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Strand 2 Leaving Certificate Ordinary Level Geometry and Trigonometry - Revised
Gain a better understanding of synthetic geometry, coordinate geometry, and trigonometry, with this free math course.
Description
Synthetic geometry is also known as axiomatic or pure geometry and is the study of geometry without the use of coordinates or formulae. It studies shapes by means of axioms and theorems. This course begins by teaching you the different concepts of synthetic geometry. You will look into the different properties of shapes and learn about geometric reasoning which is the use of critical thinking, logical arguments, and spatial reasoning to solve problems and find new relationships.
Coordinate geometry is also known as analytic geometry or cartesian geometry. It is the study of geometry using a coordinate system, in contrast to synthetic geometry. This course will teach you the different concepts of coordinate geometry. You will learn its usefulness in physics and engineering, and also in aviation and space science. You will also cover trigonometry and study the relations of the sides and angles of triangles and the relevant functions of any angles.
Synthetic Geometry and Coordinate Geometry are used in real life to help us understand the dimensions and transformations of shapes and figures such as lines, triangles, polygons, and circles. Upon the completion of this course, you will have a better understanding of key geometry axioms and theorems. So, check out the course today and learn how to properly solve for the slope and equation of a line passing through two given points, find distances and angles using Sine and Cosine Rules, and more.
Start Course NowModules
Synthetic Geometry
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Synthetic Geometry - Learning Outcomes
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Properties of Shapes
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Geometric Reasoning 1
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Geometric Reasoning 2
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Geometric Reasoning 3
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Synthetic Geometry - Lesson Summary
Coordinate Geometry
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Coordinate Geometry - Learning Outcomes
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Geometry with Coordinates
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Equation of a Straight Line
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Parallel Lines
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Perpendicular Lines
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The Graphs of y=kx^n
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Translation of Functions
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Reflection of Functions
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Stretching Functions
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General Transformation of Functions
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Equation of a Circle 1 - Centre (0,0)
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Equation of a Circle 2 - (Centre Not 0,0)
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Diameter of a Circle
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Tangent and Normal to a Circle
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Coordinate Geometry - Lesson Summary
Trigonometry
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Trigonometry - Learning Outcomes
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Finding Angles with Sine Ratio
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Finding Sides with the Sine Ratio
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Finding Angles with the Cosine Ratio
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Finding Sides with the Cosine Ratio
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Finding Angles with the Tangent Ratio
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Finding Sides with the Tangent Ratio
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Finding a Missing Side with the Sine Rule
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Finding a Missing Angle with the Sine Rule
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Problem Solving with the Cosine Rule
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Finding Areas with Trigonometry
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Area of a Segment
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Trigonometry - Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
- Recognize the different properties of shapes in mathematics
- Define what geometric reasoning is
- Discuss applying and using geometric reasoning to solve problems/work out solutions
- Discus working out the equation of both parallel and perpendicular lines
- Discuss the translation, reflection and stretching of functions
- Discuss the general transformation of Functions
- Calculate the equation of a circle
- Calculate the equation of the tangent and normal 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
- Recognize how to find a missing side or missing angle using the Sine Rule
- Calculate areas of geometric shapes using trigonometry
- Calculate the area of a segment of a circle
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 official Certification, which is a great way to share your achievement with the world. Your Alison Certification is:
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