Haryana Board HBSE Class 9th Mathematics Syllabus 2025, Download FREE PDF

I

Number systems

Chapter 1: Number systems

09

II

Algebra

Chapter 2: Polynomials  Chapter 4: Linear equations in two variables

21

III

Coordinate geometry

Chapter 3: Coordinate geometry

04

IV

Geometry

Chapter 5: Introduction to Euclid's Geometry  Chapter 6: Lines and Angles  Chapter 7: Triangles  Chapter 8: Quadrilateral  Chapter 9: Circle

25

V

Mensuration

Chapter 10: Heron's Formula  Chapter 11: Surface Area and Volume

15

VI

Statistics

Chapter 12: Statistics

06

Total

80

Internal Assessment

20

Grand Total

100

Introduction

Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/terminating decimals. Operations on real numbers.

Irrational Numbers

Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3, √5 and their representation on the number line.

Real Numbers and their Decimal Expansion

Distinguishing between Rational and Irrational numbers.

Operations on Real Numbers

Definition of nth root of a real number, simplification, rationalization of real numbers such as 1/√a+√b, 1/a+√b.

Laws of Exponents of Real Numbers

Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws).

Introduction

Polynomials In One Variable

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial, and zero polynomial. Degree of a polynomial. Constant, linear, quadratic, and cubic polynomials. Monomials, binomials, trinomials.

Zeroes Of Polynomials

Factors and multiples. Zeroes of a polynomial.

Factorisation of Polynomials

Statement and proof of the Factor Theorem. Factorization of ax² + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.

Algebraic Identities

Recall of algebraic expressions and identities. Verification of identities:Identity I : (x + y)² = x² + 2xy + y²Identity II : (x – y)² = x² – 2xy + y²Identity III : x² – y² = (x + y) (x – y)Identity IV : (x + a) (x + b) = x² + (a + b)x + abIdentity V : (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zxIdentity VI : (x + y)³ = x³ + y³ + 3xy (x + y)Identity VII : (x – y)³ = x³ – y³ – 3xy(x – y) = x³ – 3x²y + 3xy² – y³Identity VIII : x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx)and their use in factorization of polynomials.

Introduction

Recall of linear equations in one variable. Introduction to the equation in two variables.

Linear Equations

Focus on linear equations of the type ax + by + c = 0.

Solution of a Linear Equation

Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers. Provide examples of solutions and graphical representation.

Introduction

The Cartesian plane.

Cartesian System

Coordinates of a point, names and terms associated with the coordinate plane, notations.

Plotting a Point in the Plane if its Coordinates are Given

Summary

Introduction

History: Geometry in India and Euclid's geometry.

Euclid’s Definitions, Axioms and Postulates

Euclid's method of formalizing observed phenomena into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates, and theorems.  The five postulates of Euclid.  Showing the relationship between axiom and theorem, for example:  (Axiom) 1. Given two distinct points, there exists one and only one line through them.  (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

Summary

CBSE Class 9 Maths Syllabus 2025-26 Download PDF