CBSE Class 9 Maths Syllabus 2026-27

MATHEMATICS (IX-X) (CODE NO. 041)

Session 2022-23

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. The present revised syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in the Focus Group on Teaching of Mathematics which is to meet the emerging needs of all categories of students. For motivating the teacher to relate the topics to real life problems and other subject areas, greater emphasis has been laid on applications of various concepts.

The curriculum at Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distances. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying these with further observations form inherent part of Mathematics learning at this stage. The proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc.

The teaching of Mathematics should be imparted through activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments.

Objectives

The broad objectives of teaching of Mathematics at 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 ability to think, analyze and articulate logically;
• to develop awareness of the need for national integration, protection of 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 interest in mathematics as a problem-solving tool in various fields for its beautiful structures and patterns,
• to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics;
• to develop 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

COURSE STRUCTURE CLASS –IX

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18) Periods

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

2. Examples of non-recurring/non-terminating Existence of non-rational numbers (irrational numbers) such as, and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real
4. Rationalization (with precise meaning) of real numbers of the type

and (and their combinations) where x and y are natural number 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 learner to arrive at the general )

UNIT II: ALGEBRA

1. POLYNOMIALS (26) Periods

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. 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 factorization of polynomials.

History – Geometry in India and Euclid’s geometry. 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.

2. LINES AND ANGLES (15) Periods

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180^O and the
2. (Prove) If two lines intersect, vertically opposite angles are

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

TRIANGLES (22) Periods

3. (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).
4. (Prove) 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).
5. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
6. (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 (RHS Congruence)
7. (Prove) The angles opposite to equal sides of a triangle are
8. (Motivate) The sides opposite to equal angles of a triangle are

4. QUADRILATERALS (13) Periods

1. (Prove) The diagonal divides a parallelogram into two congruent
2. (Motivate) In a parallelogram opposite sides are equal, and
3. (Motivate) In a parallelogram opposite angles are equal, and
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and
5. (Motivate) In a parallelogram, the diagonals bisect each other and
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

CIRCLES (17) Periods

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

2.(Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center 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 center (or their respective centers) and conversely.

4.(Prove) The angle subtended by an arc at the center 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 equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

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

UNIT V: MENSURATION

1. AREAS (5) Periods

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

2. SURFACE AREAS AND VOLUMES (17) Periods

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

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15) Periods

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

MATHEMATICS QUESTION PAPER DESIGN

CLASS – IX (2022-23)

Time: 3 Hrs. Max. Marks: 80

COURSE STRUCTURE CLASS –X

UNIT I: NUMBER SYSTEMS

1. REAL NUMBER (15) Periods

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of

UNIT II: ALGEBRA

1. POLYNOMIALS (8) Periods

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15) Periods

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

3. QUADRATIC EQUATIONS (15) Periods

Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots.

Situational problems based on quadratic equations related to day to day activities to be incorporated.

4. ARITHMETIC PROGRESSIONS (10) Periods

Motivation for studying Arithmetic Progression Derivation of the n^th term and sum of the first n terms of A.P. and their application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY

Coordinate Geometry (15) Periods

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

UNIT IV: GEOMETRY

1. TRIANGLES (15) Periods

Definitions, examples, counter examples of similar triangles.

2. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same
3. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
4. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are
5. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
6. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are
7. CIRCLES (10) Periods

Tangent to a circle at, point of contact

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are

UNIT V: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (10) Periods

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios whichever are defined at 0o and 90o. Values of the trigonometric ratios of 30⁰, 45⁰ and 60⁰. Relationships between the ratios.

2. TRIGONOMETRIC IDENTITIES (15) Periods

Proof and applications of the identity sin²A + cos²A = 1. Only simple identities to be given.

3. HEIGHTS AND DISTANCES: Angle of elevation, Angle of Depression. (10)Periods

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30°, 45°, and 60°.

UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES (12) Periods

Area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60°, 90° and 120° only.

2. SURFACE AREAS AND VOLUMES (12) Periods

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

2. PROBABILITY (10) Periods

Classical definition of probability. Simple problems on finding the probability of an event.

MATHEMATICS-Standard QUESTION PAPER DESIGN CLASS – X (2022-23)

Time: 3 Hours Max. Marks: 80

MATHEMATICS-Basic QUESTION PAPER DESIGN CLASS – X (2022-23)

Time: 3Hours Max. Marks: 80

PRESCRIBED BOOKS:

1. Mathematics – Textbook for class IX – NCERT Publication
2. Mathematics – Textbook for class X – NCERT Publication
3. Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication
4. Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication
5. Laboratory Manual – Mathematics, secondary stage – NCERT Publication
6. Mathematics exemplar problems for class IX, NCERT
7. Mathematics exemplar problems for class X, NCERT