Mathematics
Class IX (2026 – 27)
Introduction:
The Mathematics curriculum for the Secondary stage has been redesigned in alignment with the
National Education Policy 2020 and the National Curriculum Framework for School Education
(NCF – SE) 2023, prioritizing deep conceptual understanding and logical reasoning. The revised
syllabus places strong emphasis on developing core mathematical competencies, including
problem-solving, visualisation, mathematical modelling, mathematical communication,
computational thinking, and data analytics. The syllabus integrate Indian Knowledge System with
contemporary mathematical knowledge, highlighting the rich contributions of Indian
mathematicians to foster a sense of pride and historical context. A deliberate shift from rote
learning to competency-based education ensures that students build deep conceptual
understanding and logical reasoning rather than mere procedural fluency. Greater emphasis has
been laid on the integration of real-life applications and experiential learning, encouraging students
to connect mathematical concepts with everyday situations and cross-disciplinary contexts.
Greater emphasis has been laid on competency based learning outcomes encouraging students
to connect mathematical concepts with everyday situations and inter-disciplinary contexts.
Continuous and holistic assessment through projects, activities, and investigations forms an
integral part of the learning process, moving beyond summative examinations.
At the secondary stage, the curriculum focuses on developing essential global mathematical
competencies, including mathematical representation through quantities and relations,
mathematical modelling and algorithm building, and effective mathematical communication. The
study of the number system, algebra, geometry, mensuration, statistics and probability is designed
to build a strong foundation for higher education while enhancing functional life skills. The
curriculum thus aims to build rich mathematical learning frameworks not only for higher academic
pursuits but also for the practical demands of life in a rapidly changing, data-driven world.
Objectives: The broad objectives of teaching Mathematics at the secondary stage are to help the
learners to:
develop logical thinking, critical reasoning, and a structured approach to problem-solving;
build the ability to recognise, analyse, and solve diverse problems with confidence and
adaptability;
communicate mathematical ideas effectively using appropriate language, symbols, and
representations;
appreciate the beauty, history, and real-life relevance of Mathematics as a discipline;
connect mathematical concepts to fields such as Science, Technology, Engineering, and
Economics;
engage in both collaborative and independent mathematical exploration and learning;
develop habits of precision, accuracy, and logical consistency in mathematical work;
build confidence to explore, experiment, and grow in mathematical understanding without
fear of failure.
, Curricular Goals (CGs) and Competencies (Cs) from the NCF-SE 2023
CG-1: Understands numbers (natural, whole, integer, rational, irrational, and real), ways of
representing numbers, relationships amongst numbers, and number sets.
C-1.1 Develops understanding of numbers, including the set of real numbers and its properties.
CG-2: Builds deductive and inductive logic to prove theorems related to numbers and their
relationships (such as ‘2 is an irrational number’, a recursion relation for Virahanka numbers,
a formula for the sum of the first n square numbers).
C-2.1 Understanding of powers (radical powers) and exponents.
CG-3: Discovers and proves algebraic identities and models real-life situations in the form
of equations to solve them.
C-3.1 States and proves remainder theorem, factor theorem, and division algorithm.
C-3.2 Models and solves contextualised problems using equations (for example, simultaneous
linear equations in two variables or single polynomial equations), and draws conclusions about a
situation being modelled.
C-3.3 Learns Brahmagupta’s quadratic formula (in both symbolic and poetic form) and its derivation,
and uses it to solve some of the poetic puzzles of Bhaskara as well as modern-day problems.
CG-4: Analyses characteristics and properties of two-dimensional geometric shapes, and
develops mathematical arguments to explain geometric relationships.
C-4.1 Describes relationships including congruence of two-dimensional geometric shapes (such as
lines, angles, triangles) to make and test conjectures and solve problems.
C-4.2 Proves theorems using Euclid’s axioms and postulates for triangles and quadrilaterals, and
applies them to solve geometric problems.
C-4.3 Proves theorems about the geometry of a circle, including its chords, subtended angles,
inscribed polygons, and area in terms of pi.
C-4.4 Understands the irrationality of pi, the best approximations to be discovered over human
history, and the first exact formula (infinite series) for pi given by Madhava.
C-4.5 Specifies locations and describes spatial relationships using coordinate geometry, for
example, plotting a pair of linear equations and graphically finding the solution, or finding the area
of triangle with given coordinates as vertices.
C-4.6 Understands the definitions of the basic trigonometric functions, their history and motivation
(including the introduction of the sin and cos functions by Aryabhata using chords), and their utility
across the sciences.
CG-5: Derives and uses formulae to calculate areas of plane figures, surface area, and
volumes of solid objects.
C-5.1 Visualises, represents, and calculates the area of a triangle using Heron’s formula and its
generalisation to cyclic quadrilaterals given by Brahmagupta’s formula.
C-5.2 Visualises and uses mathematical thinking to discover formulae to calculate surface areas
and volumes of solid objects (cubes, cuboids, spheres, hemispheres, right circular cylinders or
cones, and their combinations).
