CLASS 9 MATHEMATICS – QUICK NOTES
How to use these notes
These are revision notes covering the main Class 9 Mathematics topics commonly taught in the CBSE/NCERT syllabus.
Use your school textbook and teacher’s syllabus to check which chapters are included in your examination.
Number Systems
Rational numbers can be written as p/q, where q ≠ 0. Irrational numbers cannot be written in this form. Real numbers
consist of rational and irrational numbers.
Key facts
√2, √3 and √5 are irrational. Every rational number has a terminating or recurring decimal expansion. A terminating
decimal has a finite number of digits after the decimal point.
Laws of exponents
a■ × a■ = a■■■; a■ ÷ a■ = a■■■; (a■)■ = a■■; a■ = 1 (a ≠ 0); a■■ = 1/a■.
Surds
To simplify √ab, use √a√b when a,b ≥ 0. Example: √72 = √(36×2) = 6√2.
Class 9 Mathematics • Revision Page 1 of 8
, POLYNOMIALS
Basic terms
A polynomial in x is an expression such as 3x² − 5x + 2. The highest power of the variable is its degree. A constant has
degree 0.
Types
Monomial: one term; binomial: two terms; trinomial: three terms. Examples: 5x, x+3, x²+2x+1.
Zero of a polynomial
A number k is a zero of p(x) if p(k)=0. For a linear polynomial ax+b, its zero is −b/a, where a ≠ 0.
Remainder theorem
If p(x) is divided by (x−a), the remainder is p(a). Thus, if p(a)=0, then (x−a) is a factor of p(x).
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.
Cubic identities
(a+b)³=a³+b³+3ab(a+b); (a−b)³=a³−b³−3ab(a−b); a³+b³=(a+b)(a²−ab+b²); a³−b³=(a−b)(a²+ab+b²).
Class 9 Mathematics • Revision Page 2 of 8
How to use these notes
These are revision notes covering the main Class 9 Mathematics topics commonly taught in the CBSE/NCERT syllabus.
Use your school textbook and teacher’s syllabus to check which chapters are included in your examination.
Number Systems
Rational numbers can be written as p/q, where q ≠ 0. Irrational numbers cannot be written in this form. Real numbers
consist of rational and irrational numbers.
Key facts
√2, √3 and √5 are irrational. Every rational number has a terminating or recurring decimal expansion. A terminating
decimal has a finite number of digits after the decimal point.
Laws of exponents
a■ × a■ = a■■■; a■ ÷ a■ = a■■■; (a■)■ = a■■; a■ = 1 (a ≠ 0); a■■ = 1/a■.
Surds
To simplify √ab, use √a√b when a,b ≥ 0. Example: √72 = √(36×2) = 6√2.
Class 9 Mathematics • Revision Page 1 of 8
, POLYNOMIALS
Basic terms
A polynomial in x is an expression such as 3x² − 5x + 2. The highest power of the variable is its degree. A constant has
degree 0.
Types
Monomial: one term; binomial: two terms; trinomial: three terms. Examples: 5x, x+3, x²+2x+1.
Zero of a polynomial
A number k is a zero of p(x) if p(k)=0. For a linear polynomial ax+b, its zero is −b/a, where a ≠ 0.
Remainder theorem
If p(x) is divided by (x−a), the remainder is p(a). Thus, if p(a)=0, then (x−a) is a factor of p(x).
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.
Cubic identities
(a+b)³=a³+b³+3ab(a+b); (a−b)³=a³−b³−3ab(a−b); a³+b³=(a+b)(a²−ab+b²); a³−b³=(a−b)(a²+ab+b²).
Class 9 Mathematics • Revision Page 2 of 8
