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: 5
Grade code: 2.1.1.LI.2
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.3
Indicator code: 2.1.1.LI.2
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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This lesson explores the powerful relationship between indices (powers) and logarithms. These concepts are not just abstract mathematical ideas; they are essential tools for modelling and solving real-world problems. In Ghana, they help us understand everything from how our investments grow at banks like GCB or Fidelity Bank, to how scientists measure the acidity of our cocoa farm soils, and even how we can predict population growth in our cities like Accra and Kumasi. By mastering these tools, we can describe and solve complex problems that involve rapid growth or decay.
This section serves as the core content for the lesson. It is designed to be delivered directly to learners. Part 1: Revisiting the Laws of Indices
Before we dive into logarithms, let's refresh our memory on the laws of indices, which are the foundation. For any base `a` and powers `m` and `n`:
| Law | Formula | Example | | ----------------------- | ----------------------------------- | ------------------------------------------- | | 1. Multiplication Law | `a^m × a^n = a^(m+n)` | `2^3 × 2^4 = 2^(3+4) = 2^7 = 128` | | 2. Division Law | `a^m ÷ a^n = a^(m-n)` | `3^5 ÷ 3^2 = 3^(5-2) = 3^3 = 27` | | 3. Power of a Power Law | `(a^m)^n = a^(m×n)` | `(5^2)^3 = 5^(2×3) = 5^6 = 15625` | | 4. Zero Index | `a^0 = 1` (for `a ≠ 0`) | `100^0 = 1`, `(-7)^0 = 1` | | 5. Negative Index | `a^(-n) = 1 / a^n` | `4^(-2) = 1 / 4^2 = 1/16` | | 6. Fractional Index | `a^(m/n) = (n√a)^m = n√(a^m)` | `8^(2/3) = (³√8)^2 = 2^2 = 4` | Part 2: Introduction to Logarithms
A logarithm is simply the inverse of an exponent. It answers the question: "What power do I need to raise a specific base to, in order to get a certain number?"