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Higher level maths help

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  • 30-05-2015 1:45pm
    #1
    Kbvdpo
    Registered Users Posts: 60 ✭✭


    Does anyone know what theorems we need to know for the maths paper? Our teacher briefly did thoerms with us & I don't know what all of the necessary thoerms are! I've got a book with a load of them but what's the nescesary ones? Thanks


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    #2
    spurious
    Moderators, Category Moderators, Education Moderators Posts: 27,188 CMod ✭✭✭✭spurious


    From page 18 of the syllabus - available here:
    http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Syllabuses_and_Assessment/JC_Maths_for_examination_in_2015.pdf(.pdf file)

    Theorems: [Formal proofs are not examinable at OL]
    1.
    Vertically opposite angles are equal in measure.
    2.
    In an isosceles triangle the angles opposite the equal sides are equal. Conversely, if two angles are equal, then the triangle is isosceles.
    3.
    If a transversal makes equal alternate angles on two lines then the lines are parallel, (and converse).
    4.
    The angles in any triangle add to 180 ̊.
    5.
    Two lines are parallel if and only if, for any transversal, the corresponding angles are equal.
    6.
    Each exterior angle of a triangle is equal to the sum of the interior opposite angles.
    9.
    In a parallelogram, opposite sides are equal and opposite angles are equal (and converses).
    10.
    The diagonals of a parallelogram bisect each other.
    11.
    If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal.
    12.
    Let ABC be a triangle. If a line l is parallel to BC and cuts [AB] in the ratio s:t, then it also cuts [AC] in the same ratio (and converse).
    13.
    If two triangles are similar, then their sides are proportional, in order (and converse).
    14.
    [Theorem of Pythagoras] In a right-angled triangle the square of the hypotenuse is the sum of the squares of the other two sides.
    15.
    If the square of one side of a triangle is the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.
    19.
    The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.

    [Formal proofs of theorems 4, 6, 9, 14 and 19 are examinable at Higher level.]

    I suggest you have a read of the syllabus - it also covers corollaries and constructions you should be able to do.


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