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Advanced Higher Maths 2012-2013 : Discussion and Help Thread

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    Hi! Just wondering if anyone could please explain to me how you find the derivative of 2/x from first principles? I get the basic idea etc, just not sure if you'd make it 2x^-1 or what first? Thanks
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    (Original post by hollieeilloh)
    Hi! Just wondering if anyone could please explain to me how you find the derivative of 2/x from first principles? I get the basic idea etc, just not sure if you'd make it 2x^-1 or what first? Thanks
    You should do it without putting into 2x^-1 (as (x+h)^-1 would be hard to manipulate).

    Let f\left(x\right) = \dfrac{2}{x}

    Then for suitable x:

    f'\left(x\right) = \displaystyle\lim_{h \to 0} \dfrac{f\left(x+h\right) - f\left(x\right)}{h} = \displaystyle\lim_{h \to 0}\dfrac{\dfrac{2}{x+h} - \dfrac{2}{x}}{h} =  \displaystyle\lim_{h \to 0}\dfrac{2x - 2\left(x+h\right)}{xh \left( x+h \right)}

    =  \displaystyle\lim_{h \to 0}\dfrac{-2h}{xh \left( x+h \right)} = \displaystyle\lim_{h \to 0}\dfrac{-2}{x \left( x+h \right)}=\dfrac{-2}{x^2}
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    (Original post by ukdragon37)
    You should do it without putting into 2x^-1 (as (x+h)^-1 would be hard to manipulate).

    Let f\left(x\right) = \dfrac{2}{x}

    Then for suitable x:

    f'\left(x\right) = \displaystyle\lim_{h \to 0} \dfrac{f\left(x+h\right) - f\left(x\right)}{h} = \displaystyle\lim_{h \to 0}\dfrac{\dfrac{2}{x+h} - \dfrac{2}{x}}{h} =  \displaystyle\lim_{h \to 0}\dfrac{2x - 2\left(x+h\right)}{xh \left( x+h \right)}

    =  \displaystyle\lim_{h \to 0}\dfrac{-2h}{xh \left( x+h \right)} = \displaystyle\lim_{h \to 0}\dfrac{-2}{x \left( x+h \right)}=\dfrac{-2}{x^2}
    Ah okay, that makes more sense, thanks again!
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    Y'know, I never did differentiation from first principles last year until Unbeliever said it was examinable...
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    (Original post by Hype en Ecosse)
    Y'know, I never did differentiation from first principles last year until Unbeliever said it was examinable...
    Haha! I'm guessing it's one of the easier types of differentiation, yeah? My teacher said it rarely comes up, but still could, and it seems pretty okay so I'll be praying for it aha..
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    (Original post by Hype en Ecosse)
    Y'know, I never did differentiation from first principles last year until Unbeliever said it was examinable...
    Is it really examinable? I never saw it any past papers when I studied AH for this year's paper, and my teacher said not to revise it... haha
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    (Original post by golfpro14)
    Is it really examinable? I never saw it any past papers when I studied AH for this year's paper, and my teacher said not to revise it... haha
    If it's on the course specifications, the SQA are within their liberty to put it in the exam. But I haven't seen it come up either.
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    (Original post by Hype en Ecosse)
    If it's on the course specifications, the SQA are within their liberty to put it in the exam. But I haven't seen it come up either.
    (Original post by golfpro14)
    Is it really examinable? I never saw it any past papers when I studied AH for this year's paper, and my teacher said not to revise it... haha
    It has only come up on commercial prelim papers, P&N and the like.

    This was posted from The Student Room's Android App on my Galaxy Nexus
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    Hey there, rather than start on another thread for this, I decided this was most relevant here:

    I've got a friend off to do psychology, she never did Maths and wants to brush up on statistics before she gets there as it'll be a good part of the course. Anyone have any resources I can pass along to her? From the very basics right up.

    Statistics for medics would be cool, too. Though I'll probably look out a textbook on it when I get to university.


    As for the new AHers who're in summer right now...enjoy it while it lasts and don't forget we're here. Will be here to help all year round.
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    (Original post by Hype en Ecosse)
    Hey there, rather than start on another thread for this, I decided this was most relevant here:

    I've got a friend off to do psychology, she never did Maths and wants to brush up on statistics before she gets there as it'll be a good part of the course. Anyone have any resources I can pass along to her? From the very basics right up.

    Statistics for medics would be cool, too. Though I'll probably look out a textbook on it when I get to university.


