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Mathematics HL paper 3 TZ2


x___x

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hey!

can we start discussing this paper now?

OMG! i've never seen a paper like this before!

there were questions that are extremely easy, and some are really haaaard!!

i enjoyed the question about the hypergeometric distribution! lovely!

i also had fun solving the question about apples, pears, and peaches!

by the way, this year's exam has someone named "Brian", May 2009 paper also had someone called "Brian", what's with the IB and Brians?

anyways, i couldn't really figure out how to solve the negative binomial question, i tried, but stuck!

also, how did you solve the chi-square question?

what about question two? how did you tackle it?

Question 1 was mostly GDC stuff. Did you solve it this way as well, or did you prefer to solve it manually?

overall, how did you find the paper?

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I did Sets, relations and groups. I found the questions quite easy, comparing with the past papers.

Also, in the past, there were huge variations in question formats in this paper.

But I've seen the same question format in this year's paper from the past paper, so...ya, kinda easy if people have done past paper.

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Who did sequences and series?

For me I would say it was just about ok, not as good as I hoped but yeah. The first question (Euler's method) was a no brainer (I hope I didn't make a mistake though!) but then question two was a bit tough and I eventually only got part A. I think I got 3 but didn't really know the beginning of 4, though I picked it up from part B/C. Five I think I got everything expect the very last part.

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I did Discrete Math. I was pleased with the paper, for many of the questions were similar to the past papers. Only a few things I didn't know, but the proofs as always are impossible for me. haha

What time zone were you?

I found it ridiculously hard and didn't get to finish the paper T_T

Question 5...I didn't know where to start?

I'm TZ2 btw.

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mister with the cherries avatar,

I did stats and probability as well. I found all questions very straightforward except number 2. Number 1 was indeed calculator, easy peasy. Number 3 was just a chi squared, also easy peasy, for the first part you had to integrate because that gave you your cumulative distribution, and for the second part you just calculate your expected frequencies, devise hypothesese, calculate your test statistic and p-value and state your conclusion. Solved. The apples and pears one was also really easy but on the first try I couldn't get it because i was minussing a variance when I was supposed to be adding. Wasted a good five minutes there. The hypergeometric was also straightforward and the negative binomial as well, only I know I made a very dumb mistake. All you had to do was look in your data booklet for the formula, plug in what you know, and solve for p in your calculator. But I wrote down the formula wrong, very dumb.

But number 2 with the type 1 and type 2 I was unsure. I knew how to do it technically but I was wavering between staying in discrete or approximating by a normal distribution. In the end I chose to stay discrete which I hope is the right choice. Anyways, what I did was make a new distribution for the sum of 10 Xi. Since they were all poison, adding them would also be a poison with, under H0:mean=1, m=10. Then, since the probability of a type 1 is that you accept H1 when really H0 is true, it is the probability that you get a value in your critical region. Thus it would be P(sum Xi >= 15) and that is just calculator work. I got something close to .08 percent. The probability of a type II is that you accept H0 when really H1 is true. Thus it is P(sum Xi < 15 | mean=2). And again this is calculator work, using the function poissoncdf with m=2. I got a value around .105 . I hope I was correct in my reasoning though, otherwise that is 10 points down the drain. What some people in my class did instead is approximate the new distribution of sum of Xi with a normal distribution. This makes calculating errors a lot simpler because now we are dealing with a continuous distribution. And this seems perfectly valid as well. So I don't know. In any case, I am praying for a 7 overall, but I doubt it. Made too many dumb mistakes.

Oh and the Brian thing is because it is a name that starts with B. Hence the logical thing to do would be to call your random variable B. The other name is usually Adam, so you would call this variable A. A and B are very familiar variables in statistics and probability, you will notice in the data packet that for all the probability equations they use A and B. Therefore Brian.

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mister with the cherries avatar,

I did stats and probability as well. I found all questions very straightforward except number 2. Number 1 was indeed calculator, easy peasy. Number 3 was just a chi squared, also easy peasy, for the first part you had to integrate because that gave you your cumulative distribution, and for the second part you just calculate your expected frequencies, devise hypothesese, calculate your test statistic and p-value and state your conclusion. Solved. The apples and pears one was also really easy but on the first try I couldn't get it because i was minussing a variance when I was supposed to be adding. Wasted a good five minutes there. The hypergeometric was also straightforward and the negative binomial as well, only I know I made a very dumb mistake. All you had to do was look in your data booklet for the formula, plug in what you know, and solve for p in your calculator. But I wrote down the formula wrong, very dumb.

