Lesson Notes By Weeks and Term v4 - SHS 2
MEASUREMENT
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MEASUREMENT
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Subject: Mathematics
Class: SHS 2
Term: 2nd Term
Week: 6
Grade code: 2.3.2.LI.3
Strand code: 3
Sub-strand code: 2
Content standard code: 2.3.2.CS.1
Indicator code: 2.3.2.LI.3
Theme: GEOMETRY AROUND US
Subtheme: MEASUREMENT
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This lesson introduces the concept of vectors, which are essential tools for describing quantities that have both a size (magnitude) and a direction. In our daily lives in Ghana, we constantly deal with vector ideas without even realising it. When giving directions from the Madina market to the University of Ghana, we don't just say "go for 2 kilometres"; we say "go 2 kilometres *along the Legon road towards the roundabout*." That direction is crucial. Vectors help us mathematically model and solve problems in navigation (like a fishing boat's journey from Axim), physics (forces acting on a building), and even in sports (the path of a football).
2.1 Scalars vs. Vectors Scalar: A quantity that has only magnitude (size or amount). *Examples:* Your age, the price of kenkey (GHS 5.00), the temperature in Accra (31°C), the distance from Cape Coast to Takoradi (80 km), the speed of a tro-tro (60 km/h). Vector: A quantity that has both magnitude and direction. *Examples:* A displacement of 10 km due East, a velocity of 60 km/h towards Kumasi, a force of 20 Newtons pulling downwards. 2.2 Representing Vectors
We can represent vectors in several ways: Graphically: As an arrow. The length of the arrow represents the magnitude, and the direction the arrow points is the vector's direction.
``` B (end point) / / / / A (start point) This represents the vector AB ``` Notation: Using bold letters (e.g., a, v) or with an arrow or line above/below (e.g., $\vec{AB}$, $\underline{a}$). In our notes, we will use bold letters. Column Vector: This is the most common way we will work with vectors algebraically. A 2D vector is written as $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$. The top number, x, represents the horizontal movement (East/West). Positive x is movement to the right (East). Negative x is movement to the left (West). The bottom number, y, represents the vertical movement (North/South). Positive y is movement upwards (North). Negative y is movement downwards (South).