Strand 2 Higher Level Geometry and Trigonometry
This course covers Geometry and Trigonometry, a third of thePaper 2 in the Leaving Certificate in the Irish curriculum.
Description
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 Coordinate 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. Coordinate geometry studies lines and circles by reference to a fixed set of coordinates. 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 realworld problems.
Start Course NowModules
Strand 2 Higher Level Geometry and Trigonometry Assessment
Module 1: 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

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

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

3D trigonometry – The cuboid

3D trigonometry – Rectangular based pyramid

Area of a segment
Learning Outcomes
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
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning
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