Lynsey Posted May 6, 2011 Report Share Posted May 6, 2011 Hello,So I did less than excellent on papers 1 and 2, and really want to make up for it on paper 3 next week. Does anybody have a list of everything that I should study and know for the exam? I need to go in and get like 100% Reply Link to post Share on other sites More sharing options...
slack Posted May 8, 2011 Report Share Posted May 8, 2011 A proper understanding of what convergence is (using proper mathematical notation!!!)Different types of series and their conditions for convergence: The power series (finding the radius and interval of convergence as well) The p-seriesTelescoping series (determining by partial fractions)Alternating series (absolute and conditional convergence should be known) Tests for convergence: Each convergence test can be used in only some series, the conditions for each test must be knownThe nth term testAlternating series testGeometric series testDirect comparison testIntegral testLimit comparison testPartial fractions testTaylor and Maclaurin polynomials: How to derive them through differentiationHow to use known polynomials to get new ones (either by direct substitution, integration, and/or differentiation)The error term (both Larange and the Integral form, you should understand to some extent how they have been derived) Euler's method (Free marks )Understand how the shape of the graph determines the magnitude of the error in Euler's estimateLimits, improper integrals (with a treat of convergence and divergence), L'Hopital's rule Good luck to everyone sitting this paper tomorrow! Might be the hardest math option, but it's certainly quite fun! 1 Reply Link to post Share on other sites More sharing options...
MajorMajor Posted May 8, 2011 Report Share Posted May 8, 2011 slack, I think you omitted the 'differential equations' part. You also need to solve homogenous differential equations (functions of y/x) and to solve linear differential equations [y'+y*P(x)=Q(x)] using the integrating factor [e^int(P(x)dx)].This option made me think the Core material wasn't that hard after all. It's basically what you do at the first year of university Mathematics course... Reply Link to post Share on other sites More sharing options...
slack Posted May 8, 2011 Report Share Posted May 8, 2011 I forgot to mention, I have seen many students ask about slope fields. Technically, they are part of our syllabus. I do remember reading somewhere (if I remember correctly it might have been a document published by the IBO), though, that we cannot be asked to draw them (it takes a great deal of time, and it's a short paper). If you read the syllabus, it's kind of implied, too. The most they can ask us to do is analyze a diagram with slope fields. I personally, in all the past papers I have seen, have not seen such a question. This certainly implies that you can always expect a question on Euler's method. I'm just looking at trends, so don't base your revision on this. IBO surprised us in P1 this year, who knows what they're cooking for P3... Good luck! Reply Link to post Share on other sites More sharing options...
slack Posted May 8, 2011 Report Share Posted May 8, 2011 slack, I think you omitted the 'differential equations' part. You also need to solve homogenous differential equations (functions of y/x) and to solve linear differential equations [y'+y*P(x)=Q(x)] using the integrating factor [e^int(P(x)dx)].This option made me think the Core material wasn't that hard after all. It's basically what you do at the first year of university Mathematics course...Oh yes, haha. Silly mistake, especially because the option is called "Series and Differential Equations"! Thank you MajorMajor! I guess I'm more worried about the series part of it :/Yes, first and second order differential equations, integrating factor differential equations and some applications on them, almost always pop-up. I should mention that, while I was solving differential equations correctly, the way I displayed my answers (in terms of crucial steps that might seem obvious but which the examiner would require) were always missing. I suggest looking at your textbook example and in the exam, follow the exact procedure of displaying answers! Reply Link to post Share on other sites More sharing options...
MajorMajor Posted May 8, 2011 Report Share Posted May 8, 2011 Oh dear, I think I didn't screw up the P1 very much, and the P2 went really well, but P3 is a whole different story... Do you have any clue what are approximately the grade boundaries for this particular option paper? I only found some for the different options, and it varied very much from one topic to another... Is it something like ~30 for a 5, ~35 for a 6 and ~40 for a 7? Reply Link to post Share on other sites More sharing options...
slack Posted May 8, 2011 Report Share Posted May 8, 2011 November 2008Paper three – Series and differential equationsComponent grade boundaries 7: 40-606: 33-395: 27-324: 20-263: 12-192: 6-111: 0-11Usually, there's a +/- 2 range between different sessions, and if I'm not mistaken, time zones too. 1 Reply Link to post Share on other sites More sharing options...
MajorMajor Posted May 8, 2011 Report Share Posted May 8, 2011 Thanks! One thing that really improved my morale before the P3 was calculating how much points do I have to score in order to get a 6 overall in maths. It seems the pessimistic variant is about 15/60, so I guess I shouldn't worry too much... Except my ambition tells me to try for the 7!One thing I just can't work out are the lower & upper bounds of finite integrals... I think I understand it, but i always get the results wrong. Also the Maclaurin and Taylor series questions are often more difficult than you'd expect, given that these topics are basically 'substitute something into the equation from the booklet'. I just hope to get an Euler question, a differential equation - preferably homogenous, and some limits to calculate using De L'Hospital's rule... Reply Link to post Share on other sites More sharing options...
Lynsey Posted May 8, 2011 Author Report Share Posted May 8, 2011 I'm crossing my finger's for some Euler and L'Hospital too. Although everything else kinda stresses me out X_X Reply Link to post Share on other sites More sharing options...
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