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Is it worth learning proofs of specific concepts in A-level maths? Watch

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    (Original post by Mr M)
    It simply isn't true that one Awarding Body has more difficult A Levels than another. It is Ofqual's job to make sure the standards are exactly the same. If they weren't the same, all schools and colleges would immediately switch to the easier exam in order to maximise their position in League Tables.
    (genuine question) What effects does their position in league tables have on the school? Is it just a case of looking good and attracting a lot of students or are there other incentives (better schools recieve more more funding or something similar)? Thanks for your time
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    (Original post by UKBrah)
    I tried a go at it but it just doesnt make sence even with livemaths.
    I've learnt the logic which is simple as it gets but proving if something is divisible by 9 leaves me clueless.

    Regardless what did you get in C1?
    Ah yes it literally is luck in my opinion, sometimes I clock on to what they want, sometimes I don't... :confused:

    C1 I did weirdly bad on, it was most definitely an off day for me, I got 79 when I should've been getting almost full marks..
    Made up for it is C2 and S1, let's see how C3 goes this Jan..
    Yourself?
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    (Original post by LogicGoat)
    (genuine question) What effects does their position in league tables have on the school? Is it just a case of looking good and attracting a lot of students or are there other incentives (better schools recieve more more funding or something similar)? Thanks for your time
    1. Good league table position. School is popular and oversubscribed and is able to attract good teachers and secure an Outstanding Ofsted report.

    2. Bad league table position. School haemorrhages students. Option choices narrow. Many teachers leave. School is put in Special Measures by Ofsted. School is forced to accept a take over by an Academy chain. Headteacher and other members of the extended Leadership Team resign.
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    (Original post by Mr M)
    1. Good league table position. School is popular and oversubscribed and is able to attract good teachers and secure an Outstanding Ofsted report.

    2. Bad league table position. School haemorrhages students. Option choices narrow. Many teachers leave. School is put in Special Measures by Ofsted. School is forced to accept a take over by an Academy chain. Headteacher and other members of the extended Leadership Team resign.
    Thanks for the info
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    (Original post by MissBetBet)
    Ah yes it literally is luck in my opinion, sometimes I clock on to what they want, sometimes I don't... :confused:

    C1 I did weirdly bad on, it was most definitely an off day for me, I got 79 when I should've been getting almost full marks..
    Made up for it is C2 and S1, let's see how C3 goes this Jan..
    Yourself?
    Do you know if you need 72/72 to get 100 UMS or can I get lower and still leave with 100?
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    (Original post by UKBrah)
    How far out would you have to expand before being able to apply the limit?
    not far, you should try it yourself and you will see cos it cancels out with the delta x or h as it approaches zero

    I can show you dinner or unless someone does before then
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    (Original post by UKBrah)
    Ye, where can I find such proofs? Is there a book dedicated to proofs? I want to be a better mathematician!


    Yeah the power rule proof is sick, but how does one expand a binomial to the power of n?!?
    I can give you another vote for Bostock and Chandler - it explains a lot of the things you'll find glossed over in modern A level texts.
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    (Original post by davros)
    I can give you another vote for Bostock and Chandler - it explains a lot of the things you'll find glossed over in modern A level texts.
    http://www.amazon.com/Core-Maths-Adv...k+and+chandler - are you refering to this book?
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    (Original post by UKBrah)
    http://www.amazon.com/Core-Maths-Adv...k+and+chandler - are you refering to this book?
    Not sure to be honest

    Mine has a bright red cover and is called Mathematics - The Core Course for A Level - it's a 2002 reprint of a 1981 book. The link you've given may be a reprint of the one I have but I'm not sure - perhaps someone else can advise...
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    (Original post by Mr M)
    It would be lovely to think that might happen (and I suppose it might in some independent schools) but state education is now a marketplace and League Table positions are everything.
    There's a school (can't remember the name :mad) who seem to have chosen the "hardest" exam boards, they do MEI for maths and OCR Salters for chemistry etc. They're independent/grammar can't remember...

