Hey there! Sign in to join this conversationNew here? Join for free

Mega A Level Maths Thread - Mark V Watch

Announcements
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    I don't think the real issue is her grades - well, there isn't an issue, but if there would be one, it'd be about choosing maths over history or something else which could stand her in good stead for her aspirations.

    Physicsmaths got an A, but remember that he decided that he wanted to apply for maths at uni, so his AS level results stepped up! I don't think it's particularly fair to use him as a benchmark here.
    Haha, no I wasn't comparing. I just think it's awesome how he got an A at GCSE but A*A* and probably will get A* SS this year!
    Offline

    16
    ReputationRep:
    (Original post by ZiggyStarDust_)
    thanks c:

    well, I would do history. but because i'm "really smart", I didn't take History GCSE. so taking it as an A Level probably wouldn't be a good idea. ;P
    Oh I gotcha Well in that case those sound fine - but be prepared to up your game in maths because some people do find the jump a bit hard: But with an A/B I think you'll be absolutely fine
    Offline

    3
    ReputationRep:
    17% get A* in maths, that's extremely high actually :eek:

    Further maths is shockingly high tbh
    Offline

    3
    ReputationRep:
    Almost twice as many males sitting further maths than males. It's the opposite with Biology where I live
    • TSR Support Team
    • Very Important Poster
    • Reporter Team
    • Welcome Squad
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by DylanJ42)
    17% get A* in maths, that's extremely high actually :eek:

    Further maths is shockingly high tbh
    A better pool of candidates will probably take FM as schools are more choosy about who they let sit the subject.

    We had some test that you had to get 90%+ in to stay. It was pretty simple but felt awkward about the people who had to go.

    (Original post by aymanzayedmannan)
    Almost twice as many males sitting further maths than males. It's the opposite with Biology where I live
    There's even a disparity with normal maths which I find slightly surprising.
    Offline

    1
    ReputationRep:
    Cheers this is really helpful
    Offline

    3
    ReputationRep:
    (Original post by DylanJ42)
    17% get A* in maths, that's extremely high actually :eek:

    Further maths is shockingly high tbh
    Nah mate, I think that it's probably because the most confident candidates take FM. Everyone does straight maths, so the percentage is lower. Where I live, Maths is seen as a "compulsory" subject at A level.
    Offline

    21
    ReputationRep:
    (Original post by Kvothe the arcane)
    Zacken, I'll be wondering this soon

    But when you make a trig sub you often end up square rooting the square of the function. Now sinx is odd so I suppose it doesn't matter? But in the cause of cosx, why is it okay?

    Are there certain cases you should think about? No need to explain yourself but if you can point me in the direction of an appropriate webpage that would be helpful.Thanks.
    First off: I'm not sure why \sin being odd or not has anything to do with square rooting it safely? You could still have: \sqrt{\sin^2 x} = \pm \sin x \neq \sin x.

    Second off: You cannot make substitutions that are not one-to-one, if you do make a substitution of a function that isn't one-to-one (injective) over the reals, then you must restrict the domain of that function such that it is injective.

    It's traditional to write something of the form: Let 2x = \cosh u, and we're all cool with that. No harm done, but what we really mean is: Let 2x = \cosh u where u \geq 0 (or potentially: u \leq 0), the choice of domain for u makes \cosh injective and makes sure that \sqrt{\cosh^2 u} = \cosh u.

    I've used the above example to demonstrate the interesting (and good!) question you asked but also to demonstrate why we take principal arc-trigs when back-substituting. That is, why we're then allowed to say: u = \text{arcosh} 2x, we've restricted the domain to make the function injective and hence invertible.

    tl;dr, we make substitutions injective but don't bother writing it down.

    That's what I understand of it, at least. Hope that helped.
    • TSR Support Team
    • Very Important Poster
    • Reporter Team
    • Welcome Squad
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by alice.ronalene)
    Cheers this is really helpful
    No worries . What modules are you doing?
    Offline

    16
    ReputationRep:
    (Original post by Zacken)
    First off: I'm not sure why \sin being odd or not has anything to do with square rooting it safely? You could still have: \sqrt{\sin^2 x} = \pm \sin x \neq \sin x.

    Second off: You cannot make substitutions that are not one-to-one, if you do make a substitution of a function that isn't one-to-one (injective) over the reals, then you must restrict the domain of that function such that it is injective.

    It's traditional to write something of the form: Let 2x = \cosh u, and we're all cool with that. No harm done, but what we really mean is: Let 2x = \cosh u where u \geq 0 (or potentially: u \leq 0), the choice of domain for u makes \cosh injective and makes sure that \sqrt{\cosh^2 u} = \cosh u.

