Strand 2 Leaving Certificate Higher Level Geometry and Trigonometry  Revised
This free online maths course covers up to a third of the new Paper 2 in the Leaving Certificate Paper in the Irish curriculum.
Description
Coordinate Geometry and Synthetic Geometry are frequently used in real life to help us understand the transformations and dimensions of shapes and figures (lines, polygons, triangles and circles). Synthetic geometry involves the examination of shapes by means of axioms and theorems. Coordinate geometry studies circles and lines using a fixed set of coordinates.
Trigonometry involves the 'real life' measurements of angles, length and circular measure in both three and two dimensions. The use of trigonometry can be seen in the areas of building and construction, quantity surveying, and in architecture generally. This strand is one of the most applicable areas of the Leaving Certificate project mathematics syllabus and it allows students to gain experience of realworld problems.
This Strand will merge the mathematical aspects of Geometry and Trigonometry with good examples of reallife application. This is a very accesable course, with interesting subject matter.
Start Course NowModules
Synthetic Geometry

Synthetic Geometry  Learning Outcomes

Properties of Shapes

Geometric Reasoning 1

Geometric Reasoning 2

Geometric Reasoning 3

Geometric Reasoning 4

Proof of Theorem 11

Proof of Theorem 12

Proof of Theorem 13

Synthetic Geometry  Lesson Summary
Coordinate Geometry

Coordinate Geometry  Learning Outcomes

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 2 Lines

Dividing a Line Segment in a Given Ratio

Coordinate Geometry  Lesson Summary
Trigonometry

Trigonometry  Learning Outcomes

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

Trigonometry  Lesson Summary
Radians

Radians  Learning Outcomes

Introducing Radians

Using Radians to Find Area of Sector

Sketching and Matching Trigonometric Functions

Graphing Trig Functions. y = sinx  Calculator Work – in Degrees

Graphing Trig Functions. y = 3sin2x  Valculator 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

Radians  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Define what geometric reasoning
 Discuss applying and using geometric reasoning to solve problems/work out solutions
 Discuss the concepts and processes used to prove a theorem to be true
 Discus working out the equation of both parallel and perpendicular lines
 Discuss the translation, reflection and stretching of functions
 Calculate the equation of a circle
 Recognize how to find angles using the Sine, Cosine and Tangent Ratios
 Recognize how to find sides on a triangle using the Sine, Cosine and Tangent Ratios
 Discuss what Radians are and their uses
 Identify how to sketch a trigonometric function on a graph
 Recognize how to solve trigonometric equations
 Recognize how to prove the sine and cosine rules to be true
 Calculate areas of geometric shapes using trigonometry
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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