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STEP Prep Thread 2018 Watch

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    (Original post by Physics Enemy)
    I wanted the applied to be made compulsory in some way, I'm happy with the Q style/difficulty as it is.
    Well, since it doesn't test anything really relevant to the degree, I can't see the point.

    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.
    I should have been more precise about what I meant by course. There's are two courses (Probability and Mechanics) where it might maybe cover 15% of that particular course. Since there are something like 10 courses covered during the 1st year, overall we're talking three percent of the 1st year. And it's not "bonus", because you're going to cover that material anyhow in the first year, and you're going to cover it from a university perspective that is probably going to supersede what you did at A-level anyhow (I'd say the Cambridge take on mechanics pretty much entirely supersedes what you did at A-level to the point where M1-M5 only really gain you a bit of familiarity at the start. For probability, the way it's taught is very alien to what you do at A-level, but the practical way you do the Tripos questions is more compatible with the A-level approach).
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    (Original post by IrrationalRoot)
    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.
    I think I've got it now, but I'm still going to look at some STEP questions.

    You mentioned that students have poor understanding of trig concepts. Could you expand upon what you mean?
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    (Original post by Desmos)
    I think I've got it now, but I'm still going to look at some STEP questions.

    You mentioned that students have poor understanding of trig concepts. Could you expand upon what you mean?
    Well they simply don't understand trigonometry well enough to answer the harder trig STEP questions. It's one of those topics at A Level which is so easy to do just by rote memorising formulae/blindly applying learned methods. But when a STEP question challenges their understanding of what they're doing, they struggle.
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    (Original post by IrrationalRoot)
    Well they simply don't understand trigonometry well enough to answer the harder trig STEP questions. It's one of those topics at A Level which is so easy to do just by rote memorising formulae/blindly applying learned methods. But when a STEP question challenges their understanding of what they're doing, they struggle.
    To be fair, it's possible to make really really horrible trig questions if you try hard enough.

    But at the same time, it's fair to say any question that merely requires confident use of the sum/product formulas will often cause people a lot of problems.
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    (Original post by solC)
    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
    Cheers m8. Already studied Pure Maths 1 and 2 from Bostock and Chandler - weren't bad but there are better books for Pure (Backhouse). Guess I'll have a look at their Mechanics books.

    P.s. 1v1 me on FIFA skrub.
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    (Original post by tomahawker314)
    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 2-3 minutes 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?
    IMO it'd be best to focus on pure and one of mech or stats, that should give you sufficient breadth but not thin-out proficiency in each.

    On exam strategy, I think that can be quite a personal thing, but will let others comment. I think you should know which type of Qs you'll attempt going in.
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    (Original post by Enigmatically)
    Cheers m8. Already studied Pure Maths 1 and 2 from Bostock and Chandler - weren't bad but there are better books for Pure (Backhouse). Guess I'll have a look at their Mechanics books.

    P.s. 1v1 me on FIFA skrub.
    +1 for Backhouse. It really is the best series for A-level pure I'm aware of

    B&C for applied might be the best there is though...
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    (Original post by Physics Enemy)
    IMO it'd be best to focus on pure and one of mech or stats, that should give you sufficient breadth but not thin-out proficiency in each.

    On exam strategy, I think that can be quite a personal thing, but will let others comment. I think you should know which type of Qs you'll attempt going in.

    I'd also like to know which is harder between STEP 2/3 in terms of getting a 1, and which tends to have relative 'gifts' in the applied.
    My advice is if you've studied the relevant modules, try the pure and applied equally. That is, if you've done M1, M2, S1 and S2 as part of your further maths choices, then for STEP II it's worth aiming, at least initially, to try everything equally and then drop the applied if you really don't like it.

    The point I think DFranklin is making is we see enough gift / relatively easy applied questions that we think it's worthwhile studying for them to maximise your chances in STEP.

    I do agree with DFranklin that applied is taught very differently at uni than it is at A-level. However, whilst M1-M6 doesn't directly come up in the Cambridge Dynamics IA course, I do think having as much mechanics as possible really helps because it develops the physical intuition and provides easier and more concrete examples to base the uni material on in your head. That's what I felt at least when I did my first year (disclaimer: at Imperial, not Cam).
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    (Original post by shamika)
    +1 for Backhouse. It really is the best series for A-level pure I'm aware of
    I'm not familiar with it; where I think B+C is very strong for STEP is the huge number of exercise questions, including questions much harder than you're likely to see at A-level. (It also benefits from predating a lot of the 'watering down' of the A-level, but Backhouse seems to be from a similar era). Do you think Backhouse is strong here too?
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    (Original post by shamika)
    The point I think DFranklin is making is we see enough gift / relatively easy applied questions that we think it's worthwhile studying for them to maximise your chances in STEP.
    To slightly clarify: I'm not so much saying (here) that the questions themselves are a "gift", but they are generous in terms of the amount of "extra" material (above the pure) you need to cover to be able to tackle them.

    I do agree with DFranklin that applied is taught very differently at uni than it is at A-level. However, whilst M1-M6 doesn't directly come up in the Cambridge Dynamics IA course, I do think having as much mechanics as possible really helps because it develops the physical intuition and provides easier and more concrete examples to base the uni material on in your head. That's what I felt at least when I did my first year (disclaimer: at Imperial, not Cam).
    I understand what you're saying, but the mechanics course at Cambridge was surprisingly abstract - very little physical intuition involved. I actually think I've seen far more interesting (and harder!) STEP mechanics questions than we actually encountered in Part IA. Part IB mechanics (Lagrangians and Hamiltonians etc) tended to be heavier in theory than application as well.
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    (Original post by DFranklin)
    To slightly clarify: I'm not so much saying (here) that the questions themselves are a "gift", but they are generous in terms of the amount of "extra" material (above the pure) you need to cover to be able to tackle them.
    I was also trying to say the same thing, so thanks for clarifying.

