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Strand 2 Higher Level Geometry and Trigonometry

  • Description
  • Outcome
  • Certification
  • Geometry and Trigonometry is the second of two strands introduced in the first phase of the new Project Maths Course. This topic covers up to a third of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum. Synthetic Geometry and Co-ordinate Geometry are used in real life to help us understand the dimensions and transformations of shapes and figures (lines, triangles, polygons and circles). Synthetic geometry studies shapes by means of axioms and theorems. Co-ordinate geometry studies lines and circles by reference to a fixed set of co-ordinates. Trigonometry is concerned with ‘real life’ measurements of length, angles and circular measure in both two and three dimensions. The use of trigonometry is commonly utilised in the areas of quantity surveying, building and construction, and architecture. This strand is without doubt the most applicable area of the Leaving Certificate mathematics syllabus and allows students gain experience of realistic solutions to real-world problems.

  • Having completed this course students will be able to:

    • Determine the slope of a line given it’s equation

    • Find the equation of a line perpendicular to a given line and passing through a given point

    • Compute the angle between two given lines

    • Determine the equation of a circle having a given centre and radius

    • Find the equation of a tangent to a given circle at a specified point

    • Find distance and angle using Sine and Cosine Rules

    • Find length of an arc and area of a sector using circular measure

    • Solve the trigonometrical equations sin(x) = r and cos(x) = r in general form

  • All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.

    Having an official Alison document is a great way to share your success. Plus it’s:

    • Ideal for including in CVs, job applications and portfolios
    • An indication of your ability to learn and achieve high results
    • An incentive to continue to empower yourself through learning
    • A tangible way of supporting the Alison mission to empower people everywhere through education.

Strand 2 Higher Level Geometry and Trigonometry
  • Free

  • 6-10 Hours

  • Advance Learning

  • Assessment

  • Certification

  • 50 Pts

Modules List( 4 )
  • Module
    Synthetic Geometry
    • Learn more about synthetic geometry.
    • Properties of Shapes
    • Geometric reasoning - Part 1
    • Geometric reasoning - Part 2
    • Geometric reasoning - Part 3
    • Geometric reasoning - Part 4
    • Proof of Theorem 11
    • Proof of Theorem 12
    • Proof of Theorem 13
  • Module 2: Coordinate Geometry
    • Learn more about coordinate geometry.
    • Geometry with coordinates
    • Equation of a straight line
    • Parallel lines
    • Perpendicular lines
    • The graphs of y=kx^n
    • Translation of functions
    • Reflection of functions
    • Stretching functions
    • General transformation of functions
    • Equation of a circle 1 - Centre (0,0)
    • Equation of a circle 2 - Centre not (0,0)
    • Equation of a circle 3
    • Diameter of a circle
    • Tangent and normal to a circle
    • Touching circles
    • Prove that a line is a tangent to a circle
    • Distance from a point to a line
    • Angle between two lines
    • Dividing a line segment in a given ratio
  • Module 3: Trigonometry
    • Learn more about trigonometry.
    • Finding angles with sine ratio
    • Finding sides with the sine ratio
    • Finding angles with the cosine ratio
    • Finding sides with the cosine ratio
    • Finding angles with the tangent ratio
    • Finding sides with the tangent ratio
    • Finding a missing side with the Sine Rule
    • Finding a missing angle with the Sine Rule
    • Problem solving with the Cosine Rule
    • Introducing Radians
    • Using radians to find area of sector
    • Sketching and matching trigonometric functions
    • Graphing trigonometric functions. y = sinx - calculator work – in degrees
    • Graphing trigonometric functions. y = 3sin2x - calculator work – in radians
    • Introducing the Unit Circle
    • The Unit Circle – drawing sine and cosine
    • Comparing degrees to radians on the Unit Circle
    • Solving trigonometric equations
    • Proving the Sine Rule
    • Proving the Cosine Rule
    • Proving Trigonometric Identity – (Sin squared + cos squared = 1)
    • Finding areas with trigonometry
    • 3-D trigonometry – The cuboid
    • 3-D trigonometry – Rectangular based pyramid
    • Area of a segment
  • Strand 2 Higher Level Geometry and Trigonometry Assessment
    • You must score 80% or more to pass this assessment.
    • Strand 2 Higher Level Geometry and Trigonometry Assessment
  • Resource: Examination Material Archive View Resource
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