Lesson Notes By Weeks and Term v4 - SHS 2
SPATIAL SENSE
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SPATIAL SENSE
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Subject: Additional Mathematics
Class: SHS 2
Term: 2nd Term
Week: 1
Grade code: 2.2.1.LI.3
Strand code: 2
Sub-strand code: 1
Content standard code: 2.2.1.CS.1
Indicator code: 2.2.1.LI.3
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: SPATIAL SENSE
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In our daily lives in Ghana, we are surrounded by circles – from the wheels of a "trotro" and the base of a cooking pot to the design of roundabouts like the Kwame Nkrumah Circle in Accra. Spatial sense helps us understand and describe these shapes not just with words, but with the precise language of mathematics. In this lesson, we will move beyond simply recognising circles and learn how to define them perfectly using equations. We will also explore the properties of lines that interact with circles, specifically tangents and normals, which are fundamental concepts in engineering, physics, and design.
This lesson is divided into two main parts: understanding the equation of the circle itself, and then understanding the lines (tangents and normals) that relate to it. Part A: The Equation of a Circle
A circle is defined as the set of all points in a plane that are at a fixed distance (the radius) from a fixed point (the centre). We can use this definition and the distance formula (derived from Pythagoras' theorem) to find its equation. The Standard Equation of a Circle
Let the centre of the circle be the point `C(a, b)` and the radius be `r`. Let any point on the circumference of the circle be `P(x, y)`.
By definition, the distance between the centre `C` and the point `P` must be equal to the radius `r`.