HBSE Class 9 Maths Syllabus 2024-25: Download Haryana Board Syllabus PDF

HBSE 9th Maths Syllabus 2024-2025: The Board of School Education Haryana (BSEH) Class 10 syllabus for Mathematics is an essential document for students and teachers to cover the 2024–25 academic year. The board has published the syllabus on its official website, which is easily accessible in PDF format. The HBSE 10th Maths syllabus 2024 is divided into theory and internal assessment. The theory part is worth 80 marks, and the internal assessment will be worth 20 marks. There are six units to cover, from which the questions will be asked in the theory paper. The units are: number systems, algebra, coordinate geometry, geometry, mensuration, and statistics.

Here, the latest HBSE 10th Maths syllabus 2024–25 PDF is provided along with the question paper design, course content, and course structure. Check the complete details and other important information regarding the Haryana Board syllabus that will be used for the 2025 board exams.

HBSE Class 9 Maths Course Structure 2024-25

The course structure is important to analyse unit-wise weightage and know the road map that will help students during their final examination to prioritise the right unit to gain more marks.

HBSE Class 9 Maths Syllabus 2024-25

UNIT I: NUMBER SYSTEMS

>CHAPTER-1. NUMBER SYSTEMS

• 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 Number:

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 Number and their decimal expansion:

Distinguish between Rational and Irrational number

• 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 Number:

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.)

• SUMMARY

UNIT II: ALGEBRA

>CHAPTER-2. POLYNOMIALS

• 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 + y² 

Identity II  : (x – y)² = x² – 2xy + y² 

Identity III  : x² – y² = (x + y) (x – y)

Identity IV : (x + a) (x + b) = x² + (a + b)x + ab 

Identity V : (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

Identity VI  : (x + y)³ = x³ + y³ + 3xy (x + y)

Identity VII : (x – y)³ = x³ – y³ – 3xy(x – y) = x³ – 3x²y + 3xy² – y³ 

Identity VIII : x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx) and their use in factorization of polynomials.

>CHAPTER-4 LINEAR EQUATIONS IN TWO VARIABLES

• 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.

UNIT-III COORDINATE GEOMETRY

>CHAPTER-3 COORDINATE GEOMETRY

• 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

UNIT-IV GOMETRY

>CHAPTER-5 INTRODUCTION TO EUCLID’S GEOMETRY

• Introduction: History - Geometry in India and Euclid's geometry
• Euclid’sn Definitions, Axioms and Postulates

Euclid's method of formalizing observed phenomenon 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

>CHAPTER-6 LINES AND ANGLES

• Introduction
• Basic Terms and Definitions

Basic Terms and Definitions such as line-segment, collinear points, non-collinear points, angle, arms, vertex, various types of Angles,

• Intersecting Lines and Non-intersecting Lines:

Intersecting Lines and parallel Lines

• Pairs of Angles

(Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180^O and the converse.

(Prove) If two lines intersect, vertically opposite angles are equal.

• Lines Parallel to the Same Line

(Motivate) Lines which are parallel to a given line are parallel.

• Summary

>CHAPTER -7 TRIANGLES

• Introduction
• Congruence of Triangles
• Criteria for Congruence of Triangles

(Motivate) Two triangles are congruent if any two sides and the included angle of one triangle are equal to any two sides and the included angle of the other triangle (SAS Congruence).

(Prove) Two triangles are congruent if any two angles and the included side of one triangle are equal to any two angles and the included side of the other triangle (ASA Congruence).

(Motivate) Two triangles are congruent if any two angles and one side of one triangle are equal to any two angles and the corresponding side of the other triangle (AAS Congruence).

• Some Properties of a Triangle

(Prove) The angles opposite to equal sides of a triangle are equal. (Motivate) The sides opposite to equal angles of a triangle are equal.

• Some More Criteria for Congruence of Triangles

(Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

(Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

• Summery

>CHAPTER-8 QUADRILATERALS

• Properties of a Parallelogram

(Prove) A diagonal of a parallelogram divides it into two congruent triangles. (Motivate) In a parallelogram opposite sides are equal and its converse . (Motivate) Opposite angles in a parallelogram are equal and its converse. (Motivate) The diagonals of a parallelogram bisect each other and its converse.

• The Mid-point Theorem

(Motivate) The line segment joining the mid-points of two sides of a triangle is parallel to the third side and is half of it and its converse.

• Summery

>CHAPTER-9 CIRCLES

• Angle Subtended by a Chord at a Point

(Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse.

• Perpendicular from the Centre to a Chord

(Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely.

• Equal Chords and Their Distances from the Centre

(Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and conversely.

• Angle Subtended by an Arc of a Circle

(Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

(Motivate) Angles in the same segment of a circle are equal.

(Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

• Cyclic Quadrilaterals

(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT –V MENSURATION

>CHAPTER-10 HERON’S FORMULA

• Area of a Triangle — by Heron’s Formula

Area of a triangle using Heron's formula

>CHAPTER-11 SURFACE AREAS AND VOLUMES

• Surface Area of a Right Circular Cone
• Surface Area of a Sphere

Surface area of spheres (including hemispheres)

• Volume of a Right Circular Cone
• Volume of a Sphere

volumes of spheres (including hemispheres)

UNIT-VI STATISTICS CHAPTER -12 STATISTICS

• Graphical Representation of Data
• Bargraphs
• Histograms of uniform width, and of varying widths
• Frequency polygons

HBSE Class 10 Maths Question Paper Design 2024-25

Check the expected question paper design here to know the paper format and marking scheme.

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HBSE Class 9 Syllabus 2024-25 PDF (All Subjects)