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    Its the worked example 1 in the step booklet



    Does this work,



    Last line is supposed to be > not =
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    Sorry, but you've gone wrong at the start.

    First line is wrong: You are only given a >= 9/8, your working assumes a = 9/8.
    Second line is wrong: You've not differentiated x^3/(1+x^2) correctly.

    Obviously the rest is meaningless after the 2nd mistake.
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    You've differentiated wrongly in the first step.
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    What level of knowledge do you have? To answer the question you need to know the product rule and chain rule for differentiation, (which I think is C3, might be C4) - it doesn't look like you do know those rules, in which case you've no chance of getting it out.
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    In fact, going from the third line to the fourth line is wrong too. These are quite basic mistakes; what level are you at?

    Edit: snap.
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    Balls, had a feeling it went wrong somewere.

    Is it not correct to use a=9/8 as a starting point, prove that it's greater for 9/8 then it should be greater for all higher numbers?

    Only done AS maths.

    Yeah I see that now too. Does not bode well.
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    (Original post by mcp2)
    Balls, had a feeling it went wrong somewere.

    Is it not correct to use a=9/8 as a starting point, prove that it's greater for 9/8 then it should be greater for all higher numbers?
    You'd have to prove it.

    (Original post by mcp2)
    Only done AS maths.
    Look up "chain rule", "product rule", "quotient rule". Also, (1 + x^2)^2 can be found by rewriting it as (1 + x^2)(1 + x^2) and multiplying out the brackets - it's not 1 + x^4.
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    (Original post by mcp2)
    Balls, had a feeling it went wrong somewere.
    To be honest, and without wanting to demoralise you, there are more lines "wrong" in that answer than right.

    Is it not correct to use a=9/8 as a starting point, prove that it's greater for 9/8 then it should be greater for all higher numbers?
    Not without justification, no.

    For example, if you'd said:

    f'(x) = a + {whatever x^3/(1+x^2) differentiates to}.

    and then say f'(x) >= 9/8 + {whatever x^3/(1+x^2) differentiates to}, since a>=9/8.

    then that would have been fine.

    Only done AS maths.
    Then you can't do the differentiation needed for the question. On the other hand, even at AS level you should know that

    \frac{1}{(1+x^2)^2} \neq \frac{1}{1+x^4}
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    Yeah I know, it was a silly mistake.
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    (Original post by mcp2)
    Only done AS maths.
    You really can't do this question without having done at least C3 differentiation (and/or C4, depending on exam board). It's in one of the Siklos booklets though, so it might be worth finding the solution there, although it doesn't run through how to do the differentiation because it assumes a full knowledge of the Core modules at A2.
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    If you want to give yourself a headstart in Year 13 mathematics, you could do worse than to get a C3 or C4 textbook from your local library and work through it. STEP questions will be largely inaccessible to you until you have completed these modules.
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    Will do. Thanks for the feedback.
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    Y'know, we really ought to make up a list of STEP questions that only need C1 and/or C2. Problem is, I don't have a great idea what's in C1/C2 so I can't do it myself.
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    (Original post by DFranklin)
    Y'know, we really ought to make up a list of STEP questions that only need C1 and/or C2. Problem is, I don't have a great idea what's in C1/C2 so I can't do it myself.
    Here is C1/C2 (the material which is in ALL the exam board AFAIK).

    http://www.maths.ox.ac.uk/files/impo...s/syllabus.pdf

    Question 1, Step 3 2008 is a really nice question for an AS student. My friend was able to do it (on a 2 1/2 hour bus journey to Cambridge....).
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    (Original post by ShortRef)
    Here is C1/C2 (the material which is in ALL the exam board AFAIK).

    http://www.maths.ox.ac.uk/files/impo...s/syllabus.pdf
    Yeah, but life's too short to go through questions cross-referencing against a syllabus. Call me lazy, but I think I'll leave it to people who've actually studied C1,C2 et. al. to classify the questions. (I'd say it's also harder for me to judge when a question is "doable with only C1,C2, but they probably expected you to use this from C3", etc).

    Question 1, Step 3 2008 is a really nice question for an AS student. My friend was able to do it (on a 2 1/2 hour bus journey to Cambridge....).
    Dunno about "nice". I wouldn't have touched it with a bargepole myself. But yes, it doesn't need anything beyond some basic algebra skills.
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    That is wrong on so many levels.

