Lesson Notes By Weeks and Term v4 - SHS 1
NUMBER AND ALGEBRAIC PATTERNS
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NUMBER AND ALGEBRAIC PATTERNS
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 1
Grade code: 1.1.1.LI.3
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.1
Indicator code: 1.1.1.LI.3
Theme: MODELLING WITH ALGEBRA
Subtheme: NUMBER AND ALGEBRAIC PATTERNS
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In our everyday lives, we perform actions that have a "neutral" or "do-nothing" effect, and actions that "undo" a previous action. For example, adding zero to your Gari soakings doesn't change the quantity. Taking five steps forward and then five steps backward brings you back to your starting point. In mathematics, these concepts are formalized as identity and inverse elements. Understanding them is crucial as it forms the foundation for more advanced topics in algebra, cryptography (securing our mobile money transactions), and computer science. This lesson will help us master how to find these special elements for any given mathematical operation.
A. The Identity Element (Symbol: `e`)
The identity element is the "neutral" element in a set for a specific binary operation. When you combine any element with the identity element, the original element remains unchanged.
Think about it like this: For addition on the set of real numbers, what number can you add to 7 to still get 7? It is 0. (`7 + 0 = 7`). So, 0 is the identity element for addition. For multiplication on the set of real numbers, what number can you multiply by 5 to still get 5? It is 1. (`5 × 1 = 5`). So, 1 is the identity element for multiplication.
Formal Definition: For a set `S` and a binary operation `*`, an element `e` in `S` is the identity element if for every element `a` in `S`: `a * e = e * a = a`