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    (Original post by Slewis99)



    Can anyone help me with this? It's a foundation module question.
    I have found the least value of the function, but I'm not sure how to get the greatest value.
    I'm not sure how I sketch the function either, without using a specific value of k
    Use your graph and mark on the endpoints on the bounds for x, you notice that the maximum value isn't a stationary point, so you just need to see where the highest point on the curve will be noting how 'k' is bounded(the values are chosen very cleverly)
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    (Original post by Slewis99)



    Can anyone help me with this? It's a foundation module question.
    I have found the least value of the function, but I'm not sure how to get the greatest value.
    I'm not sure how I sketch the function either, without using a specific value of k
    Complete the square to get the upward facing parabola. Minimum value is the local minimum but the max value is one of the two boundary values depending on k<0 or k>=0. When k>2 the local minimum would be out of range, so both min and max are boundary values.
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    (Original post by Slewis99)
    I'm not sure how I sketch the function either, without using a specific value of k
    Hint: all you need to know is where the curve intersects the axes
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    Hey guys, any idea how to go about sketching functions such as f(x) = ln(x) divided by x? ( ln(x)/x )
    Obviously I know how to draw ln(x), and I know how to draw 1/x, but how do I draw the combined result? Thanks!
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    (Original post by iMacJack)
    Hey guys, any idea how to go about sketching functions such as f(x) = ln(x) divided by x? ( ln(x)/x )
    Obviously I know how to draw ln(x), and I know how to draw 1/x, but how do I draw the combined result? Thanks!
    The kind of questions you need to ask yourself with sketch questions are:
    Where do I expect the function to be defined?
    Are there any roots? Are there any stationary points - if yes what kind?
    What happens when  x \to 0 or  x \to \pm \infty ?

    Then at the end connect the dots essentially (with a tiny bit of thought so that the slopes aren't horribly wrong).
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    Hi, I've just started looking into maths admissions tests and was after some help! I'm looking at using it to boost my application (as I don't study further maths) for MORSE at Warwick and/or Southampton.

    1) When are the STEP papers taken? On the website it looks as if they are sat June time....

    2) If this is the only time they are taken are they done pre- or post- application? I'm in yr13 just going through the UCAS process - or am I too late?

    3) Would a TMUA have a similar value?

    Thank you x
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    (Original post by pink.lemonade)
    Hi, I've just started looking into maths admissions tests and was after some help! I'm looking at using it to boost my application (as I don't study further maths) for MORSE at Warwick and/or Southampton.

    1) When are the STEP papers taken? On the website it looks as if they are sat June time....

    2) If this is the only time they are taken are they done pre- or post- application? I'm in yr13 just going through the UCAS process - or am I too late?

    3) Would a TMUA have a similar value?

    Thank you x
    1) They are taken in June of Year 13 when you are taking all your A-Level exams.

    2) Yes, this is the only time they are taken. They are done post application. It is usually a condition of an offer.

    3) For MORSE? Probably.
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    (Original post by Zacken)
    1) They are taken in June of Year 13 when you are taking all your A-Level exams.

    2) Yes, this is the only time they are taken. They are done post application. It is usually a condition of an offer.

    3) For MORSE? Probably.
    Thank you so much!!!
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    (Original post by pink.lemonade)
    Thank you so much!!!
    No problem.
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    STEP
    This question refers to the 1994 STEP1 paper question 8. I have done the first two parts but I dont know how they relate to the last part.

    so far I have tried manipulating (1+sinx)/(1+cosx) to get 1 + tan(x). I tried splitting the integral, using the property of logarithms, and I have gotten nowhere.

    what am I not seeing?

    p.s. please can you nudge and not give the whole question away.

    thanks
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    (Original post by Bangz)
    STEP
    This question refers to the 1994 STEP1 paper question 8. I have done the first two parts but I dont know how they relate to the last part.

    so far I have tried manipulating (1+sinx)/(1+cosx) to get 1 + tan(x). I tried splitting the integral, using the property of logarithms, and I have gotten nowhere.

    what am I not seeing?

    p.s. please can you nudge and not give the whole question away.

    thanks
    I just told you on another thread that you need to use a similar substitution...

