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STEP Prep Thread 2018 Watch

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    (Original post by tomahawker314)
    I disagree, at this level I get the feeling that applied is very limited, almost a gimmick. Without pure the applied is just impossible. It's more or less the same imo, a couple of formula then the maths is the same. Can anyone at uni with more insight agree with this or am I just talking out my arse (wouldn't be the first time).
    Many avoid most/all of the applied, and that's after harder applied units were ditched from M/FM/STEP post 2006. At the mo you can go to Cam by scraping Bs/Cs in M1-M2 and S1-S2 and avoiding it in STEP.

    I think you under appreciate applied maths due to the 2006 reforms and 'pure culture' in STEP e.g) on TSR. Applied is important at e.g) Cambridge.
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    I've been on the fence about sitting STEP I next year, but already got 16 exams next year. Need to ask my college about this when term starts again.
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    (Original post by IrrationalRoot)
    Dw I used to take modulus to just mean ± before I started STEP; consequently, I failed the first STEP question I tried lol (the first one in the Siklos booklet).
    These kinds of misconceptions generally get cleared up from practising STEP questions and doing more A-Level content - based maths in general.
    I've finished year 13, which makes having this misconception pretty bad. I even sat the AEA this year, and I think I got a merit at least, and am predicted a solid A*.

    I think a lot of misconceptions boil down to poor teaching and the fact that Pearson's specification rarely requires students to go any further than what they're initially taught, mainly because exam questions are repeated year-on-year.

    Perhaps I should still look at STEP questions to quell my confusion, but I'm hoping you can humour me anyway. This is my understanding of the modulus function currently: If |x| = constant, then is a modulus equation, and we solve for x how we normally would. But |x| = variable, then this isn't a modulus equation but an application of the modulus function if you get what I mean. So whatever x is, variable will always be the modulus of that.

    Is that a correct understanding or am I still missing something?

    Thanks!
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    (Original post by K-Man_PhysCheM)
    I just finished year 12, so will be applying this October. Most likely to Cambridge, Imperial, Durham, Southampton, Warwick or something, to read Physics (or maybe physics with chemistry) or physical Natural Sciences at Cambridge if I am made an offer.
    After oxbridge, Durham and Imperial have the highest physics offers as far as I can tell however I asked Durham about a-levels done a year early and they said they would be included in offer where as I think physical natsci at cambridge is one of the rare cases where they might give a 4 A-level offer if maths is studied in y12 and fm y13. I get the impression that with physics courses, doing further maths is quite sufficient in terms of extending your maths past a-level- step only required for the top unis to distinguish between the most talented mathematicians for maths courses. Of course doing more maths is always good and the more you do the more likely you are to be good at it.
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    (Original post by Physics Enemy)
    Many avoid most/all of the applied, and that's after harder applied units were ditched from M/FM/STEP post 2006. At the mo you can go to Cam by scraping Bs/Cs in M1-M2 and S1-S2 and avoiding it in STEP.

    I think you under appreciate applied maths due to the 2006 reforms and the 'pure culture' in STEP e.g) on TSR. Applied is very important at e.g) Cambridge.
    I like the look of the Cambridge degree as there is so much choice to do theoretical physics, in fact at other unis I will apply for maths with physics etc, so I do enjoy the mechanics modules. I was meaning more that like you said it just isn't needed to get anywhere, it's an after thought in the a level.

    So anyway would you say it is still worth practicing the applied questions, both mech and stats, or just focus on pure as there isn't enough questions on applied in a paper to make it worthwhile.
    Another thing that worries me is if you have practised all styles how do you decide which of the 13 to answer. If you spent 2-3minutes reading and understanding each question then that's easily 40mins burned? How do you select which questions you are going to answer in the actual exam?
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    (Original post by Desmos)
    I've finished year 13, which makes having this misconception pretty bad. I even sat the AEA this year, and I think I got a merit at least, and am predicted a solid A*.

