CBSE Syllabus for Class 9 Maths 2024-2025

CBSE Class 9 Mathematics Syllabus

The syllabus for mathematics has been getting progressively more difficult over the past academic years. This year's syllabus took a significant leap in difficulty this year, with the introduction of new concepts and refining the topics from the previous year in pursuit of making the students’ understanding of the topics thorough and deep.

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Objectives

• The broad objectives of teaching Mathematics at the secondary stage are to help the learners to
• consolidate the Mathematical knowledge and skills acquired at the upper primary stage;
• acquire knowledge and understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles and symbols and underlying processes and skills;
• develop mastery of basic algebraic skills;
• develop drawing skills;
• feel the flow of reason while proving a result or solving a problem;
• apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method;
• to develop the ability to think, analyze and articulate logically;
• to develop an awareness of the need for national integration, protection of the environment, observance of small family norms, removal of social barriers, elimination of gender biases;
• to develop necessary skills to work with modern technological devices and mathematical software's.
• to develop an interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns, etc.
• to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;
• to develop an interest in the subject by participating in related competitions;
• to acquaint students with different aspects of Mathematics used in daily life;
• to develop an interest in students to study Mathematics as a discipline.

90 minutes Single Paper

FIRST-TERM 

UNIT 1 - NUMBER SYSTEMS

NUMBER SYSTEM

1. Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/ terminating decimals.
2. Operations on real numbers.Examples of non-recurring/non-terminating decimals. Existence of non-rational
   • a. numbers (irrational numbers) such as , √2,√3 and their representation on the number
   • b. Rationalization (with precise meaning) of real numbers of the t1.ype 1 ?+?√? and 1 √?+√√? (and their combinations) where x and y are natural numbers and a and b are integers.
   • c. 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-ALGEBRA 1. LINEAR EQUATIONS IN TWO VARIABLES

Recall 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. Graph of linear equations in two variables. Examples, problems from real life with algebraic and graphical solutions being done simultaneously 

UNIT-COORDINATE GEOMETRY 1. COORDINATE GEOMETRY

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

UNIT 2 - GEOMETRY

1. LINES AND ANGLES

• (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180˚ and the converse.
• (Prove) If two lines intersect, vertically opposite angles are equal.
• (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.
• (Motivate) Lines which are parallel to a given line are parallel.
• (Prove) The sum of the angles of a triangle is 180˚.
• (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

2. TRIANGLES

• (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).
• (Motivate) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
• (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)
• (Prove) The angles opposite to equal sides of a triangle are equal.
• (Motivate) The sides opposite to equal angles of a triangle are equal.

UNIT 3 - MENSURATION

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

UNIT 4 - STATISTICS & PROBABILITY

STATISTICS

• Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped/ grouped, bar graphs, histograms

UNIT 1 - ALGEBRA

1. POLYNOMIALS

• Definition of a polynomial in one variable, with examples and counterexamples. 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. Factorization of ax2 + bx + c, a ≠ 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 and their use in the factorization of polynomials.

UNIT 2 - GEOMETRY

1. QUADRILATERALS

• (Prove) The diagonal divides a parallelogram into two congruent triangles.
• (Motivate) In a parallelogram opposite sides are equal, and conversely.
• (Motivate) In a parallelogram opposite angles are equal, and conversely.
• (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
• (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
• (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.

2. CIRCLES Through examples, arrive at a definition of a circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.

• (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse.
• (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line is drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
• (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and conversely.
• (Motivate) 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) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

3. CONSTRUCTIONS

• Construction of bisectors of line segments and angles of measure 60˚, 90˚, 45˚ etc., equilateral triangles.
• Construction of a triangle given its base, sum/difference of the other two sides and one base angle.

UNIT 3 - MENSURATION SURFACE AREAS AND VOLUMES

• SURFACE AREAS AND VOLUMES

UNIT 4 - STATISTICS & PROBABILITY

1. PROBABILITY

• History, Repeated experiments and observed frequency approach to probability. The focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations, and from examples used in the chapter on statistics).