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* Honours Maths Paper 2 " Let's fight back :)

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Comments

  • #122
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    partyatmygaff wrote: »
    I was thinking the same thing. If the Pi approximation does come up it'll be something along the lines of the following

    A theoretical question as to why the Leibniz series isn't a good approximation for X followed by perhaps a question on the inverse tan result and then at last an approximation for Pi. That'd be worst case scenario though.


    That said, it'd be an excellent Q8c though. I'd much rather a Pi approximation question than a nasty Max/Min question.

    Agreed. Going to look over it very quickly tomorrow I think.


  • #123
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    Inverse tan pi approximation question, for when you need to practice.
    2002. 8 C
    Also, Leibniz? Another name for McLaurin? :P
    I used to know the theory why it's not accurate, why is it again?


  • #124
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    Sooo, no-one knows why you start with Ur+1 instead of Ur then? (As mentioned in my previous post)


  • #125
    partyatmygaff
    Registered Users, Registered Users 2 Posts: 10,992 ✭✭✭✭partyatmygaff


    PJelly wrote: »
    Inverse tan pi approximation question, for when you need to practice.
    2002. 8 C
    Also, Leibniz? Another name for McLaurin? :P
    I used to know the theory why it's not accurate, why is it again?
    Well a Leibniz series is just the Maclaurin series of arctan(x) that Leibniz used to try and approximate Pi (Or something like that anyway).

    The reason why using the series isn't a great approximation for Pi is because it converges very slowly to Pi.


  • #126
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    partyatmygaff wrote: »
    Well a Leibniz series is just the Maclaurin series of arctan(x) that Leibniz used to try and approximate Pi (Or something like that anyway).

    The reason why using the series isn't a great approximation for Pi is because it converges very slowly to Pi.

    Damn you beat me to it! I always like saying "inefficient" though. I only read about that stuff in a book a month or so ago, as it were!


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  • #127
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    I just remembered that the syllabus says something about it is assumed that you know how to do all the junior cert stuff. So perhaps looking over constructing triangles and stuff that we have forgotten might be an idea.

    Also you know that trig question in 2009 I think it was 5 and you had to draw a graph for sin ...... Something along those lines. Maybe look over that aswell.

    ...


  • #128
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    Patriciamc93 wrote: »
    I just remembered that the syllabus says something about it is assumed that you know how to do all the junior cert stuff. So perhaps looking over constructing triangles and stuff that we have forgotten might be an idea.

    Also you know that trig question in 2009 I think it was 5 and you had to draw a graph for sin ...... Something along those lines. Maybe look over that aswell.

    ...

    That came up on my mock. I mis-read it and thought it was sine, not the inverse sine function and drew a sine function off memory ><


  • #129
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    Patriciamc93 wrote: »
    Also you know that trig question in 2009 I think it was 5 and you had to draw a graph for sin ...... Something along those lines. Maybe look over that aswell.

    ...
    2009, Q5 B (i) (ii) (iii)
    It was for inverse sin. Was a strange question indeed.


  • #130
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    PJelly wrote: »
    2009, Q5 B (i) (ii) (iii)
    It was for inverse sin. Was a strange question indeed.

    Ya i remember doing it .... Hated it! If it came up it would ruin trig for me. :(


  • #131
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    Function_Review_61.gif

    Just remember that's what it should look like.


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  • #132
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    I've always found trig a little tricky. When it gives you reams of information in a diagram and then says Show X = (something)
    It's like, where do I start!


  • #133
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    Oh and my teacher said that transformations will be big this year. He said the same about matrices in paper 1..... So I am gonna trust him on it!


  • #134
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    Michael_E wrote: »
    Function_Review_61.gif

    Just remember that's what it should look like.
    Do you like have those memorised? :p


  • #135
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    PJelly wrote: »
    Do you like have those memorised? :p

    I just know what they look like :P .... so.... yeah :P


  • #136
    partyatmygaff
    Registered Users, Registered Users 2 Posts: 10,992 ✭✭✭✭partyatmygaff


    Drawing graphs is hardly a worry. For a regular trig graph here is what i'd do.

    Say you have to draw sin(x) from -Pi -> Pi

    Change your calculator to radians, change to table mode and enter sin(x) as the function. Then put your start value at -Pi and your end value at Pi and then just set the step to Pi/12.

    Then you'll get a list of coordinates, plot the coordinates on graph paper and join the dots. Very easy.

    For an inverse trig function, just change your range to be from -1 to 1 and your step to be 0.25.


  • #137
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    PJelly wrote: »
    I've always found trig a little tricky. When it gives you reams of information in a diagram and then says Show X = (something)
    It's like, where do I start!


    If its a rectangular or square base always get the length of the diagonal.

    If it is that a pole is vertical in the air (or something similar) imagine it in the corner of a room, you might be able to see the right angles easier.

    For the 3-d diagrams it will always be cosine or sin rules and phythagours.

    Hope that helps in some way


  • #138
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    OHHH i remember what I did.

    I got the dots all right, so if I had joined them properly, like the diagram I linked, then I'd have gotten full marks. But I went and joined them so they resembled the sine curve, not the inverse one :P


  • #139
    River Song
    Registered Users, Registered Users 2 Posts: 355 ✭✭River Song


    Patriciamc93 wrote: »
    If its a rectangular or square base always get the length of the diagonal.

    If it is that a pole is vertical in the air (or something similar) imagine it in the corner of a room, you might be able to see the right angles easier.

    For the 3-d diagrams it will always be cosine or sin rules and phythagours.