    I think a lot of misconceptions boil down to poor teaching and the fact that Pearson's specification rarely requires students to go any further than what they're initially taught, mainly because exam questions are repeated year-on-year.

    Perhaps I should still look at STEP questions to quell my confusion, but I'm hoping you can humour me anyway. This is my understanding of the modulus function currently: If |x| = constant, then is a modulus equation, and we solve for x how we normally would. But |x| = variable, then this isn't a modulus equation but an application of the modulus function if you get what I mean. So whatever x is, variable will always be the modulus of that.

    Is that a correct understanding or am I still missing something?

    Thanks!
    Well yeah unfortunately you don't need to understand the content particularly well at all to do well at A Level, so a conscious effort must be made to do so with every topic (especially trig, so many people don't understand trig properly even when they've done a lot of STEP).

    Best way to think of any new function/notation is in terms of its definition, not shortcuts. |x| is a piecewise defined function, defined by |x|=x if x≥0 and |x|=-x if x<0. So whenever you see an equation with a modulus function (say, |x|), always separate it into these two cases, one where you suppose x≥0 and one where you suppose x<0. Remember these assumptions when you're solving the cases because you might get a contradiction which would imply no solutions in that case. Of course, if you have more than one modulus you will have many cases. The first question in Siklos' booklet is a very good example of this and will hopefully clear things up.
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    (Original post by Physics Enemy)
    I've shown DFranklin M3 and M6 papers from the early 2000s, makes a mockery of M1/M2 people reach now (plus M1/M2 was harder then).
    I agree that the loss of M3 material from the standard A-level results in a significant loss of difficuty (plus some useful exposure to some differential equation tricks for solving SHM).

    But "further applied" tends very much towards "here's a concept and then 16 related formulas/approaches"; most of the "work" just comes back to pure mathematics ability. (e.g. many CofM and MI questions are just integration fests).

    STEP was 4:3 pure:applied. IMO pure should be 4 Qs and pick 3, applied 4 Qs and pick 3. Would be more balanced, better discriminator. With current lopsided syllabi that's tricky, so perhaps enforce 2 applied Qs.
    And comment above holds for STEP too. The examiners can't use more advanced concepts than you get in the A-level, so the applied questions tend to be "it's just like an A-level question, only with harder algebra/integrals".

    In terms of forcing people to do particular areas, I see three big reasons Cambridge is unlikely to do that:

    (1) Culturally, Cambridge exams have always tended to give a lot of choice (Technically, the IA Tripos might ask for 7 questions out of 10, but when 4 questions are probably enough for a first, it's really more like "5 questions out of 10" at most).

    (2) There's significantly more choice in the applied modules at A-level than the pure. So if you're going to be fair to all possible applied choices, if you made some applied questions compulsory, you'd need to increase the number of applied questions significantly.

    (3) Although the degree material has a lot of "applied", when you actually look at what's involved, in A-level terms it's actually mainly "pure" maths. There's really not much I did in A-level applied that I think was much help in part IA.
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    (Original post by DFranklin)
    I agree that the loss of M3 material from the standard A-level results in a significant loss of difficuty (plus some useful exposure to some differential equation tricks for solving SHM).

    But "further applied" tends very much towards "here's a concept and then 16 related formulas/approaches"; most of the "work" just comes back to pure mathematics ability. (e.g. many CofM and MI questions are just integration fests).
    FM's been hit arguably more; in addition to direct reform, dumbing down in M spills over to FM. P3-P6 + M4-M6 (or M4/M5/S1) vs FP1-FP4 + S1/S2. Big difference. Pure content skimmed, applied units thrown out, easier exams.

    (Original post by DFranklin)
    And comment above holds for STEP too. The examiners can't use more advanced concepts than you get in the A-level, so the applied questions tend to be "it's just like an A-level question, only with harder algebra/integrals".
    You're good/experienced at applied, so applied STEP Qs don't seem a big deal. Infact you tell people to not write it off and give it a go, as it's doable. I agree, but people avoid it. Same goes for why you aren't phased by (the old) M4-M6.

