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!! HL Maths 2015 - predictions, guesses, Q & A, discussion ...

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  • Registered Users Posts: 942 ✭✭✭Kremin


    Troxck wrote: »
    I feel Paper One is just easier to study for. I'm not great with Proof by Induction or Sequences but I can at least get high attempt marks in them.

    I'm going to go through my Papers tomorrow and might PM you with questions I'm not sure about, if that's okay? When in doubt I usually just get the centre, radius, slope etc and see where I can go from there! I'm surprisingly good with Stats on Paper Two idk why.

    The question you think will come up are the ones I struggle with, how would you approach it? Sorry for all the questions but Maths is such an important subject!

    I love statistics but if it's a long question, gotta watch that time.. on the mocks I must have spent 20 mins drawing a bar chart... but that was okay because I couldn't do any other part of the paper! And yeah it's okay if you pm me, I'll try help if I can.


  • Closed Accounts Posts: 1,386 ✭✭✭Troxck


    Kremin wrote: »
    I love statistics but if it's a long question, gotta watch that time.. on the mocks I must have spent 20 mins drawing a bar chart... but that was okay because I couldn't do any other part of the paper! And yeah it's okay if you pm me, I'll try help if I can.

    Everyone in my year was the exact same. At the time of the mocks we have very little done on Paper II and I still got a C in it, Paper I destroyed me.

    Thanks!


  • Registered Users Posts: 9 Katezz


    Just wondering in hypothesis testing, how do you know which statement is the null hypothesis? Is it for or against the claim?


  • Registered Users Posts: 284 ✭✭skippy1977


    Best explained with a few examples. We assume that the initial claim (generally) is true and then try and find sufficient evidence to prove against it.

    The mean lifetime of light bulbs produced by a company has, in the past, been 1500 hours. A sample of 100 bulbs, recently produced by the company, had a mean lifetime of 1475 hours with a standard deviation of 110 hours. Test the hypothesis that the mean lifetime of the bulbs has not changed, using a 0.05 level of significance.

    H_0: μ=1500, the mean lifetime of light bulbs produced by the company is still 1500 hours.
    H_1: μ≠1500, the mean lifetime of light bulbs produced by the company is not 1500 hours.

    A new diet is advertised with the claim that participants will lose an average of 4 kg during the first week on this diet. A random sample of 40 people on this diet showed a mean weight loss of 3.8 kg, with a standard deviation of 1 kg.

    Carry out a hypothesis test. State clearly your null and alternative hypothesis and your conclusion.
    H_0: μ=4, the average weight loss during the first week of this diet is 4kg.
    H_1: μ≠4, the average weight loss during the first week of this diet is not 4kg.

    Note, that the null hypothesis, may not necessarily be in the opening of the question.

    A study addressed the issue of whether pregnant women can correctly guess the sex of their baby. Among 104 recruited subjects, 57 correctly guessed the sex of the baby. Use these sample data to test the claim that the success rate of such guesses is no different from the 50% success rate expected with random chance guesses. Use a 5% significance level.

    H_0: μ=0.5 The chance of pregnant women guessing the sex of the baby is 50% (the same as a guess)
    H_1: μ≠0.5 The chance of pregnant women guessing the sex of the baby is not 50%

    Note, the alternate hypothesis is NOT that the chance of guessing correctly is 55% (57/104)

    The burden is on the experimental evidence (the sample conducted) to contradict the assumption.


  • Registered Users Posts: 126 ✭✭BlueWolf16


    Can you guys help me out on the calculator 'mode' thing? There's a D one, and an R one, I always get mixed up which one should be used for each question.


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  • Registered Users Posts: 1,336 ✭✭✭Blue giant


    BlueWolf16 wrote: »
    Can you guys help me out on the calculator 'mode' thing? There's a D one, and an R one, I always get mixed up which one should be used for each question.

    D is for degrees and R is for radians. Put your calculator in whichever mode the angle is measured in. For example if your dealing with a 30 degree angle you would put your calculator in degrees.


  • Registered Users Posts: 251 ✭✭OMGeary


    In General:If it's got anything to do with circles use radians.


  • Registered Users Posts: 297 ✭✭oktplz


    Anyone know where I could get my hands on the 2015 DEB mock paper? I heard it was extremely challanging and wouldn't mind having a go at it!


