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Senior Maths Challenge 2015 predicted thresholds and past thresholds watch

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    (Original post by theworkkid)
    How did yoh prepare for the BMO?
    Did you put a lot of work into it?
    What?! Do we actually have to prepare for BMO? I thought you can't prepare for it and that is the point of test.
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    (Original post by Ramil Ahmadov)
    What?! Do we actually have to prepare for BMO? I thought you can't prepare for it and that is the point of test.
    Lol. Should have done that for the rest of your exams.


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    (Original post by Ramil Ahmadov)
    What?! Do we actually have to prepare for BMO? I thought you can't prepare for it and that is the point of test.
    If I were you, I wouldn't bother preparing tbh.

    Olympiads are a distraction in my opinion.

    I'm not sure why olympiads were created in the first place but for the most part it has hindered many generations of mathematicians.

    Just imagine if instead of all those olympiad books. students had read undergraduate textbooks, independently instead.

    Some people spend years preparing for olympiads when they could have used that same time to study an entire maths degree.

    Anyone who can do well in olympiads would be better of learning more advanced maths. At the end of the day, once you get to advanced maths, it comes down to how familiar you are with the material, and the intuition you have built up. And the earlier you start the better.

    I found that much of the success in olympiads simply comes down to knowing obscure tricks.

    You can compete if you want, but don't expect it to be a massive help later on.

    I personally chose to ignore maths competitions and instead I focused on studying calculus and algebra more rigorously. This has personally made university a lot more enjoyable, I don't have to work as hard as other students, and I'm seeing all of the relationships between different subjects more easily.

    I've heard of countless numbers of IMO participants arriving at university only to find that their preparation was quite useless.

    In fact you can read about any of the most successful mathematicians in modern history, and you will find that they all spent time understanding and honing their intuition for the relevant mathematics of their time.

    Anyway, just wanted to warn anyone reading this. Olympiads are a massive distraction from real mathematics.
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    (Original post by theworkkid)
    Ahh i see, how long before did you start?

    And do you have any good resources to read induction on because i tried googling it but it was so basic that i didnt rrally know how to apply it to the bmo questions
    Hmm, probably around now for BMO1, then straight after BMO1 for BMO2 since I knew I got enough solutions to get me through.

    I have no good resources sorry since I just asked my friend for help last year. All you need is a knowledge of it at first, then try to apply it to some questions. The q4 of last year was the first induction question I properly got, so if you understand the concept, see what you can do with it. Also, try to be flexible with your induction hypotheses, sometimes you'll need strong induction (search it up).
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    Hey - just wondering what everyone else thought about the question where you had 4 lines on a piece of paper and had to make them cross, the answers being 1,2,3,4,5, and you had to circle whichever one was impossible... I don't understand why they weren't all possible? Was I missing something?
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    (Original post by Xenorebrem)
    .
    But I don't want to study for a degree before even going to uni... it takes all the fun out of it. I do it because I enjoy it, it's not meant to be preparation for uni. In any case, it is one of those things that you can no longer be truly involved in after you leave school, so why not put your heart into it while you can?
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    (Original post by 08mtwist)
    Hey - just wondering what everyone else thought about the question where you had 4 lines on a piece of paper and had to make them cross, the answers being 1,2,3,4,5, and you had to circle whichever one was impossible... I don't understand why they weren't all possible? Was I missing something?
    I think the wording of this question was poor. I think you're meant to assume that the lines are continuous and indefinite or something, even though a piece of paper is finite. Clearly if you had an actual piece of paper you could draw two pairs of lines that each form an x, and so have two intersections overall. But if those lines carried on they would meet, so you have to imagine the lines carrying on, and it turns out that you can't have just two intersections. It is easy to work out ways of drawing 1,3,4,5 so the cheap way is just to try and draw them all and conclude that the one you can't draw is the one that is impossible.

    But to "prove" it, imagine trying to draw the situation of just 2 intersections. Note that we must have one line intersecting another. If we draw the third line through this intersection point, then we can't draw the fourth line through that point or else there is only one intersection point, but if we draw the fourth line anywhere else then it will form more than one new intersection point. So that doesn't work. Whereas if we draw the third line somewhere else - indeed, it must be parallel to one of the first two lines in order to only create one new intersection - then dropping a fourth line will create at least one intersection point, so we have at least three overall. Try drawing it or just go on the UKMT solutions if that doesn't make sense.

    Edit: Perhaps the wording is technically correct due to the fact that they refer to lines and not line segments, but we still have to assume we have infinite paper lol
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    (Original post by 13 1 20 8 42)
    I think the wording of this question was poor. I think you're meant to assume that the lines are continuous and indefinite or something, even though a piece of paper is finite. Clearly if you had an actual piece of paper you could draw two pairs of lines that each form an x, and so have two intersections overall. But if those lines carried on they would meet, so you have to imagine the lines carrying on, and it turns out that you can't have just two intersections. It is easy to work out ways of drawing 1,3,4,5 so the cheap way is just to try and draw them all and conclude that the one you can't draw is the one that is impossible.