    (Original post by DFranklin)
    In terms of forcing people to do particular areas, I see three big reasons Cambridge is unlikely to do that:

    (1) Culturally, Cambridge exams have always tended to give a lot of choice (Technically, the IA Tripos might ask for 7 questions out of 10, but when 4 questions are probably enough for a first, it's really more like "5 questions out of 10" at most).

    (2) There's significantly more choice in the applied modules at A-level than the pure. So if you're going to be fair to all possible applied choices, if you made some applied questions compulsory, you'd need to increase the number of applied questions significantly.
    But do the exams test specific topics/areas, or mixed content on one paper? Big difference in picking from 10 applied Qs, vs avoiding it altogether. I don't see the problem in picking 3 of 4 applied Qs in STEP (2 mech, 2 stats) assuming people don't do D1(!). Especially STEP 3 (FM = done more applied).
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    (Original post by Physics Enemy)
    FM's been hit arguably more; in addition to direct reform, dumbing down in M spills over to FM. P3-P6 + M4-M6 (or M4/M5/S1) vs FP1-FP4 + S1/S2. Big difference. Pure content skimmed, applied units thrown out, easier exams.
    But TBH there's hardly any content in the "old" FM mechanics modules either.

    You're good/experienced at applied, so applied STEP Qs don't seem a big deal. Infact you tell people to not write it off and give it a go, as it's doable. I agree, but people avoid it. Same goes for why you aren't phased by (old) M4-M6.
    Yes, I tell people not to write off the applied, but by no means am I "good / experienced at applied". Basically my POV is "I'm a pure mathematician, who took not a single applied course at university once the exam system let me avoid doing so. And it's 30 years since I did the applied material at A-level. If I can do these questions, tackling them shouldn't be beyond any one else seriously attempting STEP II/III".

    And if you look at the reasoning I give, it's "don't write it off, because it really doesn't take much work to cover the applied material you need for STEP, and the questions don't really test super deep understanding of applied mechanics, they test your ability to grind through the equations". It's not "do this 'cos it's super important and useful and will help you at university". (which I would say to someone about the pure content if they were seriously intending to only answer applied questions).

    But do the exams test specific topics/areas, or mixed content on one paper? Big difference in picking from 10 applied Qs, vs avoiding it altogether. I don't see the problem in picking 3 of 4 applied Qs in STEP (2 Mech, 2 Stats) assuming people don't do D1(!). Especially STEP 3 (FM = done more applied).
    Because for STEP III to test "FM pure", it needs to cover FP1, FP2, FP3. But for it to test "FM applied", even if you exclude decision maths it needs to cover S2, S3, S4, M2, M3, M4, M5. Factor in the different topics covered (particularly in stats) and you'd need significantly more applied questions than pure (this is what actually happens by the time of Part II in the Tripos).

    Now it could still be done, but honestly, what's the point? Repeating myself: the applied material you do at A-level is not particularly useful at degree level.
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    P3-P6 > FP1-FP4 and (old) M4-M6 > S1/S2, so it's still dumbed down. Modern S1/S2 is a joke btw.

    I agree with your reasoning on doing STEP applied, if anything it shows how weak/averse people are to it given it's avoided.

    For my system of 3 Qs from 4, it wouldn't cover M1-M5 and S1-S5 for STEP III, or whatever on STEP I/II. Would be more confined, at least people would be doing it.
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    (Original post by Physics Enemy)
    P3-P6 > FP1-FP4 and (old) M4-M6 > S1/S2, so it's still dumbed down. Modern S1/S2 is a joke btw.
    But as I've said, the old courses were basically a joke too (for Cambridge level applicants).

    For my system of 3 Qs from 4, it wouldn't cover M1-M5 and S1-S5 for STEP III, or whatever on STEP I/II. Would be more confined, at least people would be doing it.
    Again: since the applied material isn't relevant at degree level, who cares enough to want to change this?