But number 2 with the type 1 and type 2 I was unsure. I knew how to do it technically but I was wavering between staying in discrete or approximating by a normal distribution. In the end I chose to stay discrete which I hope is the right choice. Anyways, what I did was make a new distribution for the sum of 10 Xi. Since they were all poison, adding them would also be a poison with, under H0:mean=1, m=10. Then, since the probability of a type 1 is that you accept H1 when really H0 is true, it is the probability that you get a value in your critical region. Thus it would be P(sum Xi >= 15) and that is just calculator work. I got something close to .08 percent. The probability of a type II is that you accept H0 when really H1 is true. Thus it is P(sum Xi < 15 | mean=2). And again this is calculator work, using the function poissoncdf with m=2. I got a value around .105 . I hope I was correct in my reasoning though, otherwise that is 10 points down the drain. What some people in my class did instead is approximate the new distribution of sum of Xi with a normal distribution. This makes calculating errors a lot simpler because now we are dealing with a continuous distribution. And this seems perfectly valid as well. So I don't know. In any case, I am praying for a 7 overall, but I doubt it. Made too many dumb mistakes.

Oh and the Brian thing is because it is a name that starts with B. Hence the logical thing to do would be to call your random variable B. The other name is usually Adam, so you would call this variable A. A and B are very familiar variables in statistics and probability, you will notice in the data packet that for all the probability equations they use A and B. Therefore Brian.

oh, it's "Miss" not "Mister",

i can see how much you're in tune with probability and statistics from your signature, in contrast to me, who's more in tune with algebra and trig, so to discuss the difficulty of an option that is from your field is quite unfair, or is it? :)

anyways, for the negative binomial question, i did use the rule, but it just didn't work out for me. i don't know why. Perhaps you used another method, or you just figured out a trick that i couldn't figure. How did you solve for p?

Question 2 was just beyond me, but your reasoning seems perfectly fine to me, i hope it's as well to the examiner.

BTW, good luck with your application to Cambridge, and don't rely on probability to calculate your chances of being accepted! :P

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Oh I am very sorry Miss Cherry, I somehow always assume that people online are guys.

In any case, yes I do like probability and statistics because it is so applicable. The way you had to solve for p was by plugging in everything you were given (r, and x) and simplify the combination of (x-1)C(r-1). This gave you a complicated polinomial set equal to whatever your probability was for P(X=10). What you could then do is move this value to the other side giving you (x-1)C(r-1)p^r(1-p)^(x-r)-P(X=10)=0 (of course it would look much simpler if I had the values, but pretty much you know every value in this expression except for p.) Hence, all you do is chuck this into your calculator as a function, set p=x, graph, and find the zero where 0<p<1. That gave you the value for p. Sadly however, what I plugged into my calculator was (x-1)C(r-1)p^r(1-p^(x-r))-P(X=10)=0 giving me the wrong answer. I'm hoping for some follow through marks though.

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Hey guys

I did probability and statistics, it was very easy. About the question that was about the negative binomial, you should have had returned to the data booklet to apply the rules for the negative binomial and them to solve for p using solver on the GDC. If you did so, you would find two values for p. You should take the one that is less than 0.5 as it was given in the question.

Any way, I hope that all of you guys have did well, to compensate what we have lost in the first two papers

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TZ 2 Series and differential equations for me

did you get 5.89 for Eulers method?

and 0 for the l hopital one?

I could have seriously gotten 100% but I did one careless mistake per qs so ridiculous............

so then i will get 80% or so

which will result in me ionly getting a 6 overall.............cry.

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TZ 2 Series and differential equations for me

did you get 5.89 for Eulers method?

and 0 for the l hopital one?

I could have seriously gotten 100% but I did one careless mistake per qs so ridiculous............

so then i will get 80% or so

which will result in me ionly getting a 6 overall.............cry.

To be honest I don't remember the answers I got but for some reason I don't think it was zero for the l'hopital's one. How did you do the last part of question 5?

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  • 10 months later...

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