    But to "prove" it, imagine trying to draw the situation of just 2 intersections. Note that we must have one line intersecting another. If we draw the third line through this intersection point, then we can't draw the fourth line through that point or else there is only one intersection point, but if we draw the fourth line anywhere else then it will form more than one new intersection point. So that doesn't work. Whereas if we draw the third line somewhere else - indeed, it must be parallel to one of the first two lines in order to only create one new intersection - then dropping a fourth line will create at least one intersection point, so we have at least three overall. Try drawing it or just go on the UKMT solutions if that doesn't make sense.

    Edit: Perhaps the wording is technically correct due to the fact that they refer to lines and not line segments, but we still have to assume we have infinite paper lol
    Ahhhh, okay, I did not think of it in this way at all.. but nicely explained - thanks very much!! Annoying though - I picked 3 haha
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    This may sound completely random to mention on here, but since you all know a lot about maths, could you help me please? I'm writing an EPQ on maths, and need to find some relevant resources on whether maths was invented or discovered. Does anyone know of any books/journals that would be useful for this? Thanks guys
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    (Original post by LaurenLovesMaths)
    This may sound completely random to mention on here, but since you all know a lot about maths, could you help me please? I'm writing an EPQ on maths, and need to find some relevant resources on whether maths was invented or discovered. Does anyone know of any books/journals that would be useful for this? Thanks guys
    I like the choice of topic - I'd be interested to read! (But obviously if there is a risk of plagiarism stuff, don't show it online to anyone including me!)
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    (Original post by Student403)
    I like the choice of topic - I'd be interested to read! (But obviously if there is a risk of plagiarism stuff, don't show it online to anyone including me!)
    Thank you, I find it very interesting & don't worry aha, I'll make sure of that!
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    (Original post by LaurenLovesMaths)
    This may sound completely random to mention on here, but since you all know a lot about maths, could you help me please? I'm writing an EPQ on maths, and need to find some relevant resources on whether maths was invented or discovered. Does anyone know of any books/journals that would be useful for this? Thanks guys
    Wow, that's a tricky question to answer. I've thought of it myself, but haven't been able to come up with a definite answer.
    I guess it would be the same answer to the question, was energy discovered or invented?
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    (Original post by PrimeLime)
    Wow, that's a tricky question to answer. I've thought of it myself, but haven't been able to come up with a definite answer.
    I guess it would be the same answer to the question, was energy discovered or invented?
    Not really. Mathematics is a tool we use to model the real world, whereas energy is something we can prove is contained in objects
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    (Original post by 13 1 20 8 42)
    I think the wording of this question was poor. I think you're meant to assume that the lines are continuous and indefinite or something, even though a piece of paper is finite.

    Imo a lot of lower level maths makes assumptions like this.

    (Original post by Student403)
    Not really. Mathematics is a tool we use to model the real world, whereas energy is something we can prove is contained in objects
    But mathematics grows naturally from logic... or some form of logic, at least, that seems natural to us

    Energy is contained in objects? So you say, but what is that energy, and what are these objects?
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    (Original post by Johann von Gauss)
    But mathematics grows naturally from logic... or some form of logic, at least, that seems natural to us

    Energy is contained in objects? So you say, but what is that energy, and what are these objects?
    We should make a separate thread for this where we can get everyone's ideas!
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    (Original post by PrimeLime)
    Wow, that's a tricky question to answer. I've thought of it myself, but haven't been able to come up with a definite answer.
    I guess it would be the same answer to the question, was energy discovered or invented?
    It is hard to come up with a definite answer, but at least it gives me a variety of arguments and counter-arguments to explain
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    (Original post by Student403)
    We should make a separate thread for this where we can get everyone's ideas!
    We should!!
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    (Original post by LaurenLovesMaths)
    We should!!
    Done I tagged you
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    (Original post by Student403)
    Done I tagged you
    thank you!!
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    (Original post by Johann von Gauss)
    Imo a lot of lower level maths makes assumptions like this.
    True but often it's permissible because everybody at a certain level will make that assumption themselves anyway. Whereas in this case I feel someone doing the SMC is probably going to read "on a flat piece of paper" and think about an actual piece of paper, rather than an infinite plane. Many will realise what the question is really asking, as all configurations are possible on an actual piece of paper, but the fact that any energy might be devoted to thinking about this, and that some might get the question wrong even though they would have got it right if it was worded more accurately, suggests to me that this question is badly written.
 
 
 
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