Lesson Notes By Weeks and Term v4 - SHS 2
APPLICATION OF ALGEBRA
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APPLICATION OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 2
Term: 1st Term
Week: 10
Grade code: 2.1.1.LI.7
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.3
Indicator code: 2.1.1.LI.7
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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In our daily lives, we often face situations with limits or constraints. A driver must stay below the speed limit. A small business owner has a limited budget for supplies. A student has a limited amount of time to study for different subjects. These scenarios are not about finding a single, exact answer (like in an equation) but a range of possible, acceptable outcomes. Algebra, specifically systems of linear inequalities, gives us a powerful visual tool to model these constraints and identify all possible solutions at once. This skill is crucial in fields like business, economics, engineering, and logistics for making the best possible decisions under given restrictions.
This lesson builds on your knowledge of graphing linear equations (`y = mx + c`). The key difference is that an inequality represents a whole region of points, not just a single line. Part 1: Understanding and Graphing a Single Linear Inequality
A linear inequality in two variables (e.g., `x` and `y`) can be written in forms like: `ax + by c` `ax + by ≤ c` `ax + by ≥ c`
The solution to such an inequality is not a single point, but a region of all points `(x, y)` that make the statement true. We find this region by following these steps:
Step-by-Step Guide to Graphing a Single Inequality: Draw the Boundary Line: Temporarily replace the inequality symbol (` , ≤, ≥`) with an equals sign (`=`) to get the equation of the boundary line. For example, for `2x + y > 4`, the boundary line is `2x + y = 4`. Draw this line on the graph. The easiest way is to find the x- and y-intercepts. To find y-intercept, set `x=0`. To find x-intercept, set `y=0`. Choose the Line Type (Solid or Dashed): Use a dashed line for strict inequalities (` `). This shows that the points *on the line* are NOT part of the solution. Use a solid line for non-strict inequalities (`≤` or `≥`). This shows that the points *on the line* ARE part of the solution. Select a Test Point: Choose any point that is not on the boundary line. The easiest point to use is the origin, (0, 0), as long as the line doesn't pass through it. Test and Shade: Substitute the coordinates of your test point into the *original inequality*. If the inequality becomes a true statement, shade the entire region on the side of the line that contains the test point. If the inequality becomes a false statement, shade the entire region on the opposite side of the line.