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    (Original post by usycool1)
    That's a nice question, plenty of trigonometry in it.

    OK, firstly, you got \dfrac{dx}{d\theta}. There's no need to write it as \dfrac{d\theta}{dx} in this case; just substitute in:
    \sec \theta \tan \theta d\theta
    \sec^2 \theta
    and don't forget to change the limits.

    So:

    \displaystyle \int_2^3 \dfrac{1}{(x^2-1)^{\frac{3}{2}}} dx

    Write it as:

    \displaystyle \int_\frac{\pi}{3}^{arccos(\frac  {1}{3})} \dfrac{\sec \theta \tan \theta}{(\sec^2 \theta -1)^{\frac{3}{2}}} d \theta

    Now, how else can you write sec^2 \theta - 1 ? Then do some simplifying and you should get it.
    cheers bro, i was stuck on this question too, so this helps big time!
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    (Original post by Vaner)
    Hey!

    I'm stuck on question 3 and 8 in the C4 specimen paper. I'm in the early stages of solving and would really appreciate if any solves them for me as they are not in ExamSolutions.

    Thank you in advance!
    is it on integration using substitution for q.3 and the long worded question using the differential equations for q.8 ?
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    (Original post by Vaner)
    Hey!

    I'm stuck on question 3 and 8 in the C4 specimen paper. I'm in the early stages of solving and would really appreciate if any solves them for me as they are not in ExamSolutions.

    Thank you in advance!
    well if it is the same question 3 im looking at, here you go. and ill have a go at question 8 later on hope its the right question we are looking at

    first thing i would do is differentiate x = \tan \theta

    to get
    \frac{dx}{d \theta} = \sec^2 \theta

    make dx the subject to get
    dx = \sec^2 \theta d \theta

    change the limits by subbing 1 and 0 into
    x = \tan \theta to give you \frac{\pi}{4} and 0 respectively. then you are ready to go:

    (TRY ON YOUR OWN FROM THIS POINT ONWARDS, IF YOU ARE STILL STUCK. FEEL FREE TO CLICK THE SPOILER)

    Spoiler:
    Show
    \int^1_0\frac{1}{(1+x)^2}\ dx

    is then changed to
    \int^\frac{\pi}{4}_0\frac{sec^2 \theta}{(1+tan^2 \theta)^2}\ d \theta

    we know that
    1+tan^2 \theta = sec^2 \theta

    so sub that in and square it to get
    \int^\frac{\pi}{4}_0\frac{sec^2 \theta}{sec^4 \theta}\ d \theta

    simplify it to get \int^\frac{\pi}{4}_0\cos^2 \theta\ d \theta

    using cos2 \theta = 2cos^2 \theta - 1 you can sub in for
    cos^2 \theta and take out the common factor  \frac{1}{2}

    to get to
    \frac{1}{2}\int^\frac{\pi}{4}_0\  cos2 \theta + 1\ d \theta

    finally you would then integrate it, sub in the limits, multiply in by the half and you will get the answer they are looking for

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    I need 95% in both c3 and c4 to even get an A ((


    This was posted from The Student Room's iPhone/iPad Ap
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    (Original post by Flounder1)
    I need 95% in both c3 and c4 to even get an A ((


    This was posted from The Student Room's iPhone/iPad Ap
    how comes? what did you get last year? and what about your third module your doing this year?
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    (Original post by Flounder1)
    I need 95% in both c3 and c4 to even get an A ((


    This was posted from The Student Room's iPhone/iPad Ap
    If you got those scores then I'm sure you'd get the A* as you'd pass all the requirements.


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    How many papers has everyone done?

    I feel like I am focusing too much on my other Exams and not enough Maths. I did a Solomon yesterday and I found it challenging, or more challenging that I should have done.
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    (Original post by Better)
    How many papers has everyone done?

    I feel like I am focusing too much on my other Exams and not enough Maths. I did a Solomon yesterday and I found it challenging, or more challenging that I should have done.
    I've only done about 6 Solomons for C4 and about 2 for C3, I'll have to pick it up after my May exams are finished though! 100 UMS in both here I come!


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    (Original post by MathsNerd1)
    I've only done about 6 Solomons for C4 and about 2 for C3, I'll have to pick it up after my May exams are finished though! 100 UMS in both here I come!


    Posted from TSR Mobile
    Okay perfect cheers again Maths Nerd, Yeah glad your doing that, I will try to pick it up a bit like next week! Keep up the good work mate haha !!
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    (Original post by Better)
    How many papers has everyone done?