    As for the new AHers who're in summer right now...enjoy it while it lasts and don't forget we're here. Will be here to help all year round.
    It depends on what part of statistics would be useful for her course (or you). I only know the resources for AH Applied Maths Statistics (and even then it's mostly just textbooks). Dunno if that'd be useful.
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    (Original post by Hype en Ecosse)
    I've got a friend off to do psychology, she never did Maths and wants to brush up on statistics before she gets there as it'll be a good part of the course. Anyone have any resources I can pass along to her? From the very basics right up.
    I could've sworn I had various beginners' resources I used saved on Delicious, but apparently not. I've not used this course, so I can't vouch for it's quality. Obviously Princeton has an excellent reputation, but that isn't always reflected in lecture quality. Having said that, the syllabus looks like a suitably-gentle introduction that covers most of what she's likely to encounter in some form or another. University lecture notes may also be useful, although she'd do well to look at courses from applied departments rather than as part of maths courses. Less useful now but handy later are the many, many varieties of flowcharts to help select an appropriate test. The Maths in Action textbooks for AH Statistics are not utterly useless, either.
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    (Original post by ukdragon37)
    It depends on what part of statistics would be useful for her course (or you). I only know the resources for AH Applied Maths Statistics (and even then it's mostly just textbooks). Dunno if that'd be useful.

    (Original post by TheUnbeliever)
    I could've sworn I had various beginners' resources I used saved on Delicious, but apparently not. I've not used this course, so I can't vouch for it's quality. Obviously Princeton has an excellent reputation, but that isn't always reflected in lecture quality. Having said that, the syllabus looks like a suitably-gentle introduction that covers most of what she's likely to encounter in some form or another. University lecture notes may also be useful, although she'd do well to look at courses from applied departments rather than as part of maths courses. Less useful now but handy later are the many, many varieties of flowcharts to help select an appropriate test. The Maths in Action textbooks for AH Statistics are not utterly useless, either.
    Thanks you guys. If you notice anything you think would be useful for us, please do send it my way.
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    So how hard will/is Adv Higher Maths? Aiming for A/B - Is it a big step up from Higher, or is it manageable?
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    (Original post by IsaacJ)
    So how hard will/is Adv Higher Maths? Aiming for A/B - Is it a big step up from Higher, or is it manageable?
    Manageable. It requires a different kind of work from Higher. With Higher it was learning what was put in front of you and then repeating it, with AH it's understanding what's put in front of you.
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    (Original post by Hype en Ecosse)
    Manageable. It requires a different kind of work from Higher. With Higher it was learning what was put in front of you and then repeating it, with AH it's understanding what's put in front of you.
    :ditto:

    And I just never understood
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    (Original post by Ecosse_14)
    :ditto:

    And I just never understood
    That's alright. Judging by the annual results day errors, mathematical skill isn't a requirement for SQA employment. Ooooooh!

    I want this website to still be running in 30 years, and to come back to visit, and still see ukd helping out in the Maths threads. Like a monolith, he will stand the test of time.
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    (Original post by Hype en Ecosse)
    That's alright. Judging by the annual results day errors, mathematical skill isn't a requirement for SQA employment. Ooooooh!

    I want this website to still be running in 30 years, and to come back to visit, and still see ukd helping out in the Maths threads. Like a monolith, he will stand the test of time.
    Oooh, burn! I still passed :awesome:
    Probably will, he's a trooper :yep:
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    (Original post by Ecosse_14)
    Oooh, burn! I still passed :awesome:
    Probably will, he's a trooper :yep:
    SAM can pass this around the office.

    It makes me think, though, how the courses will've changed in 30 years time. Probably when my kids'll be doing it!

    Also makes me wonder what the most recent mathematical concept that's taught in school-level maths is.
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    (Original post by Hype en Ecosse)
    That's alright. Judging by the annual results day errors, mathematical skill isn't a requirement for SQA employment. Ooooooh!

    I want this website to still be running in 30 years, and to come back to visit, and still see ukd helping out in the Maths threads. Like a monolith, he will stand the test of time.

    (Original post by Ecosse_14)
    Oooh, burn! I still passed :awesome:
    Probably will, he's a trooper :yep:
    Congrats!

    Wouldn't that be a bit creepy? :eyeball:


    (Original post by Hype en Ecosse)
    SAM can pass this around the office.

    It makes me think, though, how the courses will've changed in 30 years time. Probably when my kids'll be doing it!

    Also makes me wonder what the most recent mathematical concept that's taught in school-level maths is.
    Everything in AH's absolutely ancient If you include courses that teach group theory (some A-level Further Maths Pure modules, IB modules) those concepts are more recent, around 19th century. Some concepts in set theory that are taught (again A-level, IB) are newer still, in the early 20th century. If you also include "discrete maths" (A-level D modules, IB HL module), some things they teach like quicksort and graph algorithms were actually invented only around 50 years ago.
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    (Original post by ukdragon37)
    Wouldn't that be a bit creepy? :eyeball:
    Not if you don't try to hook up with anyone in the thread...

    Everything in AH's absolutely ancient If you include courses that teach group theory (some A-level Further Maths Pure modules, IB modules) those concepts are more recent, around 19th century. Some concepts in set theory that are taught (again A-level, IB) are newer still, in the early 20th century. If you also include "discrete maths" (A-level D modules, IB HL module), some things they teach like quicksort and graph algorithms were actually invented only around 50 years ago.
    Why A-Levels gotta be so far ahead?

    I like to remind the maths classes whenever they're doing algebra that the principles they're using are thousands of years old. Gets a twinkle in their eye.

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Updated: December 13, 2013
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