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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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    (Original post by Electric-man7)
    I have completed STEP II ans STEP I and working on the remaining STEP III papers.
    how's that a good thing? you dont have anymore practice material for step and the exam is in 9 months...
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    (Original post by Student1256)
    how's that a good thing? you dont have anymore practice material for step and the exam is in 9 months...
    I never claimed it was a good thing, but I have been preparing for a long time now (atleast 11 months) so its easy to see how I ran out of practice material. Its partially my schools fault for forcing me to take all 4 A-levels a year early.
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    (Original post by Electric-man7)
    I never claimed it was a good thing, but I have been preparing for a long time now (atleast 11 months) so its easy to see how I ran out of practice material. Its partially my schools fault for forcing me to take all 4 A-levels a year early.
    What subjects did you do and what did you get ?????
    Also......what are you doing this year then?

    P.S........start panic when seeing someone has already done all the papers.....!
 
 
 
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