CBSE Class 9 Maths Syllabus 2024-25: Updated Curriculum

Unit I - Number Systems

1. REAL NUMBERS 

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

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as, \[\sqrt{2}\], \[\sqrt{3}\] and their representation on the number line. This explains that every real number is represented by a unique point on the number line, and conversely, every point on the number line represents a unique real number.

3. Definition of the nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type \[\frac{1}{a + b\sqrt{x}}\] and \[\frac{1}{\sqrt{x} +\sqrt{y}}\] and their combinations) where x and y are natural numbers and a and b are integers.

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

Unit II - Algebra

1.  POLYNOMIALS

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. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorisation of $ax^{2}+bx+c, a\neq 0$ where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. 

Recall of algebraic expressions and identities. Verification of identities:

$\left ( x+y+z \right )^{2}=x^{2}+y^{2}+z^{2}+2xy+2yz+2zx$

$\left ( x\pm y \right )^{3}=x^{3}\pm y^{3}\pm 3xy(x \pm y)$

$x^{3} \pm y^{3}=(x \pm y)(x^{2} \mp xy+y^{2})$

$x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)$

and their use in the factorisation of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLE

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax+by+c=0. Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. 

Unit III - Coordinate Geometry

COORDINATE GEOMETRY

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

Unit IV - Geometry

1. INTRODUCTION TO EUCLID'S GEOMETRY

History - Geometry in India and Euclid's geometry. Euclid's method of formalising observed phenomena into rigorous mathematics includes 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, one and only one line exists through them. (Theorem) 2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES

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

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

3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.

3. TRIANGLES

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

2. (Motivate) 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).

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

4. (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)

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

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

4. QUADRILATERALS 

1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 

2. (Motivate) In a parallelogram, opposite sides are equal and conversely. 

3. (Motivate) In a parallelogram, opposite angles are equal and conversely. 

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. 

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely. 

6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and in half of it and (motivate) its converse. 

CIRCLES 

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

2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 

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

4. (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. 

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

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

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

Unit V - Mensuration

1. AREAS 

Area of a triangle using Heron's formula (without proof) 

2. SURFACE AREAS AND VOLUMES 

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

Unit VI - Statistics & Probability

STATISTICS

Bar graphs, histograms (with varying base lengths), and frequency polygons. 

Mathematics Question Paper Design Class – IX (2024-25)

Marking Scheme for Internal Assessment

Deleted Syllabus of Class 9 Maths Exercise wise

Prescribed Books: 

Mathematics Textbook for Class IX, Published by NCERT

Benefits of Downloading Class 9 Maths Syllabus 2024-25 PDF

• Class 9 Maths Syllabus 2024-25 helps to understand what topics will be covered in math throughout the year.

• It outlines a structured learning path, making planning studies and tracking progress easier.

• Knowing the syllabus in advance allows students to prepare thoroughly for exams and assignments.

• It helps gather relevant study materials and resources aligned with the curriculum.

• Ensures that teaching and learning activities are aligned with CBSE standards, enhancing academic performance.

• It enables parents to support their child's learning by knowing what concepts and skills will be taught.

Tips to Prepare for Class 9th Maths Exam

• Focus on thoroughly understanding the basic concepts. Ensure you understand fractions, decimals, geometry, and algebraic expressions.

• Practise regularly to improve your understanding. Solve problems from your textbook, worksheets, and previous years' question papers.

• Create a study schedule that includes regular maths sessions. Break down your study time into manageable sections to cover different topics.

• Use diagrams, charts, and tables to understand and remember geometrical shapes, theorems, and problem-solving methods.

• Learn and practise problem-solving strategies, such as drawing diagrams, making tables, and using logical reasoning.

• Review what you've learned regularly and revise key concepts. Make summary notes or flashcards for quick revision before exams.

• Improve your mental arithmetic skills by practising calculations mentally. This can help speed up problem-solving during exams.

The Class 9 Maths Syllabus 2024-25 provides a clear overview for students to build a strong foundation in mathematical concepts. By understanding these topics, students can improve their problem-solving abilities, prepare effectively for exams, and learn maths concepts better. This syllabus helps teachers and students work together for academic success throughout the year.

Related Topic Pages for Maths Class 9 

Related Study Materials for Class 9 Maths

To complete Maths preparation for CBSE Class 9 exams, check out the following links for different study materials available at Vedantu.