    I'll also note that (IMHO) there are some fairly easy "tweaks" Cambridge could make to make to improve applied take-up (a big one would be to have a much higher proportion of results being "show that...", since a big reason to avoid applied in the exam is that it's much easier to get a question wrong without realising it). But instead they've taken the attitude "not many people do the applied, so let's cut the number of applied questions". So I just don't see it changing in the direction you suggest.
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    (Original post by DFranklin)
    And if you look at the reasoning I give, it's "don't write it off, because it really doesn't take much work to cover the applied material you need for STEP, and the questions don't really test super deep understanding of applied mechanics, they test your ability to grind through the equations". It's not "do this 'cos it's super important and useful and will help you at university". (which I would say to someone about the pure content if they were seriously intending to only answer applied questions) [...]

    Now it could still be done, but honestly, what's the point? Repeating myself: the applied material you do at A-level is not particularly useful at degree level.
    +1 for this.

    @Physics Enemy: Applied at A-Level and Applied at university are very different things. Mechanics and stats which is what applied is taken to mean at A-Level forms a very small subset of applied at university. A large portion of the pure on STEP (solving DE's, integrals, anything computationty) is considered applied at uni.

    So, as DFranklin said - doing more "applied material" on STEP will pretty much only help with one applied course at Cambridge (D&R). Which means making STEP 50% applied rather nonsensical. The pure on STEP is much better preparation for most applied courses at uni, than mechanics & stats.
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    (Original post by DFranklin)
    Again: since the applied material isn't relevant at degree level, who cares enough to want to change this?

    I'll also note that (IMHO) there are some fairly easy "tweaks" Cambridge could make to make to improve applied take-up (a big one would be to have a much higher proportion of results being "show that...", since a big reason to avoid applied in the exam is that it's much easier to get a question wrong without realising it). But instead they've taken the attitude "not many people do the applied, so let's cut the number of applied questions". So I just don't see it changing in the direction you suggest.
    I'd be surprised if pre-2006 M1-M6 and S1-S6 was mostly useless at Cam, I don't know. Surely someone could put it to use if they picked applied throughout the degree, not sure about 1st/2nd year tho.

    Main reason for applied aversion IMO are 2006 reforms and 'pure culture' around STEP/A-Levels, coupled with not making applied Qs compulsory.

    I don't think turning applied Qs into pseudo pure/proof Qs is sensible, defeats the point.
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    (Original post by Physics Enemy)
    I'd be surprised if pre-2006 M1-M6 and S1-S6 was mostly useless at Cam, but I wouldn't know. Surely someone could put it to use if they picked applied throughout the degree, not sure about 1st/2nd year tho.

    Main reason for applied aversion IMO are 2006 reforms and 'pure culture' around STEP/A-Levels. Coupled with not making applied Qs compulsory. I don't think turning applied Qs into pseudo pure/proof Qs is sensible, defeats the point.
    I think you're misunderstanding what applied is. Let's take a concrete example, in your first year, the applied courses are Differential Equations (with no reference to physical systems or modeling real life phenomena), Vectors and Matrices (just working with vectors, matrices, eigenvectors, eigenvalues, no reference to physical phenomena and involving a fair amount of proofs), Vector Calculus (again, very little reference to physical phenomena, just doing calculus on R^n) , Dynamics and Relativity (the only course in this list that is applied and has any relevance to what you call applied).

    So doing M1-6 will help you with Dynamics and Relativity in your first year in Cambridge and then become forevermore useless, whilst doing pure modules and the pure questions on STEP involving things DE's, Vectors, Matrices, integrals, etc... are the ones that are actually going to be useful to you if you pick only applied courses.

    To emphasise: applied does not mean mechanics.
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    (Original post by Physics Enemy)
    I'd be surprised if pre-2006 M1-M6 and S1-S6 was mostly useless at Cam, but I wouldn't know. Surely someone could put it to use if they picked applied throughout the degree, not sure about 1st/2nd year tho.
    Then perhaps you should listen to someone who actually took the courses. If you picked your courses really carefully, you just might find a course where you'd save roughly 1 lecture of material in a 12 lecture course. [In the "intro to probabilty" course the entirety of S1-S4 just might save you 1.5 lectures].

