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    (Original post by john1234567)
    for question 8 you could change cot2x=0 to cos2x/sin2x=0 and so you have cos2x=0. i did the same as you though
    however there don't seem to be any solutions in the given range :awesome: i really hope i got all seven marks there
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    any idea on high grade boundaries will be?
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    i hope so, i dropped about 22 marks i think according to arsey's solutions :/
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    argh i dont want to wait for marchhh!!!!
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    (Original post by Arsey)
    Very hard I thought. Here are my solutions
    =) myonly doubt was finding a & b but i guess it should be right considering you & plenty of other people also got the same answer
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    For Question 8

    cosec^22x - cot2x = 1

    (1 + cot^22x) - cot2x = 1

    cot^22x - cot2x = 0

    cot2x(cot2x - 1) = 0

    cot2x = 0 and cot2x = 1

    For cot2x = 1.....tan2x = 1 so x = 22.5, 112.5

    For cot2x = 0, even though it said Math error on the calculator, if you somehow remembered the graph, you would remember that the cotx graph cuts the x-axis!

    You get tan2x = \infty and thats at 2x = 90, 270....Thus, x = 45, 135 as well

    OR
    I just saw a better way of doing it: cot2x = 0

    Thus cos2x/sin2x = 0

    Thus cos2x = 0, Thus x = 45, 135
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    (Original post by john1234567)
    also for the last question (the range of fg) i got it's >4 because the minimum is already at the point (1,1) before the +3
    Someone told me that aswell, I didn't understand what he meant but it was something to do with x>1 from the function f but I didn't know how it would work so I just put x \geq 3
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    (Original post by .:excel4100%:.)
    x = 45, 135 as well
    but if you plug that into the equation you get a math error because you're dividing by tan90 and tan270
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    (Original post by john1234567)
    ....
    On a glance it looks like we got the same answers for most of them. The only real question which I had to think about was the differentiate x=tany one, got there in the end though. I think it went very well, hoping for near 100.
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    (Original post by john1234567)
    for question 8 you could change cot2x=0 to cos2x/sin2x=0 and so you have cos2x=0. i did the same as you though
    of course, so 45 and 135 will also work.
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    (Original post by milliondollarcorpse)
    On a glance it looks like we got the same answers for most of them. The only real question which I had to think about was the differentiate x=tany one, got there in the end though. I think it went very well, hoping for near 100.
    i smiled when i saw that cos it looked like the method for differentiating arcsinx
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    I think I dropped 20 marks overall. Should still be a high B with adjusted UMS I think.
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    (Original post by john1234567)
    also for the last question (the range of fg) i got it's >4 because the minimum is already at the point (1,1) before the +3
    not sure what you mean but if you use x>1 then fg>3
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    (Original post by john1234567)
    but if you plug that into the equation you get a math error because you're dividing by tan90 and tan270
    But when you put it back into the equation:


    cosec^22x - cot2x = 1

    Remember cot2x = 0 at those points, so you don't need to put any values in for those, so it's effectively just:

    cosec^22x = 1 and the answers to that are at x = 45 and x = 135
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    I thought it was an alright exam, according to arsey's answer, the only mistakes I made were the same one as him
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    for question 8 if you got the right answers but you also solved for tan2x=0 then how many marks you lose? for q4 i diffrentiate it right but when i simplify it i got it wrong. how many marks would i lose?
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    (Original post by john1234567)
    i smiled when i saw that cos it looked like the method for differentiating arcsinx
    I don't know how to differentiate arcsinx, lucky I still managed to do it anyway
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    (Original post by Kd3239)
    for question 8 if you got the right answers but you also solved for tan2x=0 then how many marks you lose? for q4 i diffrentiate it right but when i simplify it i got it wrong. how many marks would i lose?
    i cant believe i made some silly mistakes
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    (Original post by .:excel4100%:.)
    Remember cot2x = 0 at those points, so you don't need to put any values in for those
    :confused: i'm not sure i agree with that. if cot2x = 0 then you should be able to put x=45 in and get 0
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    (Original post by .:excel4100%:.)
    For Question 8

    cosec^22x - cot2x = 1

    (1 + cot^22x) - cot2x = 1

    cot^22x - cot2x = 0

    cot2x(cot2x - 1) = 0

    cot2x = 0 and cot2x = 1

    For cot2x = 1.....tan2x = 1 so x = 22.5, 112.5

    For cot2x = 0, even though it said Math error on the calculator, if you somehow remembered the graph, you would remember that the cotx graph cuts the x-axis!

    You get tan2x = \infty and thats at 2x = 90, 270....Thus, x = 45, 135 as well

    OR
    I just saw a better way of doing it: cot2x = 0

    Thus cos2x/sin2x = 0

    Thus cos2x = 0, Thus x = 45, 135
    I got the same first 2 solutions as this, but for the last ones i'm not too sure. Oh, and for the ranges/domains on the last questions, did people get x greater than one and fg greater than or equal to 3
 
 
 
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