Lesson Notes By Weeks and Term v4 - SHS 1
APPLICATIONS OF EXPRESSIONS, EQUATIONS AND INEQUALITIES
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APPLICATIONS OF EXPRESSIONS, EQUATIONS AND INEQUALITIES
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 12
Grade code: 1.2.1.LI.3
Strand code: 2
Sub-strand code: 1
Content standard code: 1.2.1.CS.1
Indicator code: 1.2.1.LI.3
Theme: ALGEBRAIC REASONING
Subtheme: APPLICATIONS OF EXPRESSIONS, EQUATIONS AND INEQUALITIES
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In our daily lives, from market calculations to construction and design, we often look for shortcuts to make our work faster and more efficient. In algebra, one of the most powerful shortcuts is understanding the "difference of two squares". This concept not only helps in factorising complex expressions but also provides a brilliant trick for quick mental calculations. By the end of this lesson, you will see how a simple algebraic pattern can be used to solve problems that look difficult at first glance, making you a faster and more confident problem-solver. This skill is a foundation for more advanced topics in mathematics like quadratic equations and calculus.
Part 1: What is a Perfect Square?
A perfect square is a number or expression that is the product of a number or expression multiplied by itself.
a) Numerical Perfect Squares: These are numbers obtained by squaring an integer. 1 x 1 = 1² = 1 2 x 2 = 2² = 4 3 x 3 = 3² = 9 10 x 10 = 10² = 100 The numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc., are all perfect squares.
b) Algebraic Perfect Squares: These are algebraic terms obtained by squaring another term. To be a perfect square, the numerical coefficient must be a perfect square, and the exponents of the variables must be even numbers. `x * x = x²` `(3y) * (3y) = 9y²` (Here, 9 is a perfect square and the exponent of y, which is 2, is even). `(5m²) * (5m²) = 25m⁴` (Here, 25 is a perfect square and the exponent 4 is even).