CLASS 9 - MATHEMATICS NOTES
BISE Peshawar Board
CHAPTER 1: REAL NUMBERS
1.1 Natural Numbers: 1, 2, 3, 4, 5...
1.2 Whole Numbers: 0, 1, 2, 3, 4...
1.3 Integers: ...-2, -1, 0, 1, 2...
1.4 Rational Numbers: p/q form, q ≠ 0
Example: 1/2, 3/4, -5/2
1.5 Irrational Numbers: Cannot be written as p/q
Example: √2, √3, π
FORMULAS:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- a² - b² = (a + b)(a - b)
SOLVED EXAMPLE:
Q: Simplify (2x + 3)²
Ans: (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9
CHAPTER 2: LOGARITHMS
2.1 Definition: logₐ b = c means a^c = b
2.2 Laws:
- log(ab) = log a + log b
- log(a/b) = log a - log b
- log a^n = n log a
CHAPTER 3: ALGEBRAIC EXPRESSIONS
3.1 Factorization:
- ax + ay = a(x + y)
- x² + (a+b)x + ab = (x+a)(x+b)
CHAPTER 4: LINEAR EQUATIONS
ax + b = 0 → x = -b/a
KEYWORDS FOR STUVIA: Class 9, Mathematics, Peshawar Board, Algebra, Logarithm,
Real Numbers
BISE Peshawar Board
CHAPTER 1: REAL NUMBERS
1.1 Natural Numbers: 1, 2, 3, 4, 5...
1.2 Whole Numbers: 0, 1, 2, 3, 4...
1.3 Integers: ...-2, -1, 0, 1, 2...
1.4 Rational Numbers: p/q form, q ≠ 0
Example: 1/2, 3/4, -5/2
1.5 Irrational Numbers: Cannot be written as p/q
Example: √2, √3, π
FORMULAS:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- a² - b² = (a + b)(a - b)
SOLVED EXAMPLE:
Q: Simplify (2x + 3)²
Ans: (2x)² + 2(2x)(3) + 3² = 4x² + 12x + 9
CHAPTER 2: LOGARITHMS
2.1 Definition: logₐ b = c means a^c = b
2.2 Laws:
- log(ab) = log a + log b
- log(a/b) = log a - log b
- log a^n = n log a
CHAPTER 3: ALGEBRAIC EXPRESSIONS
3.1 Factorization:
- ax + ay = a(x + y)
- x² + (a+b)x + ab = (x+a)(x+b)
CHAPTER 4: LINEAR EQUATIONS
ax + b = 0 → x = -b/a
KEYWORDS FOR STUVIA: Class 9, Mathematics, Peshawar Board, Algebra, Logarithm,
Real Numbers