    Also, while some people say boards are not easier than others... Some papers are a lot easier to tackle across boards, although the grade boundaries may account for this...

    Like OCR MEI M1 is a lot harder than my WJEC for example... I thought anyway.
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    (Original post by L'Evil Fish)
    Like OCR MEI M1 is a lot harder than my WJEC for example... I thought anyway.
    It is only your perception - promise!
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    (Original post by Mr M)
    It is only your perception - promise!
    Hmmm... I say I do a test, one paper from all exam boards, all from the same season :lol: see how much they differ... But content is different for mechanics... I don't even know how to differentiate and Integrate vectors.
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    MEI is different in various ways... perhaps the most obvious is the C4 comprehension paper... this can really make or break your grade and it varies so much in difficulty.
    also there is still coursework in C3 ( they dropped D1 and M1 coursework some time ago )
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    (Original post by The Polymath)
    It's definitely worth looking at them and understanding them, and most of them are in the book (it just says "you will not need to know this"). As for 'learning' them off by heart, there's no need, and not even the finest mathematicians will bother, as there are proofs for everything in maths, so you'd never be able to learn them all. As long as you've seen it and are convinced that 'the proof is nice, it can be proven' then your mind will accept it.

    e.g. I remember looking at the power rule for differentiation in the C1 book, accepting it as a nice proof, but I can't remember the proof itself.
    W
    hich book were you talking about?
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    (Original post by cheeriosarenice)
    W
    hich book were you talking about?
    The standard Heinemann textbooks for Edexcel by Keith Pledger.
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    (Original post by The Polymath)
    The standard Heinemann textbooks for Edexcel by Keith Pledger.
    Ah, he's a lad
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    (Original post by The Polymath)
    The standard Heinemann textbooks for Edexcel by Keith Pledger.
    What are you talking about? There is no proof for the power rule in that book for the general case of x^n. All it shows you is how to derive x^2, x^3, and x^-1 from first principles, demonstrates a pattern between them, and asserts that the pattern is true for all n. But the actual proof for the general case of x^n requires the binomial expansion which you don't learn until C2.
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    (Original post by Quivai)
    What are you talking about? There is no proof for the power rule in that book for the general case of x^n. All it shows you is how to derive x^2, x^3, and x^-1 from first principles, demonstrates a pattern between them, and asserts that the pattern is true for all n. But the actual proof for the general case of x^n requires the binomial expansion which you don't learn until C2.
    Sorry, it had been two years since I'd done C1 when I posted that, so I probably got things mixed up.

    In any case the point I was making still stands
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    As someone who has been self-teaching A Level maths for the sake of learning, I really hate the Edexcel specification for calculus. It skips over so many proofs and concepts that a deep understanding is all but impossible unless you go out of your way to learn from other sources. In addition, the order that material is presented makes things needlessly more difficult.

    As an example, you are introduced to the number e early on in C3 by being shown the derivatives of 2^x, 3^x, etc. and being told that because of a noticeable pattern, there must be such a number as e. The problem with this approach is that at this stage, you don't even know how to even derive 2^x or 3^x. Moreover, deriving them requires you to use logs in base e, making the entire proof circular.

    Another example is the fundamental theorem of calculus. The Edexcel textbooks simply skip over it, giving only an extremely brief explanation on how to find definite integrals. So you're left wondering just why taking the definite integral of a function will magically find the area under a curve.

    To compound matters, the Americans teach calculus in a completely different order, and teach concepts we don't need to know for A Levels, such as discontinuous functions and taking limits from both sides. So when you try turning to internet resources focused on the American curriculum, you'll occasionally find you're expected to have knowledge of things you either haven't learnt yet, or won't learn for A Levels.

    All in all, calculus as taught by Edexcel is extremely frustrating if you like understanding things.
 
 
 
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