    Main reason for applied aversion IMO are 2006 reforms and 'pure culture' around STEP/A-Levels. Coupled with not making applied Qs compulsory. I don't think turning applied Qs into pseudo pure/proof Qs is sensible, defeats the point.
    Why don't you try to set a suitable STEP level applied question that isn't a "psuedo pure/proof" question? It is far harder than setting the type of question typically set now (although a few do get set), and I can assure you that if those questions became the norm, the takeup of those questions would be far lower than it is now. (So low, in fact, that I suspect if it was the norm, and "do 1 applied question" was made compulsory, most candidates would just accept "tanking" the applied question rather than hoping to score well on it).
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    (Original post by Zacken)
    Dynamics and Relativity (the only course in this list that is applied and has any relevance to what you call applied).
    Plus dynamics + relativity turns out to be largely differential equations in practice. I never felt M1-M6 helped that much.
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    (Original post by Enigmatically)
    Was waiting for this thread to start. Thank you very much Zacken. Guess I'll check in here.

    Could anyone recommend some resources for Mechanics? I have Understanding Mechanics by A.J. Sadler, but I'd also like to have more resources, as I'm planning to blitz through M1-5 this summer.(school offers just stats :/)
    I recommend the Bostock and Chandler books. The best out there IMO.
    Together volume I and II should cover all the mechanics you need for STEP, and both contain plenty of questions, some of which are quite challenging.
    The second one also covers some things that aren't on syllabus anymore but are on the older papers (motion in polar coordinates, combined rotational & translational motion and some other stuff) as well as giving a very good intro to vectors at the start.

    https://www.amazon.co.uk/d/cka/Appli...matics+bostock

    https://www.amazon.co.uk/Mathematics...matics+bostock
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    (Original post by DFranklin)
    Why don't you try to set a suitable STEP level applied question that isn't a "psuedo pure/proof" question? It is far harder than setting the type of question typically set now (although a few do get set), and I can assure you that if those questions became the norm, the takeup of those questions would be far lower than it is now. (So low, in fact, that I suspect if it was the norm, and "do 1 applied question" was made compulsory, most candidates would just accept "tanking" the applied question rather than hoping to score well on it).
    I don't have a problem with the current difficulty of applied STEP Qs, just the uptake of them (hence my proposed system). I don't think making them harder is a good idea if they're already avoided.

    You've convinced me it's really worth going over mech/stats notes and practising those Qs for STEP. The 'tanking' issue is why I proposed the idea, to see who does and doesn't.

    RE Cam's course, seems M1-M6 is useful in one 1st year course, S1-S5 useful in another. Good foundation if you decide to pick applied further down the line, but I agree pure is usually much more useful throughout.
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    (Original post by Physics Enemy)
    I don't have a problem with the difficulty of STEP applied Qs as they are, just the uptake of them (hence my proposed system).
    Well you said:

    (Original post by Physics Enemy)
    I don't think turning applied Qs into pseudo pure/proof Qs is sensible, defeats the point.
    which is (IMHO) pretty much the current state of affairs. So I assumed you wanted applied questions that actually really tested your applied knowledge/intuition.

    RE Cam's course, it seems M1-M6 is useful in one 1st year course and S1-S5 useful in another.
    As I said, it's "useful" in the sense that it helps with maybe 15% of the course. In practical terms, my college had a fair number of people who hadn't come through the English A-level system and didn't have much "applied FM" knowledge, and it seemed to have no noticeable effect on how they did on the courses.
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    I wanted the applied to be made compulsory in some way, I'm happy with the Q style/difficulty as it is.

    I was against the idea of changing Qs as described, whereby increasing difficulty would probs scare away the few who attempt it.

    I think the Cam course is versatile enough to make M1-M6 and S1-S5 either a bonus for ~15% of 1st year, or a footing to become an applied mathematician.
 
 
 
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