  • Registered Users Posts: 130 ✭✭Fiona G


    If we were asked to prove De Moivre's theorem, I'm assuming it'd be on paper 1? But can you be asked for formal proofs on paper 1? Maybe there's no set rules about it.


  • Registered Users Posts: 942 ✭✭✭Kremin


    Fiona G wrote: »
    If we were asked to prove De Moivre's theorem, I'm assuming it'd be on paper 1? But can you be asked for formal proofs on paper 1? Maybe there's no set rules about it.

    It's not a formal proof as such, they'll ask you to prove it by induction... so i.e TEST FOR N=1, assume true for n=k, test for n=k+1


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  • Registered Users Posts: 45 Bah_Humbug


    oktplz wrote: »
    Anyone know where I could get my hands on the 2015 DEB mock paper? I heard it was extremely challanging and wouldn't mind having a go at it!

    I can email it to you if you want. It is challenging, I did it today D:


  • Registered Users Posts: 297 ✭✭oktplz


    Bah_Humbug wrote: »
    I can email it to you if you want. It is challenging, I did it today D:

    That would be brilliant, thank you so much :D ugh should be fun.

    Also, does anyone know if implicit differentiation is definitely off the course?


  • Registered Users Posts: 23 DaveMc90


    Really struggling to know which deifinitions to learn in maths such as stats one's , anyone have any site links to where I can find the list of definitions on our course or any help at all!


  • Registered Users Posts: 271 ✭✭Peg14


    is there really any point learning definitions? apart from stats/basic probability. Well unless you're aiming for a real high grade, i'm looking for a C/B so don't know if I'll bother.


  • Registered Users Posts: 23 DaveMc90


    Peg14 wrote: »
    is there really any point learning definitions? apart from stats/basic probability. Well unless you're aiming for a real high grade, i'm looking for a C/B so don't know if I'll bother.

    I'm aiming for as close to an A as I can so those small definitions can add up and can make a huge difference because they're such easy marks


  • Closed Accounts Posts: 1,386 ✭✭✭Troxck


    Does anyone else find the sample papers much more difficult than the actual SEC papers for the real exam? I have the educate.ie papers and I find them more difficult. Should I expect our exam to be closer to the SEC papers than the sample ones?


  • Registered Users Posts: 12 Gem957


    Troxck wrote: »
    Does anyone else find the sample papers much more difficult than the actual SEC papers for the real exam? I have the educate.ie papers and I find them more difficult. Should I expect our exam to be closer to the SEC papers than the sample ones?

    I'm the same, I find sec much easier. As regards to our exam you've to remember the department made the sec papers while the samples are only samples that they came up with themselves, while they are good for practice, I think the real exam will be more like the sec papers with of course the odd hard q thrown in :)


  • Registered Users Posts: 284 ✭✭skippy1977


    Last year approximately 10% of the paper was for the:
    Proof By Induction of Sum of a Series (not really a learned proof, but headings n=1, n=k etc can be)
    Differentiation from 1st Principles
    Cos2A
    Theorem 13 (similar triangles)
    Construction 18 - Angle of 60 degrees

    All stuff that could be learned off by heart. It's a big chunk of the paper. There were no definitions mind.

    The year before however they asked definitions of:
    Sample Space, Mutually Exclusive, Independent Events, Circumcentre, Incircle, Centroid, Stratified Random Sample...along with the proof of Sine Rule and Construction of Orthocentre....that would be a lot of marks to leave out.

    Absolutely no pattern to what is being asked at the minute so unfortunately it's a big risk to leave out anything. For each person the question I suppose is do I learn definitions for next few days or practice questions?

    For Paper 1 I would learn:
    Definition of an irrational number (also be well aware of the other types of numbers N,Z etc...)
    A proof by contradiction (most people do the proof that root 2 is irrational) (asked 2011)
    Know the constructions of root 2 and root 3 (asked 2011)
    Sum of a Geometric Series by Induction (2012)
    Proof of De Moivre's Theorem by Induction
    De Moivre's Theorem to prove special Trigonometric Identity
    Definitions of Injective, Bijective and Surjective Functions
    Learn off by heart the headings for differentiation by 1st Principles (though the actual question given will be unique) (asked 2014)
    Derive Amortisation formula

    Unfortunately there is no list of definitions. The above is not exhaustive and you can get asked questions like 'What is meant by the indefinite integral', which I guess is a definition also?
    Also, they can ask Paper 2 definitions on Paper 1. In 2012 Paper 1 you had to give definitions of discrete and continuous models (which some people might leave til Saturday to learn!)

