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: 10
Grade code: 1.1.2.LI.4
Strand code: 1
Sub-strand code: 2
Content standard code: 1.1.2.CS.1
Indicator code: 1.1.2.LI.4
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
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In our daily lives, many things are connected. The amount you pay for 'waakye' depends on the number of ladles you buy. The time it takes to travel from Accra to Kumasi depends on the speed of the bus. Algebra gives us a powerful tool to describe these relationships precisely. This tool is called a function. A function is like a rule or a machine that takes an input (like the number of waakye ladles) and gives a specific output (the total cost). Today, we will learn the language of functions, how to use them, and understand which inputs are allowed. This skill is a foundation for science, engineering, economics, and many other fields.
Concept 1: What is a Function?
Think of a function as a machine. It has an input, a process (a rule), and an output. Input: The value you put into the machine (e.g., a number, `x`). Process: The rule the machine follows (e.g., "double the input and add 1"). Output: The result that comes out of the machine (e.g., the value `f(x)`).
The most important rule for a machine to be a function is that for every single input, it must produce exactly ONE output. Example: If you put `3` into a function machine, it cannot give you `7` one time and `10` another time. It must be consistent.
Formal Definitions: Relation: Any set of ordered pairs, (input, output). Function: A special type of relation where each input value (the first element of the pair) is associated with exactly one output value (the second element). Domain: The set of all possible *input* values (`x`-values) that are allowed for a function. Co-domain: The set of all possible *output* values. Range: The set of all *actual output* values (`f(x)`-values) that the function produces. The range is a subset of the co-domain.