  IB Math Helper

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1. For mathematics that is in the curriculum such as Pearson's correlation, you do not have to explain the derivation behind them. For the Pearson's case, showing the linear regression graph accompanied by the correlation coefficient (r) and it's meaning (e.g. strong negative correlation between the two variables) would be sufficient. However for mathematics that is not obvious or not in the curriculum, the derivation (or meaning) should be explained. For instance, going back to the Pearson's correlation coefficient (r), there is something known as the co-efficient of determination which is the square of the correlation co-efficient (r^2) and helps explain how well the model fits the data. If r= -0.9, for example, then the co-efficient of determination is r^2 = 0.81. This means that the linear regression model helps explain 81% of the data and the other 19% is explained by random error (or other variables not explained by the model). I would probably find a source for the co-efficient of determination and then explain its meaning and relevance within the context of the exploration. Going back to your question, you'll have to explain what the Spearman's rank is and how it is derived. The clearer the explanation, the more in-depth knowledge you demonstrate. To find sources, go to the Spearman's rank correlation wiki page and look at the bottom of the page where it cites its own references. Consult those referenced books or articles and then make your own citations. Finally, to get a 7 does not just require the math. You can have the most succinct and clearest explanations for the new mathematics you are using but this only means that you'll do well in Criterion E (Mathematical Understanding) which is worth 6 points out of a maximum of 20 for the whole exploration. To get a 7 make sure you focus on the Criterion C (Personal Engagement) and Criterion D (Critical Reflection).
2. Other than getting some sunrise or sunset times over a year and plotting them to get the sinusoidal graph, i'm not sure what else you can do especially on the Personal Engagement and Critical Reflection front. This would be a very basic investigation. Perhaps you can do something with amount of sunshine over the year and integrate the graph to find the amount of sunshine you could potentially convert from solar into electric energy? That may be one direction to go.
3. What are some things you are interested in? Start from there and brainstorm some ideas. For instance, let's say you like reading in general. These are some ideas that I've just come up with: 1) Take your favourite adventure book and plot the tension (or level of drama) on the page vs the page number. [That is, x=page number, y=tension]. You can define tension from a scale of 1-10 where 1 = no tension (relaxed day) and 10 = intense (running away from home). Of course this is based on your own judgment but that's ok. Plot this on a graph and you should expect something that's sinusoidal in nature. Come up with a function and discuss this. Perhaps the structure of an adventure novel can be described mathematically. 2) Get the written essays of some of your friends and note the number of spelling errors or grammatical errors per 100 words. You have to do this for a large number of people. Plot this data on a histogram. Hopefully it will look like a normal distribution. If not, you can use the binomial probability distribution to find the expected number of spelling/grammatical mistakes on a 4000 word essay like your EE. These are 2 ideas that just came off the top of my head. Start with something you are interested in and write down 5-10 ideas (not matter how crazy they sound). After you write them down, eliminate the ones that seem unfeasible. Surely, you will find one that is manageable.
4. No, it's not enough. I can answer this question better if I knew what your topic was about.
5. Just to be clear about this, the example you provided that got top marks (posted on reddit) was for Math Studies. The criteria for Math studies is completely different from the Math SL criteria. The Math SL IA is marked at a much higher level. Though some things can be learned from the Wards and Supporting IA, it's not a fair comparison. This IA would not get a high mark with the Math SL criteria. I think you're on the right track if you're thinking about the mathematical concepts needed to get a high mark on your IA. (I couldn't read your proposal because you made it by request only. Please change the settings of the document so that anyone can view it). Make sure you have enough math concepts and then focus on the personal engagement component of your IA (meaning what lessons can you draw from it).
6. First of all, how exactly would you do the correlation? In order to do a correlation, you need numerical values for both the x- and y- variables. Based on your survey, I don't see how you can do a correlation (or linear regression). The only thing I can think of is the chi-square test of independence. But even then, you need to think about how you're going to apply it.
7. Can you start off by listing your interests? Simply begging for a topic will not help you. Also, how good are you at math?
8. 2cos(x) = sin(2x) 2cos(x) = 2sin(x)cos(x) cos(x) = sin(x)cos(x) cos(x)-sin(x)cos(x) = 0 cos(x) ( 1 - sin(x) ) = 0 So, cos(x) = 0 which means x = pi/2, 3*pi/2 and 5*pi/2 from 0 to 3*pi and sin(x) = 1 which means x = pi/2 and 5*pi/2 from 0 to 3*pi Hope this helps.
9. If Sin(B)=2/3, you also need to know in which quadrant B is in. Otherwise, you can have two possible answers. For this question, the double angle is not necessary to find cos(B). Just draw a right angle triangle with the opposite side of 2 and hypotenuse of 3 and use Pythagoras to find the last side. Once you have that, the adjacent to the hypoteneuse is the ratio you want for cos(B).
10. Go for it but explain it clearly (i.e. step-by-step) because the math here is beyond the scope of the curriculum.
11. This sounds like the secretary problem. Check out the math here: https://en.wikipedia.org/wiki/Secretary_problem
12. I don't agree that IB graders mark really hard. I'm an IB marker and I sometimes think the marking at times can be a little generous. It is true that it is hard to get a 7 on your IA but it's doable. If I were you, I would look at some more examples especially ones that scored very well. You can check this site out for some examples and read the comments the markers have given for each criteria. Check it out here: https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=2
13. I would actually stick with the game theory idea since probability trees and expected values are still part of the math sl curriculum and of course tie in with game theory. The prisoner's dilemma, for example, can be modelled as a probability tree diagram and one can also find the expected value of the number of years in prison for different situations. If your game theory topics involves probability and statistics, you should stick with that.
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