had to choose questions as though you were sitting in the actual exam did you come back to the questions you didn't choose and attempt them as well or and treat them as standalone questions or did you do the paper again and do all the questions that you didn't choose the first time or how did you approach that so generally i went back and just did the questions of standalone ones because the questions which i didn't do in the exam generally were the months which i wouldn't be able to do that well so um that doing them as standalone gave me more time to think about them and i guess less pressure and um and i suppose it also made you better at choosing questions as well yeah actually because i could assess whether uh like the questions i chose were the right ones and things like that once i did try doing the rest as a paper and that was what made me discover that mechanics is a good idea because the six i originally chose they were out of the six i didn't choose there was actually some which i was better out of the six i didn't choose than the ones i originally chose and i feel like question choice is extremely important in step because you could save yourself from doing a really difficult question like once you've found the questions you can do sometimes there's ones which are easier or more approachable or you might like to because sometimes instead there's topics which um are not too difficult but require a lot of time or a lot of algebra like the main example which i remember is coordinate geometry questions where generally you're going through a lot of um algebra to find things like points of intersection and things like that so in my mind those were kind of like last resort questions so because generally i could do them but if i made a mistake then they'd spend a lot of time trying to fix it and i should only really go for them if there's absolutely nothing else i can do in contrast there's the questions which are like i guess conceptually difficult but slightly shorter and you might like to go for those instead of the long and mistake upon questions so if you choose to do timed papers or going through like purposes mocks as your method of preparing then it's probably better to start from doing the order peppers because generally the peppers increase in difficulty as you get closer to the recent ones also the step specification has changed fairly recently so i think that was starting with 2019 peppers and they've added some things to the specification and taken some things away so the main thing they've added is matrices and there aren't that many questions on mhcs now because of that except really old ones so what i did was i used there was a step three module on these which didn't consist of step questions like the others but i think was worth doing because they tried to find as many step-like questions as they could to help prepare for measure these questions and there's also some really old spec image these questions so i think before the 2000s and most of like some of these are really old and use outdated topics such as group theory um while some of them could like us are not too far off what could be us today such as 1998's step three question five questions like that are worth doing for practice but you should definitely prepare me like for matrices because so far they've been generally among the more approachable questions in the purpose they've been in there also have been some like some things that have been taken away from the specification such as moments of inertia in mechanics and conditional expectation and probability generating functions in statistics which means now that statistics is even more approachable than before because there's even less content to learn like generally you only need to now be comfortable with expectation and a couple of distributions and then other than that really it's just exam technique and you won't need anything really specific such as the things like chi-square tests from further maths stats which is nice you might like to learn conditional expectation though because it's kind of fun and it's good practice as well for the other probability questions but don't bother if you don't have much time whenever there was a topic which i felt like i was kind of mediocre at like not one which i was good enough out to do in the exam but not something so bad that i felt like without like even with lots of preparation i wouldn't be able to do it um so for me that was simple harmonic martian um i just went through every single question on simple harmonic motion in the dms just like what i did with matrices so i think that's another good way to prepare like preparing by topic because if you limit yourself to papers only or like individual questions you might just end up picking the questions which you like doing such as doing the integral in every paper and once you've done a lot of integrals there's a point where you're just getting diminishing returns so you should really should try to do questions on topics which you don't really like um because question variety as i said before was is really important

