Mathematics
Subject Code – 041 & 241
Classes IX-X (2025 – 26)
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, etc.
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 discipline.
, COURSE STRUCTURE CLASS – IX
Units Unit Name Marks
I NUMBER SYSTEMS 10
II ALGEBRA 20
III COORDINATE GEOMETRY 04
IV GEOMETRY 27
V MENSURATION 13
VI STATISTICS 06
Total 80
S. Content Competencies Explanation
No.
Unit 1: Number Systems
1. REAL NUMBERS Develops a deeper Differentiates
understanding of rational and
1. Review of representation of natural numbers, including irrational numbers
numbers, integers, rational numbers the set of real based on decimal
on the number line. Representation of numbers and its representation.
terminating/non-terminating recurring properties. Represents
decimals on the number line through Recognizes and rational and
successive magnification, Rational appropriately uses irrational numbers
numbers as recurring/ terminating powers and on the number line.
decimals. Operations on real exponents. Rationalizes real
numbers. Computes powers number
2. Examples of non-recurring/non- and roots and expressions such
terminating decimals. Existence of applies them to as
1
and
𝑎+𝑏√𝑥
non-rational numbers (irrational solve problems. 1
numbers) such as √2, √3 and their , where x, y
√𝑥+√𝑦
representation on the number line. are natural
Explaining that every real number is numbers and a, b
represented by a unique point on the are integers.
number line and conversely, viz. every Applies laws of
point on the number line represents a exponents
unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise
meaning) of real numbers of the type
1 1
and (and their
𝑎+𝑏√𝑥 √𝑥+√𝑦
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 learner to
arrive at the general laws.)
UNIT II: ALGEBRA
1. POLYNOMIALS Learns the art of Defines
factoring polynomials in
1. Definition of a polynomial in one polynomials. one variable.
variable, with examples and counter Identifies different
examples. Coefficients of a terms and
polynomial, terms of a polynomial different types of
and zero polynomial. polynomials.
2. Degree of a polynomial. Finds zeros of a
3. Constant, linear, quadratic and cubic polynomial
polynomials. Monomials, binomials, Proves factor
trinomials. Factors and multiples. theorem and
4. Zeroes of a polynomial. applies the
5. Motivate and State the Remainder theorem to
Theorem with examples. factorize
6. Statement and proof of the Factor polynomials.
Theorem. Factorization of ax2 + bx + Proves and
c, a ≠ 0 where a, b and c are real applies algebraic
numbers, and of cubic polynomials identities up to
using the Factor theorem. degree three.
7. Recall of algebraic expressions and
identities. Verification of identities:
(𝑥 + 𝑦 + 𝑧)2 = 𝑥 2 + 𝑦 2 + 𝑧 2 + 2𝑥𝑦
+ 2𝑦𝑧 + 2𝑧𝑥
(𝑥 ± 𝑦) = 𝑥 ± 𝑦 3 ± 3𝑥𝑦(𝑥 ± 𝑦)
3 3
𝑥 3 + 𝑦 3 = (𝑥 + 𝑦)(𝑥 2 − 𝑥𝑦 + 𝑦 2 )
𝑥 3 − 𝑦 3 = (𝑥 − 𝑦)(𝑥 2 + 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 factorization
of polynomials.
2. LINEAR EQUATIONS IN TWO Visualizes solutions Describes and plot
VARIABLES of a linear equation a linear equation in
in two variables as two variables.
1. Recall of linear equations in one ordered pair of real
variable. numbers on its
2. Introduction to the equation in two graph
variables. Focus on linear equations
of the type ax + by + c = 0.
Subject Code – 041 & 241
Classes IX-X (2025 – 26)
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, etc.
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 discipline.
, COURSE STRUCTURE CLASS – IX
Units Unit Name Marks
I NUMBER SYSTEMS 10
II ALGEBRA 20
III COORDINATE GEOMETRY 04
IV GEOMETRY 27
V MENSURATION 13
VI STATISTICS 06
Total 80
S. Content Competencies Explanation
No.
Unit 1: Number Systems
1. REAL NUMBERS Develops a deeper Differentiates
understanding of rational and
1. Review of representation of natural numbers, including irrational numbers
numbers, integers, rational numbers the set of real based on decimal
on the number line. Representation of numbers and its representation.
terminating/non-terminating recurring properties. Represents
decimals on the number line through Recognizes and rational and
successive magnification, Rational appropriately uses irrational numbers
numbers as recurring/ terminating powers and on the number line.
decimals. Operations on real exponents. Rationalizes real
numbers. Computes powers number
2. Examples of non-recurring/non- and roots and expressions such
terminating decimals. Existence of applies them to as
1
and
𝑎+𝑏√𝑥
non-rational numbers (irrational solve problems. 1
numbers) such as √2, √3 and their , where x, y
√𝑥+√𝑦
representation on the number line. are natural
Explaining that every real number is numbers and a, b
represented by a unique point on the are integers.
number line and conversely, viz. every Applies laws of
point on the number line represents a exponents
unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise
meaning) of real numbers of the type
1 1
and (and their
𝑎+𝑏√𝑥 √𝑥+√𝑦
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 learner to
arrive at the general laws.)
UNIT II: ALGEBRA
1. POLYNOMIALS Learns the art of Defines
factoring polynomials in
1. Definition of a polynomial in one polynomials. one variable.
variable, with examples and counter Identifies different
examples. Coefficients of a terms and
polynomial, terms of a polynomial different types of
and zero polynomial. polynomials.
2. Degree of a polynomial. Finds zeros of a
3. Constant, linear, quadratic and cubic polynomial
polynomials. Monomials, binomials, Proves factor
trinomials. Factors and multiples. theorem and
4. Zeroes of a polynomial. applies the
5. Motivate and State the Remainder theorem to
Theorem with examples. factorize
6. Statement and proof of the Factor polynomials.
Theorem. Factorization of ax2 + bx + Proves and
c, a ≠ 0 where a, b and c are real applies algebraic
numbers, and of cubic polynomials identities up to
using the Factor theorem. degree three.
7. Recall of algebraic expressions and
identities. Verification of identities:
(𝑥 + 𝑦 + 𝑧)2 = 𝑥 2 + 𝑦 2 + 𝑧 2 + 2𝑥𝑦
+ 2𝑦𝑧 + 2𝑧𝑥
(𝑥 ± 𝑦) = 𝑥 ± 𝑦 3 ± 3𝑥𝑦(𝑥 ± 𝑦)
3 3
𝑥 3 + 𝑦 3 = (𝑥 + 𝑦)(𝑥 2 − 𝑥𝑦 + 𝑦 2 )
𝑥 3 − 𝑦 3 = (𝑥 − 𝑦)(𝑥 2 + 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 factorization
of polynomials.
2. LINEAR EQUATIONS IN TWO Visualizes solutions Describes and plot
VARIABLES of a linear equation a linear equation in
in two variables as two variables.
1. Recall of linear equations in one ordered pair of real
variable. numbers on its
2. Introduction to the equation in two graph
variables. Focus on linear equations
of the type ax + by + c = 0.
