## **Unit 1: Foundations of Algebra (6-8
weeks)**
### **1.1 Real Number System & Operations**
- **Classification of Real Numbers**
- Natural Numbers (ℕ): Counting numbers (1, 2, 3...)
- Whole Numbers (𝕎): Natural numbers + 0
- Integers (ℤ): Whole numbers + negatives (...-2, -1, 0, 1, 2...)
- Rational Numbers (ℚ): Any number expressible as a fraction p/q where
q≠0 (includes terminating/repeating decimals)
- Irrational Numbers (𝕀): Non-repeating, non-terminating decimals (π, √2)
- Real Numbers (ℝ): All rational and irrational numbers
- **Properties of Real Numbers**
- Commutative: a+b = b+a; a×b = b×a
- Associative: (a+b)+c = a+(b+c); (a×b)×c = a×(b×c)
- Distributive: a(b+c) = ab + ac
- Identity: a+0 = a; a×1 = a
- Inverse: a+(-a) = 0; a×(1/a) = 1 (a≠0)
- **Operations & Absolute Value**
- Perfect squares (1, 4, 9, 16... up to 15²=225)
- Square roots: √x² = |x|
- Absolute value: |a| = distance from 0 on number line
- Order of operations (PEMDAS/GEMDAS):
- Parentheses/Grouping symbols
weeks)**
### **1.1 Real Number System & Operations**
- **Classification of Real Numbers**
- Natural Numbers (ℕ): Counting numbers (1, 2, 3...)
- Whole Numbers (𝕎): Natural numbers + 0
- Integers (ℤ): Whole numbers + negatives (...-2, -1, 0, 1, 2...)
- Rational Numbers (ℚ): Any number expressible as a fraction p/q where
q≠0 (includes terminating/repeating decimals)
- Irrational Numbers (𝕀): Non-repeating, non-terminating decimals (π, √2)
- Real Numbers (ℝ): All rational and irrational numbers
- **Properties of Real Numbers**
- Commutative: a+b = b+a; a×b = b×a
- Associative: (a+b)+c = a+(b+c); (a×b)×c = a×(b×c)
- Distributive: a(b+c) = ab + ac
- Identity: a+0 = a; a×1 = a
- Inverse: a+(-a) = 0; a×(1/a) = 1 (a≠0)
- **Operations & Absolute Value**
- Perfect squares (1, 4, 9, 16... up to 15²=225)
- Square roots: √x² = |x|
- Absolute value: |a| = distance from 0 on number line
- Order of operations (PEMDAS/GEMDAS):
- Parentheses/Grouping symbols
