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Maths Definitions and Proofs

  • 25-03-2013 10:47PM
    #1
    CookieMonster.x
    Registered Users, Registered Users 2 Posts: 1,049 ✭✭✭


    Does anyone know what definitions and proofs we need to know for higher level maths? Even just the chapters for definitions would be great! Does anyone have a list of proofs and theorems we need to know?
    Thanks!


Comments

  • #2
    TheBody
    Registered Users, Registered Users 2 Posts: 5,657 ✭✭✭TheBody


    CookieMonster.x wrote: »
    Does anyone know what definitions and proofs we need to know for higher level maths? Even just the chapters for definitions would be great! Does anyone have a list of proofs and theorems we need to know?
    Thanks!

    The dept syllabus is here.

    http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Syllabuses_and_Assessment/Leaving_Cert_Maths_syllabus_for_examination_in_2013.pdf

    Everything you need should be in it.


  • #3
    skippy1977
    Registered Users, Registered Users 2 Posts: 284 ✭✭skippy1977


    I've just finished a set of notes for the students in my class and I've compiled the following list.....which I stand by with absolutely no degree of certainty. The syllabus is a nightmare to try and extrapolate information from and the Project Maths website is a maze of random resources.

    I've given mine:

    De Moivre's Theorem
    Differentiation by 1st Principles (6 of them)
    Other Differentiation Proofs (4 of them General, Sum, Product, Quotient)
    A Proof by Contradiction (Root 2)
    Trigonometric Identities (8 of them 1-7 and 9)
    Theorems 11,12,13 definitely (and 4,6,9,14,19 just in case?!?)

    They have a list of definitions such as:
    if and only if
    converse of a theorem
    is equivalent to
    etc

    There are 3 types of Proof by Induction you also need to know how to do. Series, Division and Inequality though these can't be learned off by heart as you can be asked various (infinite) versions of each.

    I'm also getting mine to learn off:

    Derivation of Cone and Sphere formula using Integration
    and De Moivre's Theorem to prove a Trigonometric Identity
    and a few other small bits that aren't really learned proofs but can be difficult to come up with yourself on the day of the exam.

    I'm convinced I've left something out but that's the situation we've been left with. Hope it helps a little...

    Oh and there are a couple of posts with a similar heading so I hope people don't mind that I've duplicated the post in a few places. Although more than one duplicate would be a triplicate?? Replicate....where are the English teachers

    James


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