    At the end of the day you can only do so much so my advice is just to keep working hard, balance all your subjects and learn what you can in the time left!


  • Registered Users Posts: 297 ✭✭oktplz


    Just to reasure myself here, the DEB mock paper was deeped as impossible yes? :P


  • Registered Users Posts: 1,336 ✭✭✭Blue giant


    skippy1977 wrote: »
    Last year approximately 10% of the paper was for the:
    Proof By Induction of Sum of a Series (not really a learned proof, but headings n=1, n=k etc can be)
    Differentiation from 1st Principles
    Cos2A
    Theorem 13 (similar triangles)
    Construction 18 - Angle of 60 degrees

    All stuff that could be learned off by heart. It's a big chunk of the paper. There were no definitions mind.

    The year before however they asked definitions of:
    Sample Space, Mutually Exclusive, Independent Events, Circumcentre, Incircle, Centroid, Stratified Random Sample...along with the proof of Sine Rule and Construction of Orthocentre....that would be a lot of marks to leave out.

    Absolutely no pattern to what is being asked at the minute so unfortunately it's a big risk to leave out anything. For each person the question I suppose is do I learn definitions for next few days or practice questions?

    For Paper 1 I would learn:
    Definition of an irrational number (also be well aware of the other types of numbers N,Z etc...)
    A proof by contradiction (most people do the proof that root 2 is irrational) (asked 2011)
    Know the constructions of root 2 and root 3 (asked 2011)
    Sum of a Geometric Series by Induction (2012)
    Proof of De Moivre's Theorem by Induction
    De Moivre's Theorem to prove special Trigonometric Identity
    Definitions of Injective, Bijective and Surjective Functions
    Learn off by heart the headings for differentiation by 1st Principles (though the actual question given will be unique) (asked 2014)
    Derive Amortisation formula

    Unfortunately there is no list of definitions. The above is not exhaustive and you can get asked questions like 'What is meant by the indefinite integral', which I guess is a definition also?
    Also, they can ask Paper 2 definitions on Paper 1. In 2012 Paper 1 you had to give definitions of discrete and continuous models (which some people might leave til Saturday to learn!)

    At the end of the day you can only do so much so my advice is just to keep working hard, balance all your subjects and learn what you can in the time left!

    Do people actually learn off the trig proofs and proofs by induction? They're really not that hard to derive yourself.


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  • Registered Users Posts: 284 ✭✭skippy1977


    There's 8 and I would agree with you on 4 or 5 of them.
    The cosine proof and cos (A-B) proof require fairly detailed sketches however and would be difficult to think of on the day. As would the proof of the sine rule which expects you to prove for acute and obtuse angles.
    For example here is the Cosine Rule...now if you learn the sketches the proof follows but you'd need at least to know the sketch to get started.
    cosine-rule.jpg


  • Registered Users Posts: 1,336 ✭✭✭Blue giant


    Our class have always just made them up on the day. All you have to do is use the rules in the tables book to solve them. The sine and cosine ones are a bit more tricky alright. I was more on about the Cos2A etc. ones.


  • Registered Users Posts: 284 ✭✭skippy1977


    It would take a fairly outstanding student to make up the one above up on the day having not seen it but there are people who can. I would suggest that the majority of students look over them at least once though.
    Have a go at cos(A-B) using the tables, not as easy as it looks. There is a specific order to the formula and you are only allowed use formulas preceding it in your proof. So the proof of cos(A-B) can only use 3 of the other formula in its proof (cos rule, sine rule and cos squared +sin squared =1)


  • Registered Users Posts: 1,034 ✭✭✭dalta5billion


    oktplz wrote: »
    Just to reasure myself here, the DEB mock paper was deeped as impossible yes? :P

    Yes, but more in terms of its length and consistent difficulty. There are good reference questions on it, but some which are poorly worded.


  • Closed Accounts Posts: 1,386 ✭✭✭Troxck


    oktplz wrote: »
    Just to reasure myself here, the DEB mock paper was deeped as impossible yes? :P

    The individual questions weren't impossible, but the entire thing together and with time restraints it was. At the time of the mocks, people wouldn't have had the course covered and most wouldn't have a lot of study done either.


