Lesson Notes By Weeks and Term v4 - SHS 1
APPLICATIONS OF ALGEBRA
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APPLICATIONS OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 9
Grade code: 1.1.2.LI.3
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.3
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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This lesson introduces the fundamental concepts of relations and functions, which are the building blocks of higher mathematics. In our daily lives in Ghana, we constantly encounter relationships between quantities: the cost of a tro-tro ride depends on the distance, the amount of mobile data you receive depends on the money you pay, and the grade you get in an exam depends on the effort you put in. By understanding relations and functions, we learn to precisely describe these connections using the language of algebra, allowing us to model, predict, and solve real-world problems.
(15 mins) - Introduction and Definitions What is a Relation?
A relation is simply a connection or relationship between two sets of values or items. In mathematics, we represent this as a set of ordered pairs `(x, y)`. The first set of values, the `x`-values, is called the domain. The second set of values, the `y`-values, is called the range. Domain: The set of all possible input values (the first elements of the ordered pairs). Co-domain: The set of all possible output values. Range: The set of the *actual* output values that are used (the second elements of the ordered pairs). The range is a subset of the co-domain.
Example 1: A Social Relation Let's consider a group of SHS1 students and their preferred subjects. Set A (Students - Domain): {Kofi, Ama, Esi} Set B (Subjects - Co-domain): {Mathematics, English, Social Studies, Science}
The relation "prefers" can be shown as a set of ordered pairs: `R = {(Kofi, Mathematics), (Ama, English), (Esi, Mathematics), (Ama, Science)}` Domain: {Kofi, Ama, Esi} Range: {Mathematics, English, Science} Co-domain: {Mathematics, English, Social Studies, Science}