    I've used the above example to demonstrate the interesting (and good!) question you asked but also to demonstrate why we take principal arc-trigs when back-substituting. That is, why we're then allowed to say: u = \text{arcosh} 2x, we've restricted the domain to make the function injective and hence invertible.

    tl;dr, we make substitutions injective but don't bother writing it down.

    That's what I understand of it, at least. Hope that helped.
    Great answer to a great question :yep: Thanks for clearing it up
    Offline

    21
    ReputationRep:
    Sorry about the hyp-trig example (for anybody reading it who hasn't done FM), too much FP3, first thing that came to my mind.
    Offline

    1
    ReputationRep:
    (Original post by Kvothe the arcane)
    No worries . What modules are you doing?
    C1, c2, s1, fp1, d1,d2
    • TSR Support Team
    • Very Important Poster
    • Reporter Team
    • Welcome Squad
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by Zacken)
    First off: I'm not sure why \sin being odd or not has anything to do with square rooting it safely? You could still have: \sqrt{\sin^2 x} = \pm \sin x \neq \sin x.

    Second off: You cannot make substitutions that are not one-to-one, if you do make a substitution of a function that isn't one-to-one (injective) over the reals, then you must restrict the domain of that function such that it is injective.

    It's traditional to write something of the form: Let 2x = \cosh u, and we're all cool with that. No harm done, but what we really mean is: Let 2x = \cosh u where u \geq 0 (or potentially: u \leq 0), the choice of domain for u makes \cosh injective and makes sure that \sqrt{\cosh^2 u} = \cosh u.

    I've used the above example to demonstrate the interesting (and good!) question you asked but also to demonstrate why we take principal arc-trigs when back-substituting. That is, why we're then allowed to say: u = \text{arcosh} 2x, we've restricted the domain to make the function injective and hence invertible.

    tl;dr, we make substitutions injective but don't bother writing it down.

    That's what I understand of it, at least. Hope that helped.
    I meant to say cosx/even :facepalm: but reading.
    Offline

    16
    ReputationRep:
    (Original post by Kvothe the arcane)
    A better pool of candidates will probably take FM as schools are more choosy about who they let sit the subject.

    We had some test that you had to get 90%+ in to stay. It was pretty simple but felt awkward about the people who had to go.



    There's even a disparity with normal maths which I find slightly surprising.
    I think FM/AFM is a very self selective pool. FM at A level has the highest percentage of A*s awarded at A level and yet it is probably one of the hardest choices
    Offline

    3
    ReputationRep:
    (Original post by Kvothe the arcane)
    A better pool of candidates will probably take FM as schools are more choosy about who they let sit the subject.

    We had some test that you had to get 90%+ in to stay. It was pretty simple but felt awkward about the people who had to g.
    (Original post by aymanzayedmannan)
    Nah mate, I think that it's probably because the most confident candidates take FM. Everyone does straight maths, so the percentage is lower. Where I live, Maths is seen as a "compulsory" subject at A level.
    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?
    Offline

    21
    ReputationRep:
    (Original post by Kvothe the arcane)
    I meant to say cosx/even :facepalm: but reading.
    Even then, you could still have \sqrt{\cos^2 x} = \pm \cos x \neq \cos x, even/odd functions have nothing to do with it.
    Offline

    21
    ReputationRep:
    (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?
    A bit too late for that, 'innit? All the top universities are asking for MAT/STEP for ages precisely because the A* FM doesn't mean much for mathematicians. They need to keep the subject relevant for physicists/engineers/stuffs though, so an upward trajectory which would be welcome by mathematics departments would be hated by other departments, so not going to happen.
    • TSR Support Team
    • Very Important Poster
    • Reporter Team
    • Welcome Squad
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by Zacken)
    Even then, you could still have \sqrt{\cos^2 x} = \pm \cos x \neq \cos x, even/odd functions have nothing to do with it.
    Please ignore my post. But thanks for the explanation .
    Offline

    21
    ReputationRep:
    (Original post by Kvothe the arcane)
    Please ignore my post. But thanks for the explanation .
    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!
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    A bit too late for that, 'innit? All the top universities are asking for MAT/STEP for ages precisely because the A* FM doesn't mean much for mathematicians. They need to keep the subject relevant for physicists/engineers/stuffs though, so an upward trajectory which would be welcome by mathematics departments would be hated by other departments, so not going to happen.
    Yea i suppose so, it just feels a little silly reading that 40% of people get A* :dontknow: maybe its just me
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Break up or unrequited love?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.