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AQA A2 Mathematics MPC4 Core 4 - 9th June 2015 [Discussion & unofficial markscheme] Watch

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    (Original post by YoloSwagginz)
    Minima and maximum occur as the cos graph changes like for cos it's max value is when cos is 1 and minima is cos = -1



    So -r is min and r is max
    Thanks.
    One last question: for the questions where you expand an equation, there is sometime question that asks you for the range or something where the answer is like |x|<2, for example, I don't understand how they find out, please help.
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    last minute practice?



    look at the links in post 2 in

    http://www.thestudentroom.co.uk/show....php?t=3353445
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    (Original post by Mgdawber)
    I haven't checked if this is right yet but this is how I would do it!Attachment 422901

    It's right thank you so much!
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    for the questions where you expand an equation, there is sometime question that asks you for the range or something where the answer is like |x|<2, for example, I don't understand how they find out, please help
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    (Original post by hamza3256)
    Thanks.
    One last question: for the questions where you expand an equation, there is sometime question that asks you for the range or something where the answer is like |x|<2, for example, I don't understand how they find out, please help.

    Binomial expansion okay so say you get given (3+x)^0.5 well to expand it using the formula you must divide by 3 so you get like 3^0.5(1+x/3)^0.5 now for a standard equation like (1+x)^0.5 the range is always -1 < x < 1 all you do now is sub x/3 for x so

    -1 < x/3 < 1 and now that hoes to
    -3<x<3

    The modulus is just another way of writing the above so just stick to what I said you will be ok
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    Hi can anyone help me with how you prove sin3x, cos3x and tan3x using the addition formulas? Thanks!!!!
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    (Original post by YoloSwagginz)
    Binomial expansion okay so say you get given (3+x)^0.5 well to expand it using the formula you must divide by 3 so you get like 3^0.5(1+x/3)^0.5 now for a standard equation like (1+x)^0.5 the range is always -1 < x < 1 all you do now is sub x/3 for x so

    -1 < x/3 < 1 and now that hoes to
    -3<x<3

    The modulus is just another way of writing the above so just stick to what I said you will be ok
    Thanks but I could not understand where do you get the x/3 from?
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    I'm going now, good luck to everyone.
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    (Original post by hamza3256)
    Thanks but I could not understand where do you get the x/3 from?
    Do you use the formula 1 + an ... Etc
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    (Original post by Cattie2312)
    Hi can anyone help me with how you prove sin3x, cos3x and tan3x using the addition formulas? Thanks!!!!
    Is there a paper that has this question cause I've never seen it
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    (Original post by YoloSwagginz)
    Is there a paper that has this question cause I've never seen it
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
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    (Original post by YoloSwagginz)
    Do you use the formula 1 + an ... Etc
    OH! I get it now. Thanks, I am actually very tired, so couldn't understand it, but now I do.

    Gud luck for the exam!.
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    (Original post by hamza3256)
    Thanks but I could not understand where do you get the x/3 from?


    If you are given a problem like (3-x)^-1

    In order to expand it you need a 1 instead of a 3 so in order to get rid of it in the bracket you simply divide out and then put the 3 outside the bracket with the same power sooo

    (3^-1)(1-x/3)^-1 = (3-x)^-1
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    (Original post by 2014_GCSE)
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
    I'm pretty sure we don't get asked proofs and also to integrate or differentiate that will be easy
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    (Original post by 2014_GCSE)
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
    Well I'd write it as sin2xcosx * cos2xsinx

    Now you need double angle for both cos and sin which is simply 2sinxcosx and cos^2x - sin^2x now sub them in then how far do you go? Cause now we can start using the basic sin^2 + cos^2 = 1
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    (Original post by 2014_GCSE)
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
    It's definitely come up at least once, you just do, for example cos3x = cos (2x+x) (for use in cos2xcosx-sin2xsinx) and solve as normal. It asks you to find it because sometimes we get asked to solve sin^2x, which you need to rearrange your solution to find and then integrate that
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    (Original post by 2014_GCSE)
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
     sin(2x+x) = sin(2x)cos(x) + cos(2x)sin(x)

sin(3x) = (2sin(x)cos(x))cos(x) + (1-2sin^2(x))sin(x)

sin(3x) = 2sin(x)cos^2(x) + sin(x) - 2sin^3(x)

sin(3x) = 2sin(x)(1-sin^2(x)) + sin(x) - 2sin^3(x)

sin(3x) = 2sin(x) - 2sin^3(x) + sin(x) - 2sin^3(x)

sin(3x) = 3sin(x) - 4sin^3(x)

    Usually the question will ask show that  sin(3x) = 3sin(x) - 4sin^3(x) or similar.
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    (Original post by 2014_GCSE)
    There isn't one, but people think it's going to come up. I don't know how you would tackle it exactly though.

    sin3x = 2sin2xcosx
    =4sinxcos^2x

    Maybe?
    Hi! I just showered and I decided to check the thread on my phone one last time before I go to sleep, so this is my actual final post for today^^.

    I don't believe it's ever been in an exam but it's definitely in the textbook.

    It's actually pretty simple to solve; you start by rewriting sin3x as sin(x + 2x). Then you just use the formula in the booklet for sin(A + B) and rewrite sin(x + 2x) in that form (where A = x and B = 2x). After that point it all becomes standard stuff .

    Alright! Sleep (for real)! Good luck guys, I guess I'll see everyone on here after the exam.
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    (Original post by s-hardayjade)
    It's definitely come up at least once, you just do, for example cos3x = cos (2x+x) (for use in cos2xcosx-sin2xsinx) and solve as normal. It asks you to find it because sometimes we get asked to solve sin^2x, which you need to rearrange your solution to find and then integrate that
    It's never came up in june 2010 to present, I've only done a few of the 2005 - jan 2010 ones
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    In 40 minutes it's my birthday
 
 
 
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