CLASS 9 MATHEMATICS
IMPORTANT FORMULAE • QUICK REVISION NOTES
Notebook-style study booklet | Common CBSE/NCERT topics
How to use these notes
Learn each formula, practise applying it, and compare this booklet with your prescribed textbook. Some topics
can vary by board or academic year.
1. NUMBER SYSTEMS
Rational numbers
• A rational number is p/q, where p and q are integers and q ≠ 0.
• A reduced fraction has a terminating decimal if its denominator has only prime factors 2 and/or 5.
• A rational number with a reduced denominator containing a prime factor other than 2 or 5 has a
non-terminating recurring decimal.
• A number between a and b can be their mean: (a + b)/2.
Laws of exponents (where defined)
• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ, for a ≠ 0
• (aᵐ)ⁿ = aᵐⁿ
• (ab)ⁿ = aⁿbⁿ ; (a/b)ⁿ = aⁿ/bⁿ, for b ≠ 0
• a⁰ = 1 and a⁻ⁿ = 1/aⁿ, for a ≠ 0
2. POLYNOMIALS & ALGEBRAIC IDENTITIES
• If p(a) = 0, then (x − a) is a factor of p(x) (Factor Theorem).
Important identities
• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a − b)(a + b)
• (x + a)(x + b) = x² + (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a − b)³ = a³ − 3a²b + 3ab² − b³
• a³ + b³ = (a + b)(a² − ab + b²)
• a³ − b³ = (a − b)(a² + ab + b²)
• a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)
• If a + b + c = 0, then a³ + b³ + c³ = 3abc
3. COORDINATE GEOMETRY
• A point is written (x, y): x is the abscissa and y is the ordinate.
• Origin: (0, 0). On the x-axis, y = 0; on the y-axis, x = 0.
• Quadrants: I (+,+), II (−,+), III (−,−), IV (+,−).
Distance and midpoint formulae are generally taught in later classes, not in the standard Class 9 CBSE basics.
4. LINEAR EQUATIONS IN TWO VARIABLES
Class 9 Mathematics • Formula Revision Page 1
IMPORTANT FORMULAE • QUICK REVISION NOTES
Notebook-style study booklet | Common CBSE/NCERT topics
How to use these notes
Learn each formula, practise applying it, and compare this booklet with your prescribed textbook. Some topics
can vary by board or academic year.
1. NUMBER SYSTEMS
Rational numbers
• A rational number is p/q, where p and q are integers and q ≠ 0.
• A reduced fraction has a terminating decimal if its denominator has only prime factors 2 and/or 5.
• A rational number with a reduced denominator containing a prime factor other than 2 or 5 has a
non-terminating recurring decimal.
• A number between a and b can be their mean: (a + b)/2.
Laws of exponents (where defined)
• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ ÷ aⁿ = aᵐ⁻ⁿ, for a ≠ 0
• (aᵐ)ⁿ = aᵐⁿ
• (ab)ⁿ = aⁿbⁿ ; (a/b)ⁿ = aⁿ/bⁿ, for b ≠ 0
• a⁰ = 1 and a⁻ⁿ = 1/aⁿ, for a ≠ 0
2. POLYNOMIALS & ALGEBRAIC IDENTITIES
• If p(a) = 0, then (x − a) is a factor of p(x) (Factor Theorem).
Important identities
• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• a² − b² = (a − b)(a + b)
• (x + a)(x + b) = x² + (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a − b)³ = a³ − 3a²b + 3ab² − b³
• a³ + b³ = (a + b)(a² − ab + b²)
• a³ − b³ = (a − b)(a² + ab + b²)
• a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)
• If a + b + c = 0, then a³ + b³ + c³ = 3abc
3. COORDINATE GEOMETRY
• A point is written (x, y): x is the abscissa and y is the ordinate.
• Origin: (0, 0). On the x-axis, y = 0; on the y-axis, x = 0.
• Quadrants: I (+,+), II (−,+), III (−,−), IV (+,−).
Distance and midpoint formulae are generally taught in later classes, not in the standard Class 9 CBSE basics.
4. LINEAR EQUATIONS IN TWO VARIABLES
Class 9 Mathematics • Formula Revision Page 1
