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Aleksejs Popovs

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  • Exams
    May 2016
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    Latvia

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    popoffka

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  1. Imagine an HL Paper 2 problem like this (real example):Given a pdf f(x) = k ln(x) for 1 ≤ x ≤ 3, find the median of X.Finding k is easy enough, and then you get a problem of the formIntegral[k ln(x) dx, 1 ≤ x ≤ m] = 1/2I imagine that the expected solution is using partial integration to obtain Integral[k ln(x) dx] = k x (ln(x) - 1), then using that to obtain an equation which can be solved numerically. In this case, the problem tests both your knowledge of the definition of a median and your ability to partially integrate ln(x).However, on an nSpire, you can define a function g(t) := Integral[k ln(x) dx, 1 ≤ x ≤ t] and then just do nSolve(g(t) = 1/2, t, 2) (the initial value 2 is required to keep it from converging on a solution below 1) to get exactly the same answer. Note that you really do need to define a function first, because otherwise the calc complains about multiple non-valued variables in a single expression. I believe that this might be impossible to do on calculators like the TI 84. In this case, the problem is a one-liner and only requires knowing the definition of a median, as well as having a recent calculator and being somewhat good at using it.The latter solution feels somewhat like cheating, but it's what came to me naturally during a test today, and I don't see any actual rule that would prohibit me from using it. Do you think both solutions would be accepted as equally valid on an exam?
  2. Aleksejs Popovs

    Further Mathematics study group/club

    Hi everyone! Sorry from being absent from the thread, I've been caught up in all the school-related stuff FM doesn't have any assessment apart from the final exam — so, no IAs or anything else. Multiple people have suggested creating a WhatsApp group, and that sounds cool to me. My phone is +371 28398774, ping me and I'll add you!
  3. Aleksejs Popovs

    Further Mathematics study group/club

    This is true! I'm currently studying from the Pearson 2012 Maths HL book's chapters on options (they are only available in digital form, but come free with the purchase of a hardcopy although there are also other ways to obtain them). I'll check it out, thanks! Covering more is better than covering less anyway (btw, after doing UPenn's online Calculus course, I was quite disappointed to find that the IB syllabus doesn't include big-O notation).
  4. Aleksejs Popovs

    Further Mathematics study group/club

    Here's the fun thing about the new (first exams this year) syllabus: there are no books on it yet The FM syllabus essentially consists of all four options from the Maths HL syllabus (one of which you're supposed to cover in your Maths HL class) and two additional topics, Linear Algebra and Geometry. For the options, you can use any Maths HL book that has them, such as the Pearson one I mentioned above. As for Linear Algebra and Geometry, you could either try using generic books on these subjects or an older Further Mathematics book. In either case, use the syllabus to keep track of the stuff you're supposed to learn.
  5. Aleksejs Popovs

    Strangest/most unique subject combinations

    As far as I know, it doesn't really — you might be asked to punch a provided formula into a calculator, but that's it. To be honest, I'm taking Geography as the "least evil" in Group 3, since my school only offers Geography, Economics, and History. History is a huge no-no for me with its overabundance of essays, and I find Economics boring (though AFAIK, it has got a little bit of maths in it, but only on HL).
  6. Aleksejs Popovs

    Strangest/most unique subject combinations

    I'm taking Maths HL, Further Maths HL, Computer Science HL, Physics SL and three Language A courses (Latvian HL, English SL, Russian SL) (also Geography SL). I guess that this is a rather unusual combination, but this is what happens when you're on the "I can't sleep because this maths problem is so beautiful" side, yet you're trying to combine your IB studies with your country's national school curriculum. To be honest, I understand now that I should've taken French B ab initio when I had the chance instead. I'd also love Classical Greek, but that's not an option at my school.
  7. Aleksejs Popovs

    Further Mathematics study group/club

    Let me quote the syllabus here: Great! You are, without a doubt, welcome here. I am currently working my way through the chapters corresponding to Topic 4 — Sets, Relations and Groups in the IB Mathematics HL textbook by Ibrahim Wazir and Tim Garry (published by Pearson in 2012). It seems to me that this topic is a fairly good choice for the beginning of the year (at least in my case of self-study), because it's got pretty much no dependencies on other core topics or options.
  8. Aleksejs Popovs

    Further Mathematics study group/club

    I, personally, am planning to pursue a career in Mathematics. Although the IBO says that Mathematics HL is sufficient for that, I find enjoyment and beauty in Maths, which is exactly why I'm taking FM (and I really want to play around with that Sets, Relations and Groups Option, but they only teach Calculus at my school!). And hey, since it's not on my diploma, it's not like I'm really risking anything (except for the time I could devote to other subjects, of course). If you, too, think of doing Mathematics as something enjoyable, I'd recommend you to at least take a look at the syllabus for FM and maybe give it a try.
  9. Hi guys! Just a little bit of personal background: I started the IBDP at Riga State Gymnasium #1 in Latvia 5 days ago. I'm taking Mathematics HL as my Group 5 subject, and also taking Further Mathematics HL as an additional subject (i.e., not included on the diploma). I love mathematics and have some background in Computer Science, which seems to be quite relevant in the Discrete Mathematics Option, with all the graph algorithms and what not. I also probably know almost all of the Calculus Option thanks to Robert Ghrist's (UPenn) wonderful Single Variable Calculus Coursera course I took this summer. My school does not have an FM teacher, so I'm left (almost) on my own, with only books to help me (although I guess I should also be able to get limited support from my Maths teacher). I seem to be the only person taking FM this year, although I have a friend who is in his second year now and also taking FM, and two of my classmates are cautiously considering joining me. Since FM is considered quite a challenging course, and is made even harder due to the recently changed syllabus (as far as I know, there isn't even a single textbook covering the syllabus for 2014's exams), I thought that it might be cool to form a little sort of a study group with my fellow IB students who are also taking FM. It could be just a thread here, a group on Facebook, a chat in Whatsapp, an IRC chatroom or even a mailing list, I don't really care, but it would be a place where we would share our progress, interesting findings and frustrations, as well as offer advice and encouragement to each other. I might also have a few relevant textbooks that I might be able to share in a more private setting. So, is anyone interested?
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