    I understand what you're saying, but the mechanics course at Cambridge was surprisingly abstract - very little physical intuition involved. I actually think I've seen far more interesting (and harder!) STEP mechanics questions than we actually encountered in Part IA. Part IB mechanics (Lagrangians and Hamiltonians etc) tended to be heavier in theory than application as well.
    I think Dynamics & Relativity has changed focus over the years. At the moment I think it is relatively abstract in that a lot of it is setting up the differential equations required to solve various issues. One year, relatively recently, the lecturer basically started with an explanation of affine planes and why that's the right setting for Newtonian Dynamics (that didn't go down well)

    In the 2000s though, a decent number of the questions were basically STEP III problems. (I picked one at random - see Q11 in https://www.maths.cam.ac.uk/sites/ww.../PaperIA_4.pdf)

    If it every moves back to that, then obviously getting a heads up on the A-level material is useful.
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    (Original post by DFranklin)
    I'm not familiar with it; where I think B+C is very strong for STEP is the huge number of exercise questions, including questions much harder than you're likely to see at A-level. (It also benefits from predating a lot of the 'watering down' of the A-level, but Backhouse seems to be from a similar era). Do you think Backhouse is strong here too?
    I'd say Backhouse's examples cover a wider range to benefit all ends of the spectrum - you have simple examples to grasp concepts with, and beyond that it takes you to near STEP difficulty with harder questions. Also, they tend to leave some parts of proofs for students to do when they are introducing a theorem or a lemma (they still do show you how to manoeuvre about the problem) - a great tool that I believe helps students to take a more logical approach to problems using provided information, and as many STEP questions come in this style, it's a great help. As there are many editions of the books, I'd
    recommend trying to get earlier editions, as per my experience, those have more challenging problems. Although you've already been to Camb so this advice is geared more at my fellow STEPers.

    I also had Understanding Pure Mathematics by Sadler which was brilliant (as good as if not better than B+C).
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    (Original post by shamika)
    I think Dynamics & Relativity has changed focus over the years. At the moment I think it is relatively abstract in that a lot of it is setting up the differential equations required to solve various issues. One year, relatively recently, the lecturer basically started with an explanation of affine planes and why that's the right setting for Newtonian Dynamics (that didn't go down well)
    Interestingly, that sounds more like it was in my day (I don't recall an "affine plane" introduction, but it wouldn't have felt terribly out of place).

    In the 2000s though, a decent number of the questions were basically STEP III problems. (I picked one at random - see Q11 in https://www.maths.cam.ac.uk/sites/ww.../PaperIA_4.pdf)
    Yeah; unless memory is totally failing me, that would never have been on one of our exams. That said, I think there's really only one tricky point here (the "instantaneous speed" thing) and the rest doesn't really require intuition. It's the questions with multiple objects where you're thinking "is momentum conserved here? And if so, for which objects?" etc. that I think really test intuition (and by all accounts the examiners get it wrong themselves on occasion - there's been quite a bit of discussion about the mechanics of a falling chain IIRC).

    The closest we had to FM material was "rocket equation" problems. But to be honest those tended to be much more exercises in differential equation solving than anything else. (The actual questions tended to be very similar year to year, so practice helped in being able to grind through some fairly tedious algebra quickly).
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    I've been doing a spot of integration practice as it has always been a weak spot, indeed it will have cost me at least 8 marks in the AEA this year but ive got rather stuck on this \int\frac{1}{1+x^4}\dx
    i broke it down into (x^2+sqrt2 x +1)(x^2 - sqrt2 x +1) and also tried a u sub but have not made much progress here. no doubt most of you guys have done it before, its a fairly famous one, any help would be nice


    edit: it also seems that i cant latex, not too hard to read i hope
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    (Original post by tomahawker314)
    I've been doing a spot of integration practice as it has always been a weak spot, indeed it will have cost me at least 8 marks in the AEA this year but ive got rather stuck on this \int\frac{1}{1+x^4}\dx
    i broke it down into (x^2+sqrt2 x +1)(x^2 - sqrt2 +1) and also tried a u sub but have not made much progress here. no doubt most of you guys have done it before, its a fairly famous one, any help would be nice


    edit: it also seems that i cant latex, not too hard to read i hope
    You have two quadratic factors in the denominator. Partial fractions. Do you know how to decompose two quadratic factors into partial fractions?
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    neither ever equals 0 tho, what i was taught is you get one equal to 0 and then the other, does this mean i need to do complex integration or something?
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    (Original post by tomahawker314)
    neither ever equals 0 tho, what i was taught is you get one equal to 0 and then the other, does this mean i need to do complex integration or something?
    This table might help: http://tutorial.math.lamar.edu/Class...Fractions.aspx

    You need to write it as (Ax + b)/(first quad factor) +( Cx + d)/(secon quad factor)
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    Ahh ok thanks bro, never seen that before, that clears things up


    god damn this integral's a mess, just done the first of the 2 partial fractions and boy am i regretting this lol
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    (Original post by tomahawker314)
    god damn this integral's a mess, just done the first of the 2 partial fractions and boy am i regretting this lol
    Yep, it's quite ugly.
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    (Original post by Zacken)
    Yep, it's quite ugly.
    How hard do the integrals get in STEP 11 and 111. Are they as long, im guessing they need similar amounts of manipulation to be able to integrate, ie adding 0 to make it simpler.
 
 
 
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