The New Mathematics Syllabus for Class 9 from 2026-2027 at the secondary stage deepens the conceptual understanding and strengthens connections between mathematical ideas, real-life applications, and reasoning.
Coordinate Geometry
1. Brief history of coordinate geometry
2. The 2-D Cartesian coordinate system
3. The distance between two points in the 2-D plane
4. Midpoint of the distance between two points in the
2-D plane
Introduction to Polynomials
1. Algebraic expressions
2. Definition of a polynomial, Degree of a polynomial
3. Introduction to linear polynomials and applications
4. Exploring linear patterns
4. Modelling linear growth and linear decay
5. Linear relationships
6. Visualising linear relationships
7. Slope and y-intercept of a line y = ax + b
Number Systems
1. Introduction to rational numbers
2. Representation of rational numbers on the number line
3. Density of rational numbers and its proof
4. Finding rational numbers between any two rational numbers
5. Decimal representation of rational numbers
6. Introduction to irrational numbers
7. Proof of the irrationality of
and
8. The square root spiral
Introduction to Euclid’s Geometry
Axioms and Postulates
1. History of geometry
2. Constructing a square with a given side as described in the Baudhayana’s Sulbasutras
3. Discovering Euclid’s definitions
4. Axioms: Axioms of measurement and rules for geometric objects
Lines and Angles
1. Rays and angles
2. Measures of angles
3. Intersecting lines and
angles
4. Pairs of angles
5. Theorems and examples
on intersecting lines
6. Theorems and examples
on parallel lines
Sequences and Progressions
1. Introduction to sequences
2. Explicit or general rule of a sequence
3. Recursive rule of a
sequence
4. Arithmetic Progressions
(AP): nth term, visualising an AP, and practical contexts leading to APs
5. Sum of the first n natural numbers
6. Geometric Progressions
(GP): nth term, visualising a GP, and practical contexts leading to GPs
7. Applications of GP in fractals
6. Tower of Hanoi puzzle
Triangles: Congruence Theorems
1. Practical applications and
uses of triangles
2. Conditions of congruence
of triangles and their proofs
3. Theorems on triangles
4. Propositions and
Converse of a proposition
5. Problems based on
applications of theorems on triangles
Mensuration: Area and Perimeter
1. Perimeter of shapes
2. Perimeter of a circle: Introduction to Pi and its irrationality
3. Length of an arc
4. Area of shapes: rectangles, parallelograms, and triangles
5. Heron’s formula
6. Squaring a rectangle: Proof from Baudhayana’s Sulbasutras
7. Area of a circle: derivation
8. Area of the sector of a circle
9. Area of a circle: derivation
10. Brahmagupta’s formula
for the area of a cyclic 4-gon
11. Heron’s formula as a special case of Brahmagupta’s formula
Exploring Algebraic Identities
1. Revisiting algebraic identities
2. Visualising identities using geometrical models
3. Factorisation of algebraic expressions using identities
4. More identities and their applications
5. Visualising factorisation of quadratic expressions through algebra tiles
6. Factorisation without using algebra tiles
7. Finding new identities
8. Simplifying rational expressions
4-gons (Quadrilaterals)
1. Properties of parallelograms
2. Important theorems related to parallelograms and their proof
3. The midpoint theorem and its applications
4. Understanding the notion of central symmetry in the context of parallelograms
Circles
1. Practical applications and uses of circles
2. Definitions related to a circle — centre, diameter, and radius
3. Chords and the angles they subtend
4. Midpoints and perpendicular bisectors of chords
5. Distance of chords from the centre
6. Subtended angles by an arc
7. Cyclicity of points
Linear Equations in Two Variables
1. Introduction to linear equations in two variables through practical examples
2. Solution of linear equations in two variables:
graphical representation
3. Slope-intercept form of a linear equation in two variables
4. Drawing graphs of linear equations when x and y assume only certain values
5. Pair of linear equations in two variables
6. Graphical method for solving a pair of linear equations in two variables
7. Nature of solutions: consistency and inconsistency
8. Algebraic methods of solving a pair of linear equations: method of
substitution and method of elimination
Mensuration: Surface Area and Volume
Surface areas and volumes of spheres(including hemispheres) and right circular cones
More topics are in this section, but not yet provided in the official syllabus
Statistics
1. Graphical representation of data
2. Measures of central tendency
Introduction to Probability
1. Concept of probability and randomness
2. The probability scale
3. Empirical probability: analysing statistical data and performing experiments
4. Theoretical probability: sample space and events
5. Representing probability through tree diagrams and tables
