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: 7
Grade code: 2.1.1.LI.3
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.3
Indicator code: 2.1.1.LI.3
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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In the world around us, from the growth of our population in Ghana to the way our savings grow in a bank, many relationships are not simple straight lines. They follow curves that can be difficult to analyse. This lesson provides us with a powerful mathematical tool: using logarithms to transform these complex curves into straight lines. By doing so, we can easily analyse experimental data, find important constants in scientific laws, and make accurate predictions. This skill is crucial for future scientists, engineers, economists, and data analysts.
This lesson is divided into two main parts: understanding the graphs of logarithmic functions and then applying this knowledge to linearize non-linear relationships. Part 1: Graphs of Logarithmic Functions
A logarithmic function is the inverse of an exponential function. The general form is `y = log_b(x)`, where `b` is the base (`b > 0`, `b ≠ 1`).
Key Features of `y = log_b(x)`: Domain: The function is only defined for positive values of `x`. So, `x > 0`. x-intercept: The graph always crosses the x-axis at the point (1, 0) because `log_b(1) = 0` for any base `b`. Vertical Asymptote: The y-axis (the line `x = 0`) is a vertical asymptote. This means the graph gets infinitely close to the y-axis but never touches it. Shape: If `b > 1`, the graph is an increasing function that grows very slowly.
Example Graph: `y = log_10(x)` (also written as `lg(x)`)