right so that basically outlined how you prepared for like doing the papers themselves what about when did you come up with any exam strategies for uh what order you do the questions in or like which questions you'd be picking or anything like that so what i did when i opened an exam paper was i read through all the questions and ranked each one of them out of 10 based on what the question looks like the topic the question is and like it was pretty much just instinctive like there wasn't really any process of how i ranked them this kind of came from practice of a lot of questions like i knew that integration was a topic which i was um all right yeah so i usually ranked those as like a 9 or 10 while some if a moment's question came for example which was my worst topic i would probably rank that like a five or like a four because that's um i might be able to do it but it's very unlikely so i should probably try to avoid that and then once i did that i just took the top six skulls which i found and if there's any ties then i just kind of tried to decide between the two and then i just decided from the first one and just tried it until i was unable to do any more or i'd finish the question so if i was unable to do any more then i usually tried for a couple of minutes and if i was making no progress then and i felt like i wasn't going to make any progress in the next few minutes then i just moved on to the next question which is the next highest rate and i think that's how this technique ends up saving time because even it takes about roughly five minutes to pick the questions but once you have picked the questions that means that you won't be spending any time looking back through all the questions again to pick the next one to do and it makes you a lot more calm when you're actually in the process of doing questions and jumping between questions because you have a clear and fixed idea of what you're going to do next that sort of structure to your exam is um pretty useful but some people like to take that structure and go even further with it and do things like 30 minutes per question which you might like to try but personally i didn't really like it because it was too structured and too rigid and kind of um would have made me feel like if i ended up spending longer than 30 minutes on a question then i'd kind of think well what if i don't have enough time to do another one and then start panicking so i personally tried to go for something which gave me a good idea of what i'll do next but not force me down a certain path or anything like that like it lets me be a bit flexible and about jumping between questions it's just like before when i mentioned about how taking breaks from questions is good even the really small breaks you get from jumping between questions can also be helpful because you'll come back possibly with a new idea of like yo like i guess you can think of it as your subconscious working on that question as you're actively working on a different one so let's say you had done one question so far and you sort of stopped halfway through you moved on to a different one and completed that one completely would you move on to the next related question or would you come back to the first one and try to see if you can now do that so like the questions you stopped would you basically come back to them after doing another question or at the end of like closer towards the end of the exam this one i actually didn't really think about much but i think looking back at what i did in the exam i feel like i would have just gone on to the next one um the next new question because the well once you start a question it generally starts out quite easy and then um gets to a more difficult part later on which means that you can kind of be picking up marks really easily right away and then once you hit a part which you can't do then you can jump because i like to ensure that i get a decent amount of marks quite quickly and then spend some time thinking later on so i think for me in step two i did this with like my question one i was stuck on and i kind of came back to it only right towards the end and hops between that and another question which i wasn't able to finish and in the end managed to finish it on a related note since you get marked on your top six questions you should try to answer like you shouldn't try to answer more than six questions but you really should try to answer six questions because generally the first few marks of a question are easier to get than the last few marks so if you've not got much time left and you've not answered six questions then it's better to work on the first parts of some other questions than to keep working on the final part of a difficult question another thing about partially done questions is that despite the front of the paper saying that it's better to try completely finished questions a lot of the time the final difficult part of a question isn't actually worth that many marks so you can sometimes get quite a lot of marks by doing the first couple of parts and leaving out the last difficult part such as in some graph sketch questions generally that they're structured to be like a lot of parts where you just gain more information about this strange function they're asking you to sketch and then the final part is to put all that together and sketch the function and that final part is usually the most difficult and the other passes are just like some sort of guided algebraic manipulation or calculus and things like that so they're not too bad and those parts usually consists of the bulk of the question so partials uh generally work quite a bit question one is usually designed to be more accessible so that can be things like topics which more people have studied such as like integrals or like opening up with things like with parts which most people have done things like before so it's like a more familiar sort of question and a lot of people feel like they have to go for question one as part of their exam strategy i personally didn't always go for question one but usually end up as one of the higher rated questions anyway so don't feel like you have to do question one but usually it's designed to kind of ease you into the more strange maths which you'll find later on in the paper another thing to look out for is the question types so one particular type is one where you're given a new idea and you're expected to work with it using techniques which you already know a good example is 2009's step 3 question 4 which is about laplace transforms and this question looks quite hard at first but part of the difficulty is getting used to this new idea so the actual things you're asked to do aren't as difficult as other questions sometimes so i once you get past this new definition and these like this new notation and things like that like in this question in particular you realize that it's just integration by parts and that isn't too rough compared to other questions another thing to look out for as well is that some topics appear quite often like you shouldn't take this as a rule but almost every year topics like integration discrete and continuous probability uh a matrix question or a vectors question or a sequences question these are all really likely topics so these topics are useful to prepare for because you're very likely to get a question on them so while it's good to have a wide range of topics to be able to do in the exam you don't need to force yourself to do all topics because you might find a topic you really don't like or you feel like you just won't be able to learn in time for me that was moments because i just really suck at physics when it spins right and for some other people i know that was complex geometry because it was like really unusual from what was in a level the good thing about the question choice is that then you can just completely avoid it but you don't want to do this with too many topics because then you leave yourself with too little to work with reiterating slightly something which has been said before later parts of questions are generally the more difficult parts you can think of these later parts of questions as like if you assume that part on its own then they'd be really difficult so generally these more difficult parts rely on what you've had to work out throughout the question so you should keep in mind trying to reuse what you've done before because a lot of the time you won't be asked to do something for no reason sometimes you'll get questions which say hence or otherwise and almost always hence is better than otherwise unless you already know like the only way you should go for otherwise is if you already know a technique to do this question in a slightly faster way but almost always hence is better to do and similarly to that there's also deduce and that usually means that you don't need to work much harder to get the result they're asking for from what you've already worked out as my last piece of advice about exam technique um in the real exam something which one of the first years told me while i was an offer holder was to keep calm and think logically in the exam and while that's easier said than done i think at that point it is the most important thing you can try to do because once you've got to the point of taking the exam you've done as much preparation as you can and there's nothing else you can really do so you just need to try and stay focused in the exam like it's really easy to start worrying about how during the exam you're running out of time because you just sat there thinking about the problem because these problems are designed to be difficult but that's normal and that's what's intended so it's not really much of a problem to have that happen uh this is something which i had to deal with when i started the mit for imperial in november because i was getting really stuck on a question and i felt like this is what i should be able to do and started to get really flustered because i was wasting time on a question which i should be able to really easily solve i became really conscious of how much time i was wasting and then stopped thinking about the question and more about the time which i was working and that made me perform a bit worse than i should so i feel like that's another reason why doing mocks is useful because doing mocks in real time gets you used to this situation of having to spend time like spend exam time thinking about a problem and overcoming this i feel like is a really important thing for doing consistently in the in set so that

