Current Year 12 Thread Mark VI

Discussion for A-Level students and for those choosing their A-Level subjects.

Announcements Posted on
Please change your TSR password 23-05-2013
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 20-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
Search Thread
Advanced Search
Sign in to Reply
  1. bananarama2's Avatar
    4121 02-06-2012  20:54
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    I'm not looking at any unofficial mark schemes.
  2. Maths_Lover's Avatar
    4122 02-06-2012  22:00
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    That isn't as easy as the series log question 1987 paper.
    I haven't looked at any papers that far back.

    (Original post by wcp100)
    I'm not looking at any unofficial mark schemes.
    That would be a wise idea - I have not done that and won't. How did FP1 go for you yesterday?

    Also... how has your day been?

    I've spent much of my day out... socialising. :eek: I only just got back...
  3. bananarama2's Avatar
    4123 02-06-2012  22:12
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)
    I haven't looked at any papers that far back.



    That would be a wise idea - I have not done that and won't. How did FP1 go for you yesterday?

    Also... how has your day been?

    I've spent much of my day out... socialising. :eek: I only just got back...
    They're easier on the whole.

    Alright I think. I wished it wasn't as long with short questions though.

    Good. I went to see my brother. I'm just doing the rest of your questions.

    How was your day?
  4. Maths_Lover's Avatar
    4124 02-06-2012  22:42
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    They're easier on the whole.

    Alright I think. I wished it wasn't as long with short questions though.

    Good. I went to see my brother. I'm just doing the rest of your questions.

    How was your day?
    I may have a look soon, then.

    I do as well. :/

    Sounds fun and I look forward to seeing your answers - I'll do your questions soon. :yep:

    My day was really, really enjoyable (tanoshii desu!). I went to town with my family and then we went back to a family friend's house (round the corner from our house) and stayed there for hours. We chatted, ate, watched some TV and I played piano for them (I played hours of piano today! :eek:) and it was extremely fun and quite a refreshing change. However, I was fed too much though... "Have some more food!" "Nah, that's alright, I'm full..." "No really, eat some more." "Okay then..." *a few bites later* Gaah... my aching stomach........ :couchpotato:

    I'm finishing off a STEP question which I was right in the middle of before we had to leave. :nooo:
  5. berryripple's Avatar
    4125 03-06-2012  09:29
    • Banned
    Re: Current Year 12 Thread Mark VI
    A trophy fell on my head and now I have a lovely swollen cut by my eyebrow
  6. Blutooth's Avatar
    4126 03-06-2012  09:43
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by Maths_Lover)

    I came across a very nice STEP I question this morning. No funny business involved, no trickery - it was just straight-forward and elegant. :love:

    You guys can try it if you want... that is, if you haven't already but I suspect you have probably already done it in your sleep.

    Attachment 153335


    And with that, I am off again.
    I've probably done this question before but if I did it's been so long ago I can't remember. At least a year and a half...
    Spoiler:
    Show
    Click image for larger version.  Name: Picture 4.png  Views: 19  Size: 44.1 KB  ID: 153503 Click image for larger version.  Name: Picture 3.png  Views: 15  Size: 64.2 KB  ID: 153504


    (Original post by wcp100)
    They're easier on the whole.

    Alright I think. I wished it wasn't as long with short questions though.

    Good. I went to see my brother. I'm just doing the rest of your questions.

    How was your day?
    Do you know on which page of this thread your questions are?

    (Original post by berryripple)
    A trophy fell on my head and now I have a lovely swollen cut by my eyebrow
    Well, at least you softened the blow to the trophy before it hit the floor.
    Attached Files
  7. File Type: pdf CodeCogsEqn (3).pdf (26.8 KB, 6 views)
  8. File Type: pdf CodeCogsEqn (2).pdf (24.4 KB, 12 views)
    9. Last edited by Blutooth; 03-06-2012 at 09:58.
  9. bananarama2's Avatar
    4127 03-06-2012  10:46
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Do you know on which page of this thread your questions are?
    ML is teaching me basic number theory. She PM'ed me the questions.
  10. Blutooth's Avatar
    4128 03-06-2012  11:34
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    ML is teaching me basic number theory. She PM'ed me the questions.
    Oh, ok that's cool.
  11. bananarama2's Avatar
    4129 03-06-2012  12:00
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Oh, ok that's cool.
    I was teaching her a bit about partial differentiation if you want the questions I sent her?
  12. Blutooth's Avatar
    4130 03-06-2012  12:03
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    I was teaching her a bit about partial differentiation if you want the questions I sent her?
    Sure. That'd be awesome. However, if you do I'm likely to return the favour.
  13. bananarama2's Avatar
    4131 03-06-2012  12:06
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Sure. That'd be awesome. However, if you do I'm likely to return the favour.
    Find all the first order partial derivatives of:

    i) f(x,y)=\arctan (y/x)
    ii) r(x,y,z)=\sqrt{x^2+y^2+z^2}

    2) Show that the differential:

    df = x^2 dy -(y^2+xy)dx

    is not exact, but dg=(xy^2)^{-1} is.

    3)Show that

    df=y(1+x-x^2)dx+x(x+1)dy

    is not a an exact differential.
    Find the differential equation that a function g(x) must satisfy if d \phi = g(x)df to be an exact differential. Verify that g(x)=e^{-x} is a solution of this equation and deduce that form on \phi (x,y) .

