CBSE Class 9 Mathematics 2026-27 Syllabus
The syllabus consists of six units: (i) Number Systems (ii) Algebra (iii) Coordinate Geometry (iv) Geometry (v) Mensuration (vi) Statistics and Probability.
Exam Structure
| Units | Marks | |
| I | Number Systems | 7 |
| II | Algebra | 20 |
| III | Coordinate Geometry | 4 |
| IV | Geometry | 25 |
| V | Mensuration | 14 |
| VI | Statistics and Probability | 10 |
| Total | 80 | |
Unit I: Number Systems
Number System
- Introduction to rational numbers
- Representation of rational numbers on the number line
- Density of rational numbers and its proof
- Finding rational numbers between any two rational numbers
- Decimal representation of rational numbers
- Introduction to irrational numbers
- Proof of irrationality of √2 and √3
- The square root spiral
Unit II: Algebra
Introduction to Polynomials
- Algebraic expressions
- Definition of a polynomial
- Degree of a polynomial
- Introduction to linear polynomials and applications
- Exploring linear patterns
- Modelling linear growth and linear decay
- Linear relationships
- Visualising linear relationships
- Slope and y-intercept of a line y = ax + b
Sequences and Progressions
- Introduction to sequences
- Explicit or general rule of a sequence
- Recursive rule of a sequence
- Arithmetic Progressions (AP): nth term, visualising an AP, and practical contexts leading to APs
- Sum of the first n natural numbers
- Geometric Progressions (GP): nth term, visualising a GP, and practical contexts leading to GPs
- Applications of GP in fractals
- Tower of Hanoi puzzle
Exploring Algebraic Identities
- Revisiting algebraic identities
- Visualising identities using geometrical models
- Factorisation of algebraic expressions using identities
- More identities and their applications
- Visualising factorisation of quadratic expressions through algebra tiles and without using algebra tiles
- Finding new identities
- Simplifying rational expressions
Linear Equations in Two Variables
- Introduction to linear equations in two variables through practical examples
- Solution of linear equation in two variables: graphical representation
- Slope-intercept form of linear equation in two variables
- Drawing graphs of linear equations when x and y assume only certain values
- Pair of linear equations in two variables
- Graphical method for solving a pair of linear equations in two variables
- Nature of solutions: consistency and inconsistency
- Algebraic methods of solving a pair of linear equations: substitution and elimination method
Unit III: Coordinate Geometry
Coordinate Geometry
- Brief history of coordinate geometry
- The 2-D Cartesian coordinate system
- Distance between two points in the 2-D plane
- Midpoint of the line-segment between two points in the 2-D plane
Unit IV: Geometry
Introduction to Euclid’s Geometry: Axioms and Postulates
- History of geometry
- Constructing a square with a given side as described in the Baudhayana’s Sulbasutras
- Discovering Euclid’s definitions
- Axioms: Axioms of measurement and rules for geometric objects
Lines and Angles
- Rays and angles
- Measures of angles
- Intersecting lines and angles
- Pairs of angles
- Theorems and examples on intersecting lines
- Theorems and examples on parallel lines
Triangles: Congruence Theorems
- Practical applications of triangles
- Proofs of conditions of congruence of triangles
- Theorems on triangles
- Propositions and their converse
- Problems based on applications of theorems on triangles
Quadrilaterals
- Properties of parallelograms
- Important theorems related to parallelograms and their proof
- Midpoint theorem and its applications
- Understanding the notion of central symmetry in the context of parallelograms
Circles
- Practical applications and uses of circles
- Definitions related to a circle - centre, diameter, and radius
- Chords and the angles they subtend
- Midpoints and perpendicular bisectors of chords
- Distance of chords from the centre
- Subtended angles by an arc
- Cyclicity of points
Unit V: Mensuration
Mensuration: Area and Perimeter
- Perimeter of shapes
- Perimeter of a circle: Introduction to Pi and its irrationality
- Length of an arc
- Area of shapes: rectangles, parallelograms, and triangles
- Heron’s formula
- Squaring a rectangle: Proof from Baudhayana’s Sulbasutras
- Area of a circle: derivation
- Area of the sector of a circle
- Brahmagupta’s formula for area of a cyclic 4-gon
- Heron’s formula as a special case of Brahmagupta’s formula
Mensuration: Surface Area and Volume
Surface areas and volumes of spheres (including hemispheres) and right circular cones
Unit VI: Statistics
Statistics
- Graphical representation of data
- Measures of central tendency
Introduction to Probability
- Concept of probability and randomness
- The probability scale
- Empirical probability: analysing statistical data and performing experiments
- Theoretical probability: sample space and events
- Representing probability through tree diagrams and tables