SC2Player

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  1. Have you tried using the formulas for the sum and product of the roots of a quadratic equation?
  2. The personal engagement section is quite confusing for me as of now. My current topic is quite abstract (logs and sin/cos/tan of complex numbers), and the actual reason I chose it was because I was just wondering what would happen if I used complex numbers as opposed to real numbers. How exactly do I demonstrate personal engagement in a Math IA in general?
  3. For my first point, I was referring to the idea of taking the logarithm of a complex number e.g. what log10(i) equals. You could also start with logs of negative numbers e.g. what ln(-1) equals. My second point is related to examples such as cos(i) or sin(1+2i), where you take the sin, cos, or tan of a complex number.
  4. What ideas have you come up with so far? You could look at ways of extending some common ideas, such as logarithms or trig functions, to complex numbers.
  5. What topic are you thinking of doing your IA in? I can't really do all the work for you and give you a question directly, but I can help direct you towards one.
  6. physics

    If you do decide to change from DT to physics, I'd suggest that you brush up on the physics material ASAP. There isn't actually that much material to truly cover - the difficulties mostly lie in the style of questioning, so doing past papers and textbook questions (especially the difficult ones) are quite important. There's quite a bit of information on the web on the physics HL syllabus, and getting your hands on an IB physics textbook wouldn't hurt either.
  7. As far as I know, law only really looks at what score you get out of 45, so just take what subjects you're best at and do well in them. Difficulty is always subjective - most people would say that my course selection is difficult, but I personally find it quite easy.
  8. I'm currently doing Further Maths, and I'll just introduce the structure to you to start with. In HL, you have four options (as you probably know). In Further Maths, you'll do all these four options, as well as two additional topics. Below is a brief description of each topic Further Maths has. I've tried to simplify them and explain things where possible, but don't worry if you can't understand some terms or topics - these are not prerequisites. Googling them may help too. Sets, relations and groups Overall this is the most abstract topic IMO. Topics include: Basic set theory Functions (more abstract look) Binary operations (e.g. addition, multiplication) Groups (sets with a binary operation that satisfy certain criteria, e.g. the set of all integers under addition) Calculus Extends the calculus in the HL core. Topics include: Infinite series Differential equations Taylor and Maclaurin series (a type of series that involves derivatives of a function) Discrete Mathematics This is basically number theory, the study of the integers. Topics include: Primes The linear Diophantine equation Graph theory Linear Algebra Mostly revolves around matrices, a topic that used to be in the IB core but was taken out in 2014-ish. Topics include: Matrix properties (definition, matrix addition and multiplication, some common computations for certain matrices, including inverse and determinant) Various methods of solving systems of linear equations Linear transformations Geometry Extends the geometry portion in the core. Topics include: Advanced triangle geometry Advanced circle geometry Ceva's theorem Statistics and Probability Only topic I haven't done much on, so unfortunately I can't say much on this one. Some additional links: http://www.ibo.org/globalassets/publications/recognition/5_furthermathhl.pdf (Brief official intro by the IB) http://www.sji.edu.sg/qql/slot/u560/Programmes/Academic Programmes/SJI IB Diploma/Six Academic Subject Groups/Further Mathematics HL guide 1st exam 2014.pdf (Official guide, includes all topics to be covered) Further Maths, in essence, assumes that you've got a firm understanding of pretty much the entire IB HL core. So, if you think you understand pretty much all of IB HL maths at this point, you're probably set for Further. The course overall is not very in-depth - it's just a broad look at a number of different common subjects in maths. Generally a good course to take if you're going to study pure mathematics, or go into a math-intensive field such as a pure science (especially physics) or engineering. I myself decided to join because I had already done most of the HL course, as well as some topics in Further Maths, by the start of IB. So far, it's been fairly straightforward.
  9. For your specific problem, a hint: try expressing everything in terms of ln (change of base formula). As for your main question, practice definitely helps, as you point out. In terms of what I do, I usually attempt to express everything in terms of one single base, and then just experiment around with simplifying everything using the log laws as appropriate. Sometimes, you may find that it helps to 'reverse' the log laws. For example, you may rewrite logc(a) + logc(b) = logc(ab), or b*logc(a) = logc(ab). Overall though, the main thing to do is to just practice, especially using difficult log and exponential equations, and don't give up on the problems, even if you really just want to look at the answers. I've found that I learn best if I just keep going until I finally get the answer independently. For exponential equations, the only thing I can really say is to become familiar using a combination of both log and exponential notation. Sometimes one is more convenient than the other, depending on the situation.
  10. There's quite a bit you could do with the natural logarithm function, and the significance of using e. However, you need to make sure that it's at the appropriate level. For example, using calculus to analyse the natural logarithm or investigating negative/complex logarithms would have a sufficient level of math, while simply investigating the log rules or other elementary properties would not have a sufficient level of math. The Wikipedia page on the natural logarithm (https://en.wikipedia.org/wiki/Natural_logarithm) is a good starting point.
  11. I'm not an alumnus, but I have read a number of guides by alumi, so here's what I've gleaned: The main thing in IB HL Math is to simply just practice as much math as you can. Best option, of course, is to do past papers in a test environment to familiarise yourself with the examination style. Set appropriate time limits and do not exceed them, not even by a second, because you won't have the luxury in a real exam. Go through the harder textbook questions too, and make sure that you can do virtually any type of problem they may throw at you in the real exams. As you probably have limited time, I would recommend you to not do problems that you find easy (i.e. problems that you can effectively do in your head), but instead focus on ones that will take you some time.
  12. Both questions are pretty good starting points for an IA. For the second one, if you find yourself needing an extension, maybe you could look at the Gaussian curvature for the general n-hole torus. This is overall related to the subject of topology, so it may be a good idea to have a few links back there in your reflection.
  13. I've already completed most of my hours, now just to BS through my reflections (already done 1 activity's worth of rubbish yay). Creativity is either MUN or a youth orchestra, both of which I've already done (and sum total of hours is over 100, so I'm just going to record 50 of one). Issue is that the youth orchestra is outside of school, and I can't get a signature anymore, so I may just use MUN. Action is skiing for 30 hours. Just need 20 more hours - I'll see if there's some random gym group around I suppose. Service is at school, which is also 50 hours. We just do services like teaching children and helping with recycling. My CAS project involves something known as Extra Life, where I literally play games and raise money through donors who watch. I'd be surprised if I raised a cent from this tbh, but I suppose the most important thing is to learn something from it.
  14. Try looking for some introductory textbooks on graph theory - this one is decent and available for free online, although it is not an easy read: http://diestel-graph-theory.com/basic.html. Wikipedia and Wolfram Alpha are always good starting points, especially in terms of their sources.
  15. Ah I see, thanks for clearing that up. I'll keep that in mind for my own IAs.