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CCEA C4 Mathematics - 22nd May 2014 watch

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    (Original post by stephen_mcgarry)
    Hmm, isn't dy/dx = -4sint/(2-2cos2t)

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    sorry just a typo error, but it works out as root2
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    Who got log 4/log 81?
    I know its wrong...
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    Wrong topic, sorry.
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    (Original post by 1MacG)
    sorry just a typo error, but it works out as root2
    I cannot get it to work out as sqrt2 when I sup 5pi/4 in :/ it always works out as -2+2sqrt2
    What am I doing wrong!?

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    (Original post by stephen_mcgarry)
    I cannot get it to work out as sqrt2 when I sup 5pi/4 in :/ it always works out as -2+2sqrt2
    What am I doing wrong!?

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    You're possibly not multiplying 5pi/4 x2?
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    (Original post by 1MacG)
    You're possibly not multiplying 5pi/4 x2?
    Ahh that was it! Thanks

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    what did you guys say for the modeling assumption? I had no idea, i said that if you put fruit in the bowl, it could hold a greater volume as it is over the top hahaha i assume this is wrong
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    (Original post by jackanator)
    what did you guys say for the modeling assumption? I had no idea, i said that if you put fruit in the bowl, it could hold a greater volume as it is over the top hahaha i assume this is wrong
    I said the bottom of the bowl wasn't flat lol.
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    (Original post by jackanator)
    what did you guys say for the modeling assumption? I had no idea, i said that if you put fruit in the bowl, it could hold a greater volume as it is over the top hahaha i assume this is wrong
    I said you must assume the fishbowl is completely spherical, but in the real world the fishbowl must have a flat bottom and top.

    I messed up the differential equation once. I started with ln(sqrtV), instead of 2V^1/2. Do you think I was lose all 10 marks? Or will I get some for working through, but using the wrong equation?
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    Did anyone say anything about the thickness of the bowl being negligible?
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    (Original post by 1MacG)
    Did anyone say anything about the thickness of the bowl being negligible?
    me!

    cant see it being wrong tbh....
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    Could someone put up an unofficial mark scheme or even just post your answers if you think they're right lol. Specifically for questions 3 and 5?
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    (Original post by Matt857)
    Could someone put up an unofficial mark scheme or even just post your answers if you think they're right lol. Specifically for questions 3 and 5?
    Q3) I got 1072/45 = 23.8 (3sf)
    Q5) 7.28PM (19.28)

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    (Original post by Mr Tall)
    me!

    cant see it being wrong tbh....
    that is so much more logical. i was thinking that, but then i tought the fruit was a better idea haha such a stupid answer when i look back
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    could you create a mark scheme please?
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    Not a hard paper. Kicking myself for losing marks in the last question though
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    did anyone else get -1/2 ln(5-x) - 3/2 ln(x+1) for q1?
    i'm aware that could be horribly wrong as i seem to find a way to mess them up every time
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    Sorry for the delay everyone; it takes quite a bit of time to type out the mark scheme :P

    Mark scheme is in first post.

    Let me know if you have any problems with the mark scheme or if you notice any typos etc.

    By the way, I stated the assumption was that the curved surface does not contribute to the volume/negligible thickness.
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    Here are my answers:
    1i: 1/(2(5-x)) - 3/(2(1+x))
    1ii: -1/2 (ln(5-x)) - 3/2 ln(1+x)

    2) AB: 4i +9j
    2ii) r = 3 + lamdba 4
    -2 9
    2iii) proved lambda was 2 for both

    3) 23.8

    4i) 24.0
    4ii) assumed that the bottom of the bowl is flat and the insides are flat

    5) 19.46 pm

    6i) 25(sinx - 1.29)
    6ii) -625 cot(x-1.29)

    7 i) f-1 : x -> tan-1 x range = -0.666< x < 0.666
    7ii) gf : x -> |tanx| range : 0< x < pi/4
    7iii) reflection in y axis of right hand side of tan onto left

    8) found t to be 3pi/4 and coordinates to be (3pi/2 + 1) (-2sqrt2
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    1)i) 1/2(5-x) - 3/2(1+x)
    ii) (-1/2)ln|5-x| (-3/2)ln|1+x|
    2) I'll do it shortly don't have answers here, edit post later
    3)1072/45 = 23.8 (3sf)
    4)i) 24.0 (3sf)
    ii) maybe the bowl must be perfectly symmetrical, must be smooth, thickness should be ignored? I'm not 100% sure sorry
    5)7.28PM (19.28)
    6)i) R=25 alpha=1.29 (3sf)
    ii) -(cot(x-1.29))/625 + c
    7)i) f^-1:x > arctan(y) [tan^-1(y)] domain (this is a guess) -1<=x<=1 range - pi/4<=f^-1(x)<=pi/4
    ii) gf:x > |tanx| range 0<=gf(x)<=1
    iii) u shaped curve, Centre point at 0,0 and goes up to pi/4,1 and -pi/4,1 (I'll attach a picture in next post)
    8) (2pi,-4) I think you are supposed to disprove this point as, somebody stated, when you sub t into dy/dx, it does not equal sqrt2. The other coordinates are ((5pi-2)/2,-2sqrt2)


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