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: 4
Grade code: 1.1.1.LI.1
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.1
Indicator code: 1.1.1.LI.1
Theme: MODELLING WITH ALGEBRA
Subtheme: NUMBER AND ALGEBRAIC PATTERNS
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In our daily lives, we often deal with perfect measurements like 2 metres of cloth or 10 cedis. However, some quantities cannot be expressed as simple whole numbers or fractions. Imagine a carpenter building a perfect square frame with sides of 1 metre each. The diagonal support beam for that frame would be √2 metres long. This is an irrational number, and we call its exact form a 'surd'. Understanding surds is crucial in fields like engineering, architecture, and even graphic design, where precise calculations are necessary. This lesson will introduce us to the world of surds, helping us understand, simplify, and work with them confidently.
Part 1: What is a Surd? (15 mins)
A surd is the root of a number (like a square root or cube root) that cannot be expressed as a whole number or a simple fraction. In other words, it is an irrational root of a rational number. Example of a Surd: √2, √3, √15, ∛7. If you type √2 into a calculator, you get 1.41421356... a decimal that goes on forever without repeating. The exact value is simply √2. Example of something that is NOT a surd: √9. The square root of 9 is 3, which is a whole number (a rational number). So, √9 is not a surd.
Key Idea: If you can't get a "nice" answer (a whole number or a fraction) when you find the root, it's a surd.
Types of Surds: Pure Surd: A surd with no rational factor other than 1. The number under the root sign (the radicand) has no perfect square factors. Examples: √5, √11, 2√3 (The surd part is √3, which is pure). Mixed Surd: A surd that has a rational coefficient other than 1. It is a product of a rational number and a surd. Example: 5√3. We can convert a pure surd into a mixed surd. For example, √12 is not in its simplest form. We can write it as √(4 × 3) = √4 × √3 = 2√3, which is a mixed surd. Like Surds: Surds that have the same irrational part. They are like "like terms" in algebra. Examples: 2√5, 7√5, and -√5 are all like surds because they all have √5. Unlike Surds: Surds with different irrational parts. Examples: 3√2 and 3√7 are unlike surds.