Lesson Notes By Weeks and Term v4 - JHS 2
Measurement
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Measurement
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Subject: Mathematics
Class: JHS 2
Term: 3rd Term
Week: 3
Grade code: B8.3.2.2.1
Strand code: 3
Sub-strand code: 2
Content standard code: B8.3.2.2
Indicator code: B8.3.2.2.1
Theme: GEOMETRY AND MEASUREMENT
Subtheme: Measurement
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This lesson introduces learners to vectors, which are mathematical quantities that have both size (magnitude) and direction. We will learn how to represent these vectors using numbers and how to perform basic operations on them: addition, subtraction, and multiplication by a number (scalar). Understanding vectors is very important as it helps us describe movement and forces in the real world, from a tro-tro's journey across Accra to the forces acting on a canoe on the Volta Lake.
What is a Vector?
In mathematics, we deal with two types of quantities: Scalar: A quantity that has only size (magnitude). *Examples:* Your age (e.g., 14 years), the price of kenkey (e.g., GHS 3.00), the temperature outside (e.g., 32°C), speed (e.g., 60 km/h). These are just numbers. Vector: A quantity that has both size (magnitude) AND direction. *Examples:* A journey of 5 km due East, a force of 10 Newtons pushing downwards, velocity (e.g., 60 km/h towards Kumasi). Representing Vectors in 2D (Column Vectors)
We can represent a vector on a graph (Cartesian plane). A vector is like a set of instructions for movement. It tells you how far to move horizontally (left or right) and how far to move vertically (up or down).
We write this as a column vector: $$ \mathbf{a} = \begin{pmatrix} x \\ y \end{pmatrix} $$ The top number, x, tells you the horizontal movement. Positive (+) `x` means move to the right. Negative (-) `x` means move to the left. The bottom number, y, tells you the vertical movement. Positive (+) `y` means move up. Negative (-) `y` means move down.