Class IX (2026 – 27)
Introduction:
The Mathematics curriculum for the Secondary stage has been redesigned in alignment with the
National Education Policy 2020 and the National Curriculum Framework for School Education
(NCF – SE) 2023, prioritizing deep conceptual understanding and logical reasoning. The revised
syllabus places strong emphasis on developing core mathematical competencies, including
problem-solving, visualisation, mathematical modelling, mathematical communication,
computational thinking, and data analytics. The syllabus integrate Indian Knowledge System with
contemporary mathematical knowledge, highlighting the rich contributions of Indian
mathematicians to foster a sense of pride and historical context. A deliberate shift from rote
learning to competency-based education ensures that students build deep conceptual
understanding and logical reasoning rather than mere procedural fluency. Greater emphasis has
been laid on the integration of real-life applications and experiential learning, encouraging students
to connect mathematical concepts with everyday situations and cross-disciplinary contexts.
Greater emphasis has been laid on competency based learning outcomes encouraging students
to connect mathematical concepts with everyday situations and inter-disciplinary contexts.
Continuous and holistic assessment through projects, activities, and investigations forms an
integral part of the learning process, moving beyond summative examinations.
At the secondary stage, the curriculum focuses on developing essential global mathematical
competencies, including mathematical representation through quantities and relations,
mathematical modelling and algorithm building, and effective mathematical communication. The
study of the number system, algebra, geometry, mensuration, statistics and probability is designed
to build a strong foundation for higher education while enhancing functional life skills. The
curriculum thus aims to build rich mathematical learning frameworks not only for higher academic
pursuits but also for the practical demands of life in a rapidly changing, data-driven world.
Objectives: The broad objectives of teaching Mathematics at the secondary stage are to help the
learners to:
develop logical thinking, critical reasoning, and a structured approach to problem-solving;
build the ability to recognise, analyse, and solve diverse problems with confidence and
adaptability;
communicate mathematical ideas effectively using appropriate language, symbols, and
representations;
appreciate the beauty, history, and real-life relevance of Mathematics as a discipline;
connect mathematical concepts to fields such as Science, Technology, Engineering, and
Economics;
engage in both collaborative and independent mathematical exploration and learning;
develop habits of precision, accuracy, and logical consistency in mathematical work;
build confidence to explore, experiment, and grow in mathematical understanding without
fear of failure.
, Curricular Goals (CGs) and Competencies (Cs) from the NCF-SE 2023
CG-1: Understands numbers (natural, whole, integer, rational, irrational, and real), ways of
representing numbers, relationships amongst numbers, and number sets.
C-1.1 Develops understanding of numbers, including the set of real numbers and its properties.
CG-2: Builds deductive and inductive logic to prove theorems related to numbers and their
relationships (such as ‘2 is an irrational number’, a recursion relation for Virahanka numbers,
a formula for the sum of the first n square numbers).
C-2.1 Understanding of powers (radical powers) and exponents.
CG-3: Discovers and proves algebraic identities and models real-life situations in the form
of equations to solve them.
C-3.1 States and proves remainder theorem, factor theorem, and division algorithm.
C-3.2 Models and solves contextualised problems using equations (for example, simultaneous
linear equations in two variables or single polynomial equations), and draws conclusions about a
situation being modelled.
C-3.3 Learns Brahmagupta’s quadratic formula (in both symbolic and poetic form) and its derivation,
and uses it to solve some of the poetic puzzles of Bhaskara as well as modern-day problems.
CG-4: Analyses characteristics and properties of two-dimensional geometric shapes, and
develops mathematical arguments to explain geometric relationships.
C-4.1 Describes relationships including congruence of two-dimensional geometric shapes (such as
lines, angles, triangles) to make and test conjectures and solve problems.
C-4.2 Proves theorems using Euclid’s axioms and postulates for triangles and quadrilaterals, and
applies them to solve geometric problems.
C-4.3 Proves theorems about the geometry of a circle, including its chords, subtended angles,
inscribed polygons, and area in terms of pi.
C-4.4 Understands the irrationality of pi, the best approximations to be discovered over human
history, and the first exact formula (infinite series) for pi given by Madhava.
C-4.5 Specifies locations and describes spatial relationships using coordinate geometry, for
example, plotting a pair of linear equations and graphically finding the solution, or finding the area
of triangle with given coordinates as vertices.
C-4.6 Understands the definitions of the basic trigonometric functions, their history and motivation
(including the introduction of the sin and cos functions by Aryabhata using chords), and their utility
across the sciences.
CG-5: Derives and uses formulae to calculate areas of plane figures, surface area, and
volumes of solid objects.
C-5.1 Visualises, represents, and calculates the area of a triangle using Heron’s formula and its
generalisation to cyclic quadrilaterals given by Brahmagupta’s formula.
C-5.2 Visualises and uses mathematical thinking to discover formulae to calculate surface areas
and volumes of solid objects (cubes, cuboids, spheres, hemispheres, right circular cylinders or
cones, and their combinations).