    You're not meant to do STEP now espically when only doing AS. You need C3 to do that question.

    P.S. The last step is genius (-8)^2-4 \times 3 \times 3=0, don't do that as you won't actually get any marks if you so blatenly fudge the calculations to work even if it doesn't make any sense. Anyway, your knowledge of what do is impressive but you really need to get a C3 book and learn differentiation using chain rule and product rule.

    For chain rule. Say we have f(x)=(x^2+10)^{10} now we could expand the bad boy using binomial theroem. However, this is when a bad boy called chain rule comes into play

    let u=x^2+10, then we have f(x)=u^{10}
    notice something
    \frac{dy}{dx}= \frac{dy}{du} \times \frac{du}{dx}

    so first lets find dy/du
    so \frac{dy}{du}=10u^9

    now find du/dx
    \frac{du}{dx}=2x

    times them together

    f'(x)=2x \times 10u^9 since we want it in x not u, so

    f'(x)=20x(x^2+10)^9

    now try to differentiate
    y=(x^3+10)^{-1}?

    Remeber the formule i.e dy/dx= dy/du times du/dx and that you make u= the inside of the thing.

    For chain rule I will explain that if you want me to.
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    I don't even think you need a C3 book, only if you want to do lots of practice questions.

    http://tutorial.math.lamar.edu/Class...tientRule.aspx
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    Hows this?

    y=(x^3+10)^{-1}\\

u=(x^3+10)\\

y=u^{-1}\\

\frac{dy}{du}=-1u^{-2}\\

\frac{du}{dx}=3x^2\\

y'=3x^2\times-1u^{-2}\\

y'=-3x^2(x^3+10)^{-2}\\

    I had the same idea of finding all AS level step questions but I would have to go through every single question not knowing if I could do it or not.
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    Correct. You'll soon find after experience you wont need to do the whole u = ... and work out dy/du and du/dx, you'll be able to do it automatically. Hard to explain on the internet, but you'll start recognising the pattern for differentiating by the chain rule.

    If you're interested, this is how i see the chain rule in my head when I need to use it.

    Spoiler:
    Show


    We use the chain rule when we want to differentiate a function with a power attached to it greater than something we want to expand it to

    let  y = [f(x)]^n

     \frac{dy}{dx} = n[f'(x)][f(x)]^{n-1}

    Looks complicated but it's not really, we've dropped n and put it at the start, we've differentiate the function and put it at the start and then we've taken 1 off the power n.

    So to take the example

     y = (x^3 + 10)^{-1}

    In my head i associate n = -1 and  f(x) = x^3 + 10

    so again in my head, i differentiate f(x), to get f'(x) = 3x^2

    So we have everything we need

    Generally speaking

     \frac{dy}{dx} = n[f'(x)][f(x)]^n

    In the example using the information above.

     \frac{dy}{dx} = (-1)(3x^2)(x^3 + 10)^{-2}

    I hope that made some sort of sense!

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    Quite a lot of the Stats and Mechanics questions on STEP I, and even occasionally STEP II and III, can be done with just M1 or S1 knowledge, so they might be worth a gander. The thing with STEP is that a lot of the questions, especially the 1st questions on papers, rely much more on a deep mathematical knowledge that might not even crop up at AS, it might only come up officially on the syllabus at GCSE, but be at a much harder level. Some pure questions that I reckon you could do with GCSE/AS knowledge, with the right level of understanding, are:
    STEP I 2009 Q1, 8
    STEP II 2009 Q4
    STEP I 2008 Q3
    STEP II 2008 Q1, 3
    STEP I 2007 Q8
    STEP II 2007 Q2
    STEP I 2006 Q1, 2, 3, 6
    STEP II 2006 Q1
    STEP I 2005 Q1
    STEP II 2005 Q2
    STEP I 2004 Q1, 5
    STEP II 2004 Q1

    These really do push the boundaries of AS knowledge though; and some of them aren't even reliant on AS/GCSE at all, so... it's hard to say. You can definitely do them without A2 though, provided you've had enough practice and have already done some preparation in the STEP direction.
 
 
 
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