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Maths Paper 2 Honors Q6/7

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  • 04-06-2007 3:22pm
    #1
    euwwy deuwwy
    Closed Accounts Posts: 56 ✭✭


    Basically Ive gone over the basics of calculus i.e first principles, simple diff equations and all that malarcy. But I'm not great in the turning points, points of inflection etc, I didnt realise there was so much of it! Could someone give me some advice on what is enough to gaurantee me either Q6 or Q7. Cheers in advance.


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    #2
    mp3guy
    Registered Users Posts: 3,970 ✭✭✭mp3guy


    Practice the Q6 and Q7's in the exam papers, and use the solutions on www.examinations.ie to help you. Also use your maths book if you get stuck or don't understand how something is done or why it's done.


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    #3
    Fuzzy_Dunlop
    Registered Users Posts: 5,500 ✭✭✭Fuzzy_Dunlop


    Well first of all Paper 1 is i'm sure what you mean. If you know the basics and first principles then you should be good for Q6 I'd say. First principles didn't come up last year so it should come up, make sure you know some of the more difficult ones like sinx and cosx and the product rule though. If you can't do turning points etc. then I would avoid Q7 because thats where you usually find the likes of them


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    #4
    sunflowerz
    Closed Accounts Posts: 74 ✭✭sunflowerz


    its simple- just read the rules in the book (consise maths has them clearly) and u can pretty much figure out when the rules apply! i only started revising the maths course yesterday, so ul be grand!


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    #5
    euwwy deuwwy
    Closed Accounts Posts: 56 ✭✭euwwy deuwwy


    Yeh, sorry, its paper 1 I'm talking about, my head is just gone at the moment ( : , I've actually gone through most of the past papers but I'm just a bit dodgy on alot of the Q7's. Cheers 4 the advice. ( :


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    #6
    euwwy deuwwy
    Closed Accounts Posts: 56 ✭✭euwwy deuwwy


    Yeh, sorry, its paper 1 I'm talking about, my head is just gone at the moment ( : , I've actually gone through most of the past papers but I'm just a bit dodgy on alot of the Q7's. Cheers 4 the advice. ( :


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    #7
    Lucas10101
    Closed Accounts Posts: 630 ✭✭✭Lucas10101


    Here are the basic rules and how I remember them:

    To find the turning points:

    1. Find dy/dx, put this equal to zero and solve the equation to get x values, then get the corresponding y-values to get the turning points.

    2. To determine the nature of those turning points, find d2y/dx2 and put the above points in and if it's PosItIve, it's mInImum and if it's a NegatIve it's a MaxImum. Notice that positive has 2 i's and so does Minimum,....Negative has 1 i and so does Maximum which corresponds them.

    3. To find the point of Inflexion, put d2y/dx2 = 0 and solve for x and y.

    4. To prove a point is a point of inflexion, show that d3y/d3x is NOT equal to zero, it must be a number >0

    5. To get the asymptotes, put the bottom line of the fraction =0 to get Vertical Asymptote and solve , use limits to get the Horizontal Asymptote.

    That's the main points of it anyway.


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    #8
    mathew
    Registered Users Posts: 1,488 ✭✭✭mathew


    Lucas10101 wrote:
    Notice that positive has 2 i's and so does Minimum,....Negative has 1 i and so does Maximum which corresponds them.

    Hehe, rote learnig!!!!
    1. Find dy/dx, put this equal to zero and solve the equation to get x values, then get the corresponding y-values to get the turning points.

    Just to clarify, to get the corresponding y-value, you sub the x value you got into the initial equation, ie the equation given on the paper before you differentiate it at all.
    Just something I have seen people fall down on before!


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    #9
    Lucas10101
    Closed Accounts Posts: 630 ✭✭✭Lucas10101


    Yes, Matthew, that would clarify.

    Speaking of clarification, whether or not you studied the chapter at all, you wouldn't have to be a genious to know what to do. For example, you are going to differentiate EVERYTHING they give you on this section. So get the attempt at least by doing that. Points are like (3,2) (4,1) so if you dy/dx and are looking for some points, use what you learned in algebra and get the points as usual. That could pass the question and you haven't read the chapter yet.

    Another common differential question on this topic is to prove that a function has no turning points. As usual differentiate.

    You'll be left with a number or a fraction(normally) and this can never be zero as you have to put dy/dx=0 to get turning points but a number can never be zero and this proves it. To prove theres no point of inflexion, get d2y/dx2 and that'll be a number, the same as turning points.


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