  • Registered Users Posts: 320 ✭✭lostatsea


    Troxck wrote: »
    Does anyone else find the sample papers much more difficult than the actual SEC papers for the real exam? I have the educate.ie papers and I find them more difficult. Should I expect our exam to be closer to the SEC papers than the sample ones?

    I did the Educate.ie papers a couple of years ago. Initially I found them hard but our teacher brought us through them and they then seemed easy. It gave us great confidence going into the exam as our class was tested on every aspect of the course so we were really stretched.

    My cousin had the Edco papers and he kept telling me how easy Project Maths was. He didn't seem to be covering all kinds of exponential functions to the same level as me.

    I'd much prefer to over prepare. Now that the Project Maths roll out is complete, the SEC are going to ask some pretty challenging questions. That is why the course was developed in the first place. Third level colleges won't accept a serious dumbing down of Maths.

    The ordinary level paper is still an entry requirement for many courses that need maths and yet many teachers are not bothering to cover the course properly.
    Peg14 wrote: »
    is there really any point learning definitions? apart from stats/basic probability. Well unless you're aiming for a real high grade, i'm looking for a C/B so don't know if I'll bother.

    Forget about definitions. Project maths wasn't set up to be a rote learning exercise.


  • Closed Accounts Posts: 1,386 ✭✭✭Troxck


    lostatsea wrote: »
    I did the Educate.ie papers a couple of years ago. Initially I found them hard but our teacher brought us through them and they then seemed easy. It gave us great confidence going into the exam as our class was tested on every aspect of the course so we were really stretched.

    My cousin had the Edco papers and he kept telling me how easy Project Maths was. He didn't seem to be covering all kinds of exponential functions to the same level as me.

    I'd much prefer to over prepare. Now that the Project Maths roll out is complete, the SEC are going to ask some pretty challenging questions. That is why the course was developed in the first place. Third level colleges won't accept a serious dumbing down of Maths.

    The ordinary level paper is still an entry requirement for many courses that need maths and yet many teachers are not bothering to cover the course properly.

    I have all exam questions attempted from both the SEC and educate. I just found the educate papers more challenging than the SEC. I did the Educate papers first and felt more prepared to attempt the SEC papers afterwards.

    Hopefully the paper isn't too challenging...


  • Registered Users Posts: 320 ✭✭lostatsea


    Yes, but more in terms of its length and consistent difficulty. There are good reference questions on it, but some which are poorly worded.

    Some of those mock papers were poorly written with material not on the course. Don't waste time doing bad questions. There are plenty of good SEC and sample papers to work on.
    Troxck wrote: »
    I have all exam questions attempted from both the SEC and educate. I just found the educate papers more challenging than the SEC. I did the Educate papers first and felt more prepared to attempt the SEC papers afterwards.

    Hopefully the paper isn't too challenging...

    It sound like you are totally prepared. You prepared by practising good questions over a long period of time. There is nothing more you can do. Cramming for the Project Maths exam is not required. It is a bit like Applied Maths in that sense.


  • Registered Users Posts: 1,307 ✭✭✭DarraghF197


    I feel like I've become extremely complacent with maths for practically the whole of leaving cert. To hear people are done with their educate exam papers is a little bit worrying! I just did the first sample paper from Educate today and yesterday, have six more to go through I think! Although I probably have a bit done already from class and stuff.

    I spend more time on Applied Maths than maths even, I just find Maths to be so boring and quite frustrating at times!


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  • Closed Accounts Posts: 1,386 ✭✭✭Troxck


    I feel like I've become extremely complacent with maths for practically the whole of leaving cert. To hear people are done with their educate exam papers is a little bit worrying! I just did the first sample paper from Educate today and yesterday, have six more to go through I think! Although I probably have a bit done already from class and stuff.

    I spend more time on Applied Maths than maths even, I just find Maths to be so boring and quite frustrating at times!

    The HL teachers would do a full paper I after school on a Monday and a paper II on the Wednesday. They'd give us the weekend to do it and if you have specific problems they'd go through it. It wasn't mandatory to do it and they didn't care but it made me work and got them done. There's obviously questions I still find tricky but I can now at least attempt them and know the steps to start them. I'm still at a loss with most The Circle/Line because I'm not always sure what they're asking.


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