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    ok,. you are given parametrically a curve C:

    x=3t^2-p , y=3t^3

    (p is a positive constant)

    dy/dx= 3/2t

    Point A (-p,O) touches the curve when t=0 and thus its gradient = 0 so point A is a minimum.

    THEN IT ASKS: SKETCH THE CURVE

    I HAVE HAD IT UP TO HERE WITH SKETCHING PARAMETRICS, CAN SOMEONE PLEASE TELL ME THE METHOD AND PRINCIPLES TO SKETCHING THESE HORRIBLE GRAPHS?????????

    ITS IRONIC HOW THE P3 NORMAL EXERCISES AND NOTES IN THE TEXTBOOK DO NOT TELL YOU HOW TO SKETCH PARAMETRICS YET PAST PAPERS KEEP THROWING IN "SKETCH THE PARAMETRIC GRAPH".......ITS REALLY PISSING ME OFF!!!!!!!! I FEEL LIKE RINGING EDEXCEL AND TELLING THEM TO REPRINT THEIR BOOKS WITH NOTES ON SKETCHING PARAMETRIC GRAPHS!
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    Have you tried finding the cartesian form of the equations?
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    (Original post by Leekey)
    Have you tried finding the cartesian form of the equations?
    You have to plot it basically, make find x and y in the range -4 < t < 4 and find where it crosses the axis, then sketch.
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    With most parametrics, the general plan should be to change the equation to cartesian form (x's and y's). You should then do the following things:
    - put in x=0, find value(s) of y
    - put in y=0, find value(s) of x
    - find dy/dx to find co-ordinates of turning points
    - find d^2y/dx^2 to find the nature of turning points
    - calulate equations of any asymptotes
    - see what happens to y when you put in x tends to infinity

    This is the basis for a thorough sketch of a curve.

    However, with the question you have, I think it would be advisable to keep it in terms of 't' since you have 'p.' So for this question follow the basic guidelines.....
    x=0, t=±√(p/3)

    These value of 't' can now be used to find the corresponding values of 'y' in terms of 'p'

    y=0, t=0 => x=-p

    So basically, the curve just looks like a "y=x^2" curve that's on its side, and is shifted to the left by 'p' units.....kinda hard to explain, but you'll understand if you draw it
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    resident evil, you should learn some of the characteristic parametric shapes, then you will recognise them easier.. or when you find where the line cuts the axes you can see what's missing.. in class we gave them nicknames, like 'ribbon' and 'flares'
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    OOOOOOOH, the P3 Text book does have parametric curves sketched as examples! I just looked at the wrong chapter .

    kimoni can u scan in some sheets for me that have parametric curve patterns? theres only 2 examples in the book unfortunately.#

    Also, do asymptotes only occur when you have a function involving x being the denominator?
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    I swear that said Paramedics the first time I read it!

    Anyway, that wasn't very helpful.

    I'm not in a maths sorta mood, otherwise I might think of something more constructive - at the moment I'm very busy ******** myself about chemistry on Wednesday.
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    no an asyptote is not always when there is an x in the denominator. another asyptote is when the function approaches to a certain number but never actually reaches that number.
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    oh yeah, of course. Is the only way to find out if that is an asymptote or not, is by tapping in numbers into the calculator? Can you show me some examples?
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    eg. f(x)=1-1/x
    so as x gets larger and larger,f(x) approaches 1(i.e the limiting factor of f(x) as x approaches infinity is 1).
    Also as x approaches zero f(x) approaches ±infinity, like f(1/100000)=-999999.
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    ok another e.g. - sketch the curve defined parametically by x = 4t-1 and
    y= (t+1)/(1-t)

    now this is cartesian form is y = (5+x)/(3-x). the denominator wil tell you x=3 is an asyptote.

    now just stick value of x as something large (e.g. 99999), the function will be close to but not quiet -1 therefore y = -1 is also an asyptote.
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    sorry to change the subject but there is a website which has edexcel p3 exam solutions,it goes something like 'ajimal',can anyone remember?
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    http://www.ajimal.com/download/alevel/main.htm

    (Original post by ResidentEvil)
    oh yeah, of course. Is the only way to find out if that is an asymptote or not, is by tapping in numbers into the calculator? Can you show me some examples?
    i think you can get them when you have, say, y = 2/(x^2-4)

    anything divided by 0 is infinity/undefined.. so when x = +/- 2, y = 2/0, and hence is undefined/infinity and there will be asymptotes at x = +/- 2

    hope this is a) right b) clear
    !

    rosie
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    thanks!
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    ah man! i thought it would have the papers as well!
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    (Original post by IntegralAnomaly)
    ah man! i thought it would have the papers as well!

    here are only a few of the papers. sorry m8.

    http://www.risctex.freeuk.com/
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    I thought you could take a graphic calculator into the exam? :confused:
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    (Original post by Jubba)
    here are only a few of the papers. sorry m8.

    http://www.risctex.freeuk.com/
    no need to apologise.
    Anyway thanks for this site!
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    (Original post by Elle)
    I thought you could take a graphic calculator into the exam? :confused:
    only in p2,p4,p5 and p6 (edexcel).
 
 
 
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