    I feel like I am focusing too much on my other Exams and not enough Maths. I did a Solomon yesterday and I found it challenging, or more challenging that I should have done.


    Yes the sciences especially biology is draining a lot of time and effort from me.
    I've done only 3 edexcel pastpapers for C1 and C2, 2 for C3, 1 for M1, none (half) for M2 and none for S1.forget Solomon and Delphis

    Edit: I forgot I did 3 M2 papers last month.

    Who's in a worse situation?

    The thing is when I do maths past papers at home its gets too boring as if revising Biology is more worth then it goes the other way.

    Anyways its not how much past papers you do but what you take out if them.
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    (Original post by Better)
    Okay perfect cheers again Maths Nerd, Yeah glad your doing that, I will try to pick it up a bit like next week! Keep up the good work mate haha !!
    If I was in your position I'd get my earlier exams out of the way first and not go crazy with these past papers as for some people they peak too early before the exam and never make up for it later on, just do about. 2-3 a week would be sufficient for now until the exam gets closer. This is only a suggestion and you don't have to follow it if you don't want to, just don't burn out from all these exams!


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    (Original post by MathsNerd1)
    If I was in your position I'd get my earlier exams out of the way first and not go crazy with these past papers as for some people they peak too early before the exam and never make up for it later on, just do about. 2-3 a week would be sufficient for now until the exam gets closer. This is only a suggestion and you don't have to follow it if you don't want to, just don't burn out from all these exams!


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    Good morning

    how are you

    can you please check this question http://www.examsolutions.net/a-level...0&solution=6.3
    6)d)ii)


    I am using substitution by parts?

    I used

    u= Inx du/dx = 1/x

    v= 1/2x2-x dv/dx = (x-1)

    so I did

    (Inx)(1/2x2-x) - integral sign (1/2x2-x)(1/x) dx

    where am I going wrong :confused:
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    (Original post by otrivine)
    Good morning

    how are you

    can you please check this question http://www.examsolutions.net/a-level...0&solution=6.3
    6)d)ii)


    I am using substitution by parts?

    I used

    u= Inx du/dx = 1/x

    v= 1/2x2-x dv/dx = (x-1)

    so I did

    (Inx)(1/2x2-x) - integral sign (1/2x2-x)(1/x) dx

    where am I going wrong :confused:
    You haven't gone wrong, this is correct so far.

    Just do the integration and evaluate using the limits, you'll get the right answer.
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    (Original post by justinawe)
    You haven't gone wrong, this is correct so far.

    Just do the integration and evaluate using the limits, you'll get the right answer.
    thanks!

    did you get my message for vectors please
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    (Original post by MathsNerd1)
    If I was in your position I'd get my earlier exams out of the way first and not go crazy with these past papers as for some people they peak too early before the exam and never make up for it later on, just do about. 2-3 a week would be sufficient for now until the exam gets closer. This is only a suggestion and you don't have to follow it if you don't want to, just don't burn out from all these exams!


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    So how's life for the chosen one
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    (Original post by ACBLISS)
    So how's life for the chosen one
    Lol, not too bad considering I'm not the chosen one Although I refused to complete a C4 paper today because I looked at the questions and they seemed incredibly easy, I could even do some of them in my head without writing anything down! STEP has definitely helped me in that manner and I'm looking for 100% in my Chemistry tests now!

    How about you?


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    not too sure where to start on this question help please !
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    (Original post by masryboy94)
    not too sure where to start on this question help please !
    The ratio of r to h is 2:3 throughout, using the concept of similar triangles.

    So r=\dfrac{2}{3}h

    Sub this into the formula for volume of a cone.
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    (Original post by masryboy94)
    not too sure where to start on this question help please !
    the first question you use the similar triangle formula which is Radius divided by the height,

    Differentiate the the volume and then from the similar triangle make R the subject and once you did that you sub that into the differentiated equation
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    (Original post by masryboy94)
    not too sure where to start on this question help please !
    You need to find an expression for r in terms of h.

    Spoiler:
    Show
    If you look at the two triangles in the cone (16 and 24 are the lengths of one triangle, and r and h are the side lengths of the other triangle), and use the fact that they are mathematically similar, you can get an expression for r in terms of h.

    Spoiler:
    Show
    As the angles are the same in each triangle, try finding tan{\theta} for each of the triangles and then setting them equal to each other.
 
 
 
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