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LCHL Project Maths Question on Stats & Probability

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  • 04-04-2012 9:02pm
    #1
    sullanefc
    Closed Accounts Posts: 57 ✭✭


    Ok, I know there are loads of threads on project maths already but I went back 7/8 pages and couldn't find anyone that is relevant to me.

    So I have a question on some material that I'm not sure if it is on or off the course for LCHL 2012 (non pilot school). I have been following the Active Maths Folens book (their first one that came out last year) for the paper 2 material and the old books for paper 1. Before anyone asks, I checked the syllabus at the start of 5th year a year and a half ago and I was sure that the book covered everything, now i'm not so sure due to seeing some questions on some of the exam papers.

    My main concern is on "Bernoulli Trials using the normal curve" and "Hypothesis Testing". I have NOT taught my pupils the formulae mean = np, sd = sqrt(npq), mean of sample = mean of population, standard deviation of sample = sd/sqrt(n). Do I need to cover these?

    The only Hypothesis test my students can do is the one from the folens book, i.e. where they work out p-hat and the margin of error (1/sprt(n)) and check if the hypothesis (as a percentage or decimal) falls within the confidence interval. So my students would be well able for Q2 (b) of the 2011 sample paper:

    pmBoards1.jpg

    However, my students would have no idea how to do this question from the 2010 paper 2 (Q9A (c)) that the project schools did:

    pmBoards2.jpg

    Similarly Q9A from the NCCA sample paper would be undoable. Should I cover these after the holidays?

    Edit: The Tukey test came up in a paper. This isn't mentioned anywhere on the syllabus!!

    On the matter of Bernoulli Trials, we covered problems where, "A die is rolled 10 times, find the probability of getting a six, 8 or more times". We use Bernoulli to get each of P(X=8), P(X=9), P(X=10) and then add them together.

    But I have not covered questions of the form: "A die is rolled 100 times, find the probability of getting a six, 60 or more times". Obviously we couldn't use Bernoulli as it would be too tedious so we use the normal curve by getting the mean (np), sd (sqrt(npq)), get the z score and then use the tables. Should I cover this?

    Sorry for the long post. I have a little bit of time after easter to cover these, but I don't want to if I don't have to. Obviously I could email the IMTA or the project maths team but I said I would try this first as it may be quicker.

    Thanks in advance for help.


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    #2
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    I think you can take some comfort from section 4 of the letter that the SEC sent to schools with the sample papers for 2012. It's available here on their website:
    http://www.examinations.ie/schools/S_77_11_Arrangements_for_Phase1_of_Project_Maths_2012.pdf

    It points out a number of parts of questions on the 2010 papers that are not relevant for 2012.

    Bear in mind that some stuff was removed from the course after the pilot schools did their Phase 1 exam, and some other stuff was deferred until the Junior Cert Phase 1 students come through.

    The Tukey quick test was on the first version of the syllabus, but was taken off and the margin-of-error hypothesis test put on instead.

    I think the students should know the expected value for a binomial distribution, (e.g., "If you rolled a fair die 600 times, how often would you expect to get a six?"). Regarding the question about the 100 trials, The syllabus does explicitly state that the normal approximation to the binomial distribution is NOT required.


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    #3
    sullanefc
    Closed Accounts Posts: 57 ✭✭sullanefc


    That's fantastic news mathsmaniac. I hadn't read that document before now. I think I had a mini heart attack when I saw some of the questions on some of the papers. I know it says hypothesis testing by margin of error on the syllabus but i thought I was missing something.

    It really is confusing having so many different versions of exam papers.


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    #4
    Mwalimu
    Registered Users Posts: 42 ✭Mwalimu


    I read on the projectmaths.ie website that the 'choice' in Q.9 was there only for the 2010 exam, since the pilot schools could not get the whole course covered, and Mathsmaniac is spot on as regards the simplified hypothesis test that replaced the Tukey test.

    The Report on the Trialling that the SEC published before the 2010 exam in the pilot schools is worth looking at. See http://www.examinations.ie/schools/Report_on_Trial_final.pdf


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    #5
    majo
    Registered Users Posts: 101 ✭✭majo


    Formulas for the mean of a sample and the standard deviation of a sample are definitely needed, as they came up on the 2012 LCHL sample paper (Q7b). God only knows what else they'll throw at the candidates in June!!! Only thing's all our pupils will be basically in the same boat!


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    #6
    Mwalimu
    Registered Users Posts: 42 ✭Mwalimu


    majo wrote: »
    Formulas for the mean of a sample and the standard deviation of a sample are definitely needed, as they came up on the 2012 LCHL sample paper (Q7b). God only knows what else they'll throw at the candidates in June!!! Only thing's all our pupils will be basically in the same boat!

    I think you'll find that the question is about sample statistics and sampling distributions, topics which are on the course. Just because a question isn't a match to one that was asked before (i.e. it is not predictable) doesn't mean that it isn't do-able. The whole idea is to move away from depending on 'prepared' questions and get students to actually learn some mathematics and then be able to use the knowledge/skills to answer different questions. Some questions just require them to think!


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    #7
    TheDriver
    Registered Users Posts: 12,418 ✭✭✭✭TheDriver


    i remember there was a clarification issued by SEC to queries by the IMTA regarding the 2012 sample paper.
    P.S. i love asking about teaching the tukey test in a maths job interview because TBH most teacher seem to think its on the syllabus because they read the sample and exam papers without looking at the syllabus and realising that pilot schools are not the rest of the schools


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