basically covers a lot of like exam strategy related stuff what about when you're doing the questions themselves how many questions should you expect to do if you're aiming for say an s or a one or two and stuff like that so for an s generally you will need about five full questions um but this isn't really set in sun or anything like that because partial questions can vary a lot in marks and can contribute a lot to whether you get like an s or a one or a two so for me i got four fours and two partials in both step two and step three but my step two score was like a fair amount higher than my step three one because i think my partials were a lot stronger except two than they were in step three while one of my friends um who also got ss he got um one full and five partials so there isn't really any fixed amount of full questions or partial questions you should be aiming for you should just try to do as much as you can on each question because like it's really easy to underestimate how much your posture can be worth 401 it's kind of similar like the general advice is to try to get four full questions but um i think it's very reasonable to do like a small amount of full questions and some partials and if you have really strong pastures you could even be getting s's or ones with just partials alone the only one where it can be slightly different is for a great two where you can try to if this is something you feel more comfortable with uh it has a slight more like a slight amount of risk but because the boundary for a 2 is generally about 60 marks you could try to get um 10 marks or so on each partial and then instead of trying to complete questions fully you could force yourself to do six questions and try to get roughly like halfway or two-thirds of the way through them and um that could help you avoid the more difficult parts of a question but whether you try that uh that's up to you so when you're saying falls and partials um so what do you mean by a fallen impartial question a full question i would say is one where you've attempted every single part of the question and you feel like you've got a good solution to each part so generally to me that's about 18 or more marks or 20 on the question um a partial is one where you haven't finished the question so there's like some part you know you haven't done or you know you've done wrong then you can kind of like get varying versions of that you can say a strong partial is one where you've done or solve the question or you've made a slight mistake or things like that and then um there's also like weak postures where you've not done that much so most of the resources you've used i'm guessing will be on your website but do you have any comments about any of the resources so um on my website will be things like the a table of great boundaries and various marketings i found throughout my time when i was preparing there's also going to be a document about step tricks which i've come across during my preparation so a question i

imagine a lot of people would have uh is when did you start doing your papers and how often were you doing all these past papers or what's your recommendation here for generally when people and how often should people be doing these so i started with my step two and step three preparation in january um i was mostly doing like a couple of questions every now and then but i did purpose like quite slowly probably a bit too slowly so i was lucky that when levels were canceled because i gave me a lot more time to prepare for step but in a normal year you also have to focus on preparing for your air levels at the same time because the air level offer is still fairly high so i would say that it's a good idea to do roughly 15 years of set papers because after that you're likely getting diminishing returns and it's better to focus on topics which you are struggling with and to do more of those than to do another integral or something like that if you're good at integration i did 20 years and i feel like that was probably a bit too much so if you're trying to do 15 years of papers that's 30 papers altogether so if you do roughly at the pace of two a week from january to june then that will give you enough time to finish all the papers and to do some extra questions as well like you should leave like at least some to what like class to the exam for example like i usually left the couple like recent purpose before my exam to give me the closest to my real exam experience um i had that with their mrt as well yeah so you mentioned step one

foundation modules being useful when would you recommend people start doing them and when should they be doing the papers themselves as well uh say the step one two and three papers providing they're doing all three so i would say that you should try to do the step one foundation modules within the summer of after year 12 because shortly after that you're likely going to be applying to imperial as well so you'll need some time to prepare for the mrt which takes place in lent october or early november the step one foundation modules will help with preparation for that as well as for the interview which will come after that in december and likewise about step one papers like sometimes the topics in step one purpose can be useful for interview like the curve sketching module for step two can be useful as well as curve sketches in step one and i would say that while it's worth doing a couple of step one purpose you shouldn't do too many of them like i think i did like four and that was a decent amount before my interview because there's resources specifically for the interview which are likely better to do than doing a lot of step one peppers and that'll some of those will be on my website which is linked in description about step two and step three peppers i think that it's fine to just do nothing over the christmas holidays after the interviews but once you get your offer in january it's likely a good idea to start doing some questions around then like slowly build up into doing more and more questions later on because you don't want to have to do the majority of your preparation at the same time as your a level revision which will be later on in the year something which i did was to try a step 2 and step 3 pepper right at the start to see how i started and then like how i ended and things like that um but you don't need to do that of course but yeah

that's basically for the video hopefully you found it useful and learn some of the ways you can be preparing for step do check out michelle's website in the description down below and he does offer some tutoring services where there should be information available on that on his website so yeah do check that out uh hopefully you found that useful and i guess we'll see you next time bye