    Hope that helps in some way

    Also, to add:

    If it gives you like ... a wedge, or loads of triangles on top of eachother, SPLIT THEM UP INDIVIDUALLY. Make sure, in doing that, you label the vertices correctly too.


  • #140
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    Michael_E wrote: »
    Also, to add:

    If it gives you like ... a wedge, or loads of triangles on top of eachother, SPLIT THEM UP INDIVIDUALLY. Make sure, in doing that, you label the vertices correctly too.
    Oh I can see right angles, and split up shapes grand. I scored in the top 1 percentile in a spatial awareness aptitude test I'll have you know :D

    It just thinking, "how do I manipulate the figures to get my desired answer"
    Like... that question with the semi circle, and you have to finish the triangle inside of it. Part (ii) of that took me AAAAAAAAAAAAAAAAAAGES


  • #141
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    And for 2-d ones which have circles. The key is the area/ length off a sector of your circle. I only found that out a few weeks ago. Makes them so much easier


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  • #142
    jamesr1775
    Registered Users, Registered Users 2 Posts: 46 ✭jamesr1775


    limits of trig functions wasnt on 2010 and is predicted this year peeps .
    http://www.mathsireland.com/LCHGeneralNotes/Trig/Comp_Angle_Form/Limits_Trig_Func.htm
    questions with answers there.
    They might throw a horrible one up this year


  • #143
    nommm
    Registered Users, Registered Users 2 Posts: 700 ✭✭✭nommm


    Anyone want to remind me how to get the general term of the Maclaurin series? I can't remember how to do it...


  • #144
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    jamesr1775 wrote: »
    limits of trig functions wasnt on 2010 and is predicted this year peeps .
    http://www.mathsireland.com/LCHGeneralNotes/Trig/Comp_Angle_Form/Limits_Trig_Func.htm
    questions with answers there.
    They might throw a horrible one up this year
    I usually just use L'Hopital's rule for them. but some of them look nasty! The Cos4x +Cos2x over something else just looks mental. I've no idea what's going on there.

    I've never seen them venture outside the realm of "Sinax/Sinbx"


  • #145
    aranciata
    Registered Users, Registered Users 2 Posts: 197 ✭✭aranciata


    nommm wrote: »
    Anyone want to remind me how to get the general term of the Maclaurin series? I can't remember how to do it...

    I really need to know this too btw! Hasn't come up in a while and I know literally nothing about them. If anyone could help...


  • #146
    Patriciamc93
    Registered Users, Registered Users 2 Posts: 372 ✭✭Patriciamc93


    nommm wrote: »
    Anyone want to remind me how to get the general term of the Maclaurin series? I can't remember how to do it...

    This might help you.....

    http://www.studentxpress.ie/papers/optionsoln3.pdf

    I am doing q8 on my own as we did the groups option in school and I found it to hard so I wont be much help.


  • #147
    partyatmygaff
    Registered Users, Registered Users 2 Posts: 10,992 ✭✭✭✭partyatmygaff


    nommm wrote: »
    Anyone want to remind me how to get the general term of the Maclaurin series? I can't remember how to do it...
    Write out the series with 1, 2, 3, 4... e.t.c under the respective terms.

    Then look at the numbers which are changing in each term. It is an arithmetic sequence. Find the general term of the sequence and that is your general term.

    If the terms alternate in sign add (-1)^n before the general term too.


  • #148
    partyatmygaff
    Registered Users, Registered Users 2 Posts: 10,992 ✭✭✭✭partyatmygaff


    PJelly wrote: »
    I usually just use L'Hopital's rule for them. but some of them look nasty! The Cos4x +Cos2x over something else just looks mental. I've no idea what's going on there.

    I've never seen them venture outside the realm of "Sinax/Sinbx"
    I've heard of L'Hopital's rule but I've never actually understood how to use it. How do you use it solve limit questions?


  • #149
    PJelly
    Closed Accounts Posts: 494 ✭✭PJelly


    partyatmygaff wrote: »
    I've heard of L'Hopital's rule but I've never actually understood how to use it. How do you use it solve limit questions?
    This is how I use it anyway.... not sure if it's how you're supposed to though :p

    Say you have Sin3x/Sin2x. Let the top be F(x) and bottom be G(x)
    Differentiate them, and you get 3Cos3x and 2Cos2x.
    Sub that back in. As X tends towards zero you get 3Cos(0)/2Cos(0)
    Which gives 3(1)/2(1)
    = 3/2

    Not sure that's now it should be used though.
    But when there's multiple trigonometric identities... I've no idea what to do.


  • #150
    mcrdotcom
    Registered Users, Registered Users 2 Posts: 131 ✭✭mcrdotcom


    Anyone think the vector proofs of the dot product might come up?


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  • #151
    GV_NRG
    Registered Users, Registered Users 2 Posts: 190 ✭✭GV_NRG


    partyatmygaff wrote: »
    Drawing graphs is hardly a worry. For a regular trig graph here is what i'd do.

    Say you have to draw sin(x) from -Pi -> Pi

    Change your calculator to radians, change to table mode and enter sin(x) as the function. Then put your start value at -Pi and your end value at Pi and then just set the step to Pi/12.

    Then you'll get a list of coordinates, plot the coordinates on graph paper and join the dots. Very easy.

    For an inverse trig function, just change your range to be from -1 to 1 and your step to be 0.25.


    its not that easy, you are not allowed to have those type of calculators in the exam with you.


This discussion has been closed.
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