
Free Course

Advance Learning

610 Hours

Assessment

Certification

Academic  Secondary  Level 2

50 Pts
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 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.

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

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Modules List( 4 )

PROJECT MATHS STRAND 2 HIGHER LEVEL: GEOMETRY AND ...

Module
1 Synthetic Geometry
Learn more about synthetic geometry.

Properties of Shapes
Start Topic

Geometric reasoning  Part 1
Start Topic

Geometric reasoning  Part 2
Start Topic

Geometric reasoning  Part 3
Start Topic

Geometric reasoning  Part 4
Start Topic

Proof of Theorem 11
Start Topic

Proof of Theorem 12
Start Topic

Proof of Theorem 13
Start Topic


Module
2 Coordinate Geometry
Learn more about coordinate geometry.

Geometry with coordinates
Start Topic

Equation of a straight line
Start Topic

Parallel lines
Start Topic

Perpendicular lines
Start Topic

The graphs of y=kx^n
Start Topic

Translation of functions
Start Topic

Reflection of functions
Start Topic

Stretching functions
Start Topic

General transformation of functions
Start Topic

Equation of a circle 1  Centre (0,0)
Start Topic

Equation of a circle 2  Centre not (0,0)
Start Topic

Equation of a circle 3
Start Topic

Diameter of a circle
Start Topic

Tangent and normal to a circle
Start Topic

Touching circles
Start Topic

Prove that a line is a tangent to a circle
Start Topic

Distance from a point to a line
Start Topic

Angle between two lines
Start Topic

Dividing a line segment in a given ratio
Start Topic


Module
3 Trigonometry
Learn more about trigonometry.

Finding angles with sine ratio
Start Topic

Finding sides with the sine ratio
Start Topic

Finding angles with the cosine ratio
Start Topic

Finding sides with the cosine ratio
Start Topic

Finding angles with the tangent ratio
Start Topic

Finding sides with the tangent ratio
Start Topic

Finding a missing side with the Sine Rule
Start Topic

Finding a missing angle with the Sine Rule
Start Topic

Problem solving with the Cosine Rule
Start Topic

Introducing Radians
Start Topic

Using radians to find area of sector
Start Topic

Sketching and matching trigonometric functions
Start Topic

Graphing trigonometric functions. y = sinx  calculator work – in degrees
Start Topic

Graphing trigonometric functions. y = 3sin2x  calculator work – in radians
Start Topic

Introducing the Unit Circle
Start Topic

The Unit Circle – drawing sine and cosine
Start Topic

Comparing degrees to radians on the Unit Circle
Start Topic

Solving trigonometric equations
Start Topic

Proving the Sine Rule
Start Topic

Proving the Cosine Rule
Start Topic

Proving Trigonometric Identity – (Sin squared + cos squared = 1)
Start Topic

Finding areas with trigonometry
Start Topic

3D trigonometry – The cuboid
Start Topic

3D trigonometry – Rectangular based pyramid
Start Topic

Area of a segment
Start Topic


END OF COURSE ASSESSMENT

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
Start Topic


RESOURCE

Resource: Examination Material Archive View Resource