CBSE Class 9 Mathematics Syllabus 2025-26

UNIT I: NUMBER SYSTEMS

Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/terminating decimals. Operations on real numbers.
Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, π, and their representation on the number line. Every real number is represented by a unique point on the number line and conversely.
Definition of nth root of a real number.
Rationalization of real numbers of the type 1/√x and their combinations where x and y are natural numbers and a and b are integers.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases.

Definition of a polynomial in one variable, with examples and counterexamples. Coefficients, terms, and zero polynomial.
Degree of a polynomial. Constant, linear, quadratic, and cubic polynomials. Monomials, binomials, trinomials.
Factors and multiples. Zeros of a polynomial.
Remainder Theorem: Motivate and state with examples.
Factor Theorem: Statement and proof. Factorization of ax² + bx + c, a ≠ 0, and cubic polynomials.
Recall of algebraic expressions and identities. Verification of identities and their use in factorization.

Recall of linear equations in one variable. Introduction to equations in two variables.
Focus on equations of the type ax + by + c = 0. Explanation that a linear equation in two variables has infinitely many solutions, written as ordered pairs and plotted on a line.

The Cartesian plane, coordinates of a point, names, and terms associated with the coordinate plane, notations.

History: Geometry in India and Euclid's Geometry.
Euclid's method of formalizing observed phenomena into rigorous mathematics.
The five postulates of Euclid. Relationship between axiom and theorem.
(Axiom) Given two distinct points, there exists one and only one line through them.
(Theorem) Two distinct lines cannot have more than one point in common.

(Motivate) If a ray stands on a line, then the sum of the two adjacent angles is 180° and the converse.
(Prove) If two lines intersect, vertically opposite angles are equal.
(Motivate) Lines parallel to a given line are parallel.

(Prove) The diagonal divides a parallelogram into two congruent triangles.
(Motivate) In a parallelogram, opposite sides and angles are equal.
(Motivate) A quadrilateral is a parallelogram if a pair of opposite sides is parallel and equal.

(Prove) Equal chords of a circle subtend equal angles at the center.
(Motivate) The perpendicular from the center to a chord bisects it.
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any other point.

Surface areas and volumes of spheres (including hemispheres) and right circular cones.