CLASS - 9
MATHEMATICS NOTES
Chapter 1: Number Systems
● Rational & Irrational Numbers
● Rational: Can be expressed as p/q, where q ≠ 0.
● Irrational: Cannot be expressed as p/q (e.g., √2, π).
● Real Numbers
● Combination of rational and irrational numbers.
● Laws of Exponents
● a^m × a^n = a^(m+n)
● (a^m)^n = a^(mn)
● a^0 = 1, etc.
Chapter 2: Polynomials
● Types of Polynomials
● Linear: ax + b
● Quadratic: ax² + bx + c
● Cubic: ax³ + bx² + cx + d
● Factorization
● Common factor method
● Splitting middle term
● Using identities:
● (a + b)² = a² + 2ab + b²
● (a - b)² = a² - 2ab + b²
● a² - b² = (a - b)(a + b)
Chapter 3: Coordinate Geometry
● Cartesian Plane (x-axis, y-axis, quadrants)
● Distance Formula:
● d = √[(x₂ - x₁)² + (y₂ - y₁)²]
● Midpoint Formula:
● M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
● Section Formula:
● (mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)
Chapter 4: Linear Equations in Two Variables
MATHEMATICS NOTES
Chapter 1: Number Systems
● Rational & Irrational Numbers
● Rational: Can be expressed as p/q, where q ≠ 0.
● Irrational: Cannot be expressed as p/q (e.g., √2, π).
● Real Numbers
● Combination of rational and irrational numbers.
● Laws of Exponents
● a^m × a^n = a^(m+n)
● (a^m)^n = a^(mn)
● a^0 = 1, etc.
Chapter 2: Polynomials
● Types of Polynomials
● Linear: ax + b
● Quadratic: ax² + bx + c
● Cubic: ax³ + bx² + cx + d
● Factorization
● Common factor method
● Splitting middle term
● Using identities:
● (a + b)² = a² + 2ab + b²
● (a - b)² = a² - 2ab + b²
● a² - b² = (a - b)(a + b)
Chapter 3: Coordinate Geometry
● Cartesian Plane (x-axis, y-axis, quadrants)
● Distance Formula:
● d = √[(x₂ - x₁)² + (y₂ - y₁)²]
● Midpoint Formula:
● M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
● Section Formula:
● (mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)
Chapter 4: Linear Equations in Two Variables
