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Mega A Level Maths Thread - Mark V Watch

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    (Original post by DylanJ42)
    Yea i suppose so, it just feels a little silly reading that 40% of people get A* :dontknow: maybe its just me
    If it helps: 40% of Trinity, Cambridge students get firsts, so. :dontknow:
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    (Original post by Zacken)
    If it helps: 40% of Trinity, Cambridge students get firsts, so. :dontknow:
    Apparently 60% of Imperial aero students graduate with firsts :erm:
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    (Original post by Student403)
    Apparently 60% of Imperial aero students graduate with firsts :erm:
    I kinda want to make a pun about soaring but I'll restrain myself.
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    (Original post by Zacken)
    I kinda want to make a pun about soaring but I'll restrain myself.
    OMG that would have been perfect
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    (Original post by Zacken)
    If it helps: 40% of Trinity, Cambridge students get firsts, so. :dontknow:
    I'm not used to the high percentages I guess. I usually think ~10% should get top grade, maybe i need to change my thinking
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    (Original post by DylanJ42)
    I'm not used to the high percentages I guess. I usually think ~10% should get top grade, maybe i need to change my thinking
    They can change as soon as we finish FM.
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    (Original post by DylanJ42)
    I mean that they should make further maths harder, so only the top 15-20% of candidates will get A*s. Otherwise the A* FM loses value ygm?
    To be fair, the data is sort of positively skewed. Boards have been making exams more difficult and have also increased grade boundaries. Candidates are just taught to have (note that 30% of school candidates get A*s) impeccable exam technique nowadays. Also, Further Maths can include "easier" units such as M2, S2 and D2 for the A* so you don't necessarily have to be great in the "real" maths units to get an A*.
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    (Original post by aymanzayedmannan)
    To be fair, the data is sort of positively skewed. Boards have been making exams more difficult and also increased grade boundaries. Candidates are just taught to have (note that 30% of school candidates get A*s) impeccable exam technique nowadays. Also, Further Maths can include "easier" units such as M2, S2 and D2 for the A* so you don't necessarily have to be great in the "real" maths units to get an A*.
    This is true. In fact due to the distribution of modules with FM students, it can be easier to get an A at AS level in Maths if you just take maths than if you take FM
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    (Original post by Zacken)
    No problemo! I love answering those types of questions, reinforces my own understanding.

    Edit: if somebody wants, I've got a great way of making integration subs more intuitive and understandable!
    So what then of other substiutions? Sorry I'm being thick.

    The substiution u=x^2 to solve \displaystyle \int xe^{x^2}dx for instance. That doesn't seem to me to be an injective substitution
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    (Original post by Zacken)
    They can change as soon as we finish FM.
    Definitely If in mid august I don't get A* I wont show my face here again :laugh:
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    (Original post by Kvothe the arcane)
    So what then of other substiutions? Sorry I'm being think.

    The substiution u=x^2 to solve \displaystyle xe^{x^2}dx for instance. That doesn't seem to me to be an injective substitution
    No, it's not injective over the reals, but your 'actual substitution' is: Let u = x^2 for x \geq 0, aaaaand, it's injective.
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    (Original post by aymanzayedmannan)
    To be fair, the data is sort of positively skewed. Boards have been making exams more difficult and have also increased grade boundaries. Candidates are just taught to have (note that 30% of school candidates get A*s) impeccable exam technique nowadays. Also, Further Maths can include "easier" units such as M2, S2 and D2 for the A* so you don't necessarily have to be great in the "real" maths units to get an A*.
    Yea that does make a lot of sense, there's only so much the examiners can do to increase difficulty

    i love the concept of the Pure Maths A-level however it means you cant do maths and further maths which sucks
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    (Original post by DylanJ42)
    Yea that does make a lot of sense, there's only so much the examiners can do to increase difficulty

    i love the concept of the Pure Maths A-level however it means you cant do maths and further maths which sucks
    I agree - it's a great idea for pure mathematicians
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    what is all this pure stuff, injective ? ...
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    (Original post by Zacken)
    No, it's not injective over the reals, but your 'actual substitution' is: Let u = x^2 for x \geq 0, aaaaand, it's injective.
    So it never really matters then. Even if you had an integral which went from +ve to -ve because you'd just piece-wise it?
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    (Original post by Kvothe the arcane)
    So it never really matters then. Even if you had an integral which went from +ve to -ve because you'd just piece-wise it?
    Preeeeecisely. I'll relax my condition: you can make a substitution as long as it's piecewise-injective.
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    (Original post by TeeEm)
    what is all this pure stuff, injective ? ...
    Shhhhh it's my version of fun
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    (Original post by Zacken)
    Shhhhh it's my version of fun
    http://www.thestudentroom.co.uk/show....php?t=3888889
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    Since I've completed TeeEm's question posted, above, here's a nice extension question for anybody who does FP1 induction:

    (Original post by Zacken)
    Here's a nice induction question, if you lot want to have a go at it.

    Show that \displaystyle \sin 2nx = \sin (2n+1)x \cos x - \cos (2n+1)x\sin x.

    Hence, by induction, prove that:

    \displaystyle

\begin{equation*} \cos x + \cos 3x + \cos 5x + \cdots + \cos (2n-1)x = \frac{\sin 2nx}{2\sin x}

    where \sin x \neq 0\end{equation*} and n \in \mathbb{N}

    Solve \displaystyle \cos x + \cos 3x = \frac{1}{2}, 0 < x < \pi
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    (Original post by Zacken)
    Since I've completed TeeEm's question posted, above, here's a nice extension question for anybody who does FP1 induction:
    Euclidean
 
 
 
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