Year 9: CBSE Class IX Mathematics

Listed Mathematics syllabus chapters at Class IX, in the words of the Central Board of Secondary Education (CBSE), with the practice on this site that covers it. Checked against the source on 3 September 2026.

The 2026-27 syllabus, redesigned against NEP 2020 and NCF-SE 2023. The text of each chapter is its Key Concepts list.

15syllabus chapters
110skills mapped
93%have practice

Coverage is the percentage of listed syllabus chapters with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus chapter, so some appear more than once below.

Number system

I.1Number systemIntroduction 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.

Algebra

II.1Introduction to polynomialsAlgebraic 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.
II.2Sequences and progressionsIntroduction 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.
II.3Exploring algebraic identitiesRevisiting 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.
II.4Linear equations in two variablesIntroduction 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.

Coordinate geometry

III.1Coordinate geometryBrief 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.

Geometry

IV.1Introduction to Euclid's geometry: axioms and postulatesHistory 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.
No practice for this one yet.
IV.2Lines and anglesRays and angles. Measures of angles. Intersecting lines and angles. Pairs of angles. Theorems and examples on intersecting lines. Theorems and examples on parallel lines.
IV.3Triangles - congruence theoremsPractical 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.
IV.44-gons (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.
IV.5CirclesPractical 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.
- Level 1: Circumference of a circle
- Level 2: Circumference of a circle

Mensuration

V.1Area and perimeterPerimeter 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.
V.2Surface area and volumeSurface areas and volumes of spheres (including hemispheres) and right circular cones.

Statistics and probability

VI.1StatisticsGraphical representation of data. Measures of central tendency.
VI.2Introduction to probabilityConcept 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.

Other Year 9 skills

Year 9 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.