    4)Using the chain rule transform the coordinate system of the operator

    \displaystyle \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}+ \frac{\partial}{\partial z^2}

    x=\rho \sin \theta \cos \phi
    y= \rho \sin \theta \sin \phi
    z= \rho \cos \theta
    \rho = \sqrt{x^2+y^2+z^2}
  14. Blutooth's Avatar
    4132 03-06-2012  12:14
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)

    is not a an exact differential.
    Find the differential equation that a function g(x) must satisfy if d \phi = g(x)df to be an exact differential. Verify that g(x)=e^{-x} is a solution of this equation and deduce that form on \phi (x,y) .

    4)Using the chain rule transform the coordinate system of the operator

    \displaystyle \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}+ \frac{\partial}{\partial z^2}

    x=\rho \sin \theta \cos \phi
    y= \rho \sin \theta \sin \phi
    z= \rho \cos \theta
    \rho = \sqrt{x^2+y^2+z^2}
    Thanks for the questions. I haven't done much on DE but I'll give em a try. Here's the only interesting DE equation I know; it's an Oxford Maths DE interview question and actually quite beautiful.

    There is a unit square with it's axes parallel to the x and y axis. The bottom left hand corner is centred on the origin. At the vertices on the square, there are 4 beatles. The beatles move in a special way: each beatle moves exactly towards the beatle on the next vertex going round clockwise.
    i) sketch the paths of the beatles as they move across our coordinate system.
    ii) Find an equation for the paths the beatles follow.
    Last edited by Blutooth; 03-06-2012 at 12:24.
  15. bananarama2's Avatar
    4133 03-06-2012  12:34
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Thanks for the questions. I haven't done much on DE but I'll give em a try. Here's the only interesting DE equation I know; it's an Oxford Maths DE interview question and actually quite beautiful.

    There is a unit square with it's axes parallel to the x and y axis. The bottom left hand corner is centred on the origin. At the vertices on the square, there are 4 beatles. The beatles move in a special way: each beatle moves exactly towards the beatle on the next vertex going round clockwise.
    i) sketch the paths of the beatles as they move across our coordinate system.
    ii) Find an equation for the paths the beatles follow.
    I've ended up with simultaneous differential equations....
  16. Blutooth's Avatar
    4134 03-06-2012  12:35
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    I've ended up with simultaneous differential equations....
    That was quick Just to find the right substitution now.
    Last edited by Blutooth; 03-06-2012 at 12:39.
  17. bananarama2's Avatar
    4135 03-06-2012  12:41
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    That was quick Just to find the right substitution now.
    Edit: in one variable?
    I don't know what to do with the pile of differential equations.

    I'll tell you my thought process I feel like I've over complicated it.

    I let each beatle be denoted a,b,c and d going clockwise of the origin. If they all move with speed u. Then:

    \vec{V_a}=u\frac{\vec{b}}{|b|}

    I feel like this is completely wrong though. I did this for all of them.
  18. Blutooth's Avatar
    4136 03-06-2012  12:45
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    I don't know what to do with the pile of differential equations.

    I'll tell you my thought process I feel like I've over complicated it.

    I let each beatle be denoted a,b,c and d going clockwise of the origin. If they all move with speed u. Then:

    \vec{V_a}=u\frac{\vec{b}}{|b|}

    I feel like this is completely wrong though. I did this for all of them.
    Don't worry about the velocities. Just try and find an equation y in terms of x.

    Look at the y and x coordinates of the points on a path, can you notice any symmetries... or anything to obtain a DE equation?

    Hint:
    Spoiler:
    Show
    Look at the gradient of the points
    Last edited by Blutooth; 03-06-2012 at 12:48.
  19. bananarama2's Avatar
    4137 03-06-2012  13:21
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Don't worry about the velocities. Just try and find an equation y in terms of x.

    Look at the y and x coordinates of the points on a path, can you notice any symmetries... or anything to obtain a DE equation?

    Hint:
    Spoiler:
    Show
    Look at the gradient of the points
    Sorry I went to have my lunch.

    \frac{dy}{dx}=\frac{1-x-y}{y-x}
    Last edited by bananarama2; 03-06-2012 at 13:24.
  20. Blutooth's Avatar
    4138 03-06-2012  13:29
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    Sorry I went to have my lunch.

    \frac{dy}{dx}=\frac{1-x-y}{y-x}
    Brill, now just to make the right sub...the same sub I used for ML's inequality question with the p-1/p+1, interestingly enough.
    Last edited by Blutooth; 03-06-2012 at 13:40.
  21. bananarama2's Avatar
    4139 03-06-2012  13:36
    • TSR Legend
    Re: Current Year 12 Thread Mark VI
    (Original post by Blutooth)
    Brill, now just to make the right sub...the same sub I used for ML's inequality question, interestingly enough.
    u=y-x ?
  22. Blutooth's Avatar
    4140 03-06-2012  13:36
    • Peer Of The TSR Realm
    • Location: London
    • Posts: 1,943
    Re: Current Year 12 Thread Mark VI
    (Original post by wcp100)
    u=y-x ?
    That's what I said at interview but no, that's not it. See my previous edit.
    Last edited by Blutooth; 03-06-2012 at 13:40.
Sign in to Reply
Search Thread
Advanced Search
Share this discussion:  
Useful resources

Articles:

The Student Room Study Help wikiRules and Posting Guidelines Study Help Member of the Month NominationsTop Ten A-Level Sixth Form/College WorriesA-Level Options HelpA Level Revision NotesAll about UMS AQA exam timetablesEdexcel A-Level exam timetablesOCR exam timetables

Quick link:

Unanswered A-level threads

Groups associated with this forum:

View associated groups
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is moderated by:

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

Shortcuts

Get Started

TSR Group

Using TSR

Info

Connect with TSR

Reputation gems:
The Reputation gems seen here indicate how well reputed the user is, red gem indicate negative reputation and green indicates a good rep.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.