    Further hint if necessary:
    Spoiler:
    Show

    As with many substitutions, the limits are a big hint.
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    (Original post by Bangz)
    STEP
    This question refers to the 1994 STEP1 paper question 8. I have done the first two parts but I dont know how they relate to the last part.
    To get the idea of what's going on, sketch the graphs of 1+sin(x) and 1+cos(x) and think about how the graphs of ln(1+cos(x)) and ln(1+sin(x)) will be related. You should be able to see a) useful symmetries and b) the value of the integral.

    Then try to apply a similar trick to the first part, but based on the symmetries of sin and cos rather than tan, to evaluate the integral more rigorously.
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    Could someone please help with the very last part of this question? I got as far as showing that angle ECF is 30 degrees, and I was just stuck there for a long time, but according to Siklos' answer, this completes the proof! I don't understand how showing that angle FCB = 120 - 2a would show that angle ACB has been trisected, since showing this doesn't show that angles ECB and FCE are equal necessarily?
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    (Original post by I hate maths)
    Could someone please help with the very last part of this question? I got as far as showing that angle ECF is 30 degrees, and I was just stuck there for a long time, but according to Siklos' answer, this completes the proof! I don't understand how showing that angle FCB = 120 - 2a would show that angle ACB has been trisected, since showing this doesn't show that angles ECB and FCE are equal necessarily?
    To trisect an angle a at a point P means to construct an angle a/3 at P.

    We must have here that

    ACB = 180-3\alpha=3(60-\alpha) \\ \Rightarrow 2ACB/3=120-2\alpha = FCB, ACB/3=60-\alpha=FCA

    So FCA is the trisection of ACB
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    (Original post by atsruser)
    To trisect an angle a at a point P means to construct an angle a/3 at P.

    We must have here that

    ACB = 180-3\alpha=3(60-\alpha) \\ \Rightarrow 2ACB/3=120-2\alpha = FCB, ACB/3=60-\alpha=FCA

    So FCA is the trisection of ACB
    Just that first line did it for me - for some reason I thought the lines FC and CE had to split the angle into three equal parts. But that's not what trisecting is - it's just making splitting the angle so you get one new angle that's a third of the original. Thanks so much!
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    (Original post by I hate maths)
    Just that first line did it for me - for some reason I thought the lines FC and CE had to split the angle into three equal parts. But that's not what trisecting is - it's just making splitting the angle so you get one new angle that's a third of the original. Thanks so much!
    Right. I only put the rest of the working there as I wasn't entirely sure what you didn't understand, and was wondering if you were misreading the angles or something.
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    Hey guys sorry If I am being redundant, but when will the 2017 papers be released? Also does anyone know any other examinations (possibly from outside the UK), like the MAT or AEA? I am considering moving unto AIME papers and the BMO, but its easy to see that the lack of calculus (integration is a very weak point of mine) being a major disadvantage.
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    (Original post by Electric-man7)
    Hey guys sorry If I am being redundant, but when will the 2017 papers be released? Also does anyone know any other examinations (possibly from outside the UK), like the MAT or AEA? I am considering moving unto AIME papers and the BMO, but its easy to see that the lack of calculus (integration is a very weak point of mine) being a major disadvantage.
    Have you done all the STEP from 87?
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    (Original post by Electric-man7)
    Hey guys sorry If I am being redundant, but when will the 2017 papers be released? Also does anyone know any other examinations (possibly from outside the UK), like the MAT or AEA? I am considering moving unto AIME papers and the BMO, but its easy to see that the lack of calculus (integration is a very weak point of mine) being a major disadvantage.
    Sometime later this month tends to be the norm.
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    I have completed STEP II ans STEP I and working on the remaining